{"id":13622,"date":"2022-04-01T11:33:32","date_gmt":"2022-04-01T06:03:32","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=13622"},"modified":"2022-04-07T11:09:53","modified_gmt":"2022-04-07T05:39:53","slug":"big-ideas-math-answers-grade-4-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4-chapter-5\/","title":{"rendered":"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers"},"content":{"rendered":"<p>Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers are included here to help the students to improve their preparation level. You must practice every question given on <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4\/\">Big Ideas Math Answers Grade 4<\/a> to aware of the different questions impose in the exam. Practice all the problems and verify the solution and explanation to find out the easy method to solve problems. Students are suggested to learn the in-depth concept of Divide Multi-Digit Numbers into One-Digit Numbers and start practicing the below questions.<\/p>\n<h2>Big Ideas Grade 4 Answer Key Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers<\/h2>\n<p>Learn from basics using Big Ideas Grade 4 Solution Key pdf. Click on the below attached links and start solving all the problems. Tips and tricks are also given to help the students to remember the process to solve different problems. So, by referring to our bigideasmathanswers.com students can get a complete grip on the concepts as well as they will become math experts easily. Find out various methods to solve problems and choose the best out of one that makes your learning easy.<\/p>\n<p><strong>Lesson: 1 Divide Tens, Hundreds, and Thousands<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.1_Divide_Tens,_Hundreds,_and_Thousands\">Lesson 5.1 Divide Tens, Hundreds, and Thousands<\/a><\/li>\n<li><a href=\"#Divide_Tens,_Hundreds_and_Thousands_Homework_&amp;_Practice_5.1\">Divide Tens, Hundreds and Thousands Homework &amp; Practice 5.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Estimate Quotients<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.2_Estimate_Quotients\">Lesson 5.2 Estimate Quotients<\/a><\/li>\n<li><a href=\"#Estimate_Quotients_Practice_5.2\">Estimate Quotients Homework &amp; Practice 5.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Understand Division and Remainder<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.3_Understand_Division_and_Remainder\">Lesson 5.3 Understand Division and Remainder<\/a><\/li>\n<li><a href=\"#Understand_Division_and_Remainder_Practice_5.3\">Understand Division and Remainder Homework &amp; Practice 5.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Use Partial Quotients<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.4_Use_Partial_Quotients\">5.4 Use Partial Quotients<\/a><\/li>\n<li><a href=\"#Use_Partial_Quotients_Practice_5.4\">Use Partial Quotients Homework &amp; Practice 5.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Use Partial Quotients with a Remainder<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.5_Use_Partial_Quotients_with_a_Remainder\">Lesson 5.5 Use Partial Quotients with a Remainder<\/a><\/li>\n<li><a href=\"#Use_Partial_Quotients_with_a_Remainder_Practice_5.5\">Use Partial Quotients with a Remainder Homework &amp; Practice 5.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Divide Two-Digit Numbers by One-Digit Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.6_Divide_Two_Digit_Numbers_by_One_Digit_Numbers\">Lesson 5.6 Divide Two-Digit Numbers by One-Digit Numbers<\/a><\/li>\n<li><a href=\"#Divide_Two_Digit_Numbers_by_One_Digit_Numbers_Practice_5.6\">Divide Two-Digit Numbers by One-Digit Numbers Homework &amp; Practice 5.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Divide Multi-Digit Numbers by One-Digit Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.7_Divide_Multi_Digit_Numbers_by_One_Digit_Numbers\">Lesson 5.7 Divide Multi-Digit Numbers by One-Digit Numbers<\/a><\/li>\n<li><a href=\"#Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Practice_5.7\">Divide Multi-Digit Numbers by One-Digit Numbers Homework &amp; Practice 5.7<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 8 Divide by One-Digit Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.8_Divide_by_One_Digit_Numbers\">Lesson 5.8 Divide by One-Digit Numbers<\/a><\/li>\n<li><a href=\"#Divide_by_One_Digit_Numbers_Practice_5.8\">Divide by One-Digit Numbers Homework &amp; Practice 5.8<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 9 Problem Solving: Division<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.9_Problem_Solving:_Division\">Lesson 5.9 Problem Solving: Division<\/a><\/li>\n<li><a href=\"#Problem_Solving:_Division_Practice_5.9\">Problem Solving: Division Homework &amp; Practice 5.9<\/a><\/li>\n<\/ul>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Performance_Task\">Divide Multi-Digit Numbers by One-Digit Numbers Performance Task<\/a><\/li>\n<li><a href=\"#Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Activity\">Divide Multi-Digit Numbers by One-Digit Numbers Activity<\/a><\/li>\n<li><a href=\"#Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Chapter_Practice\">Divide Multi-Digit Numbers by One-Digit Numbers Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_5.1_Divide_Tens,_Hundreds,_and_Thousands\"><\/a>Lesson 5.1 Divide Tens, Hundreds, and Thousands<\/h3>\n<p><strong><br \/>\nExplore and Grow<br \/>\n<\/strong><\/p>\n<p>Use a model to find each missing factor. Draw each model. Then write the related division equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 1\" width=\"561\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-1-300x161.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>What pattern do you notice?<\/p>\n<p>Answer: The pattern follows the multiplication of 4 with ones, tens, hundreds, and thousands.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-17281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-65.jpg\" alt=\"\" width=\"551\" height=\"290\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-65.jpg 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-65-300x158.jpg 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nNow,<br \/>\nThe given Expressions are:<\/p>\n<p>A) X \u00d7 2 = 8<br \/>\nSo, X can be calculated by<br \/>\nX= 8 \u00f7 2 = 4<\/p>\n<p>B) X \u00d7 2 = 80<br \/>\nSo, X can be calculated by<br \/>\nX= 80 \u00f7 2 = 40<\/p>\n<p>C) X \u00d7 2 = 800<br \/>\nSo, X can be calculated by<br \/>\nX= 800 \u00f7 2 = 400<\/p>\n<p>D) X \u00d7 2 = 8,000<br \/>\nSo, X can be calculated by<br \/>\nX= 8,000 \u00f7 2 = 4,000<br \/>\nHence, from the above,<br \/>\nWe can conclude that the pattern follows the multiplication of 4 with ones, tens, hundreds, and thousands.<\/p>\n<p><strong>Repeated Reasoning<\/strong><\/p>\n<p>Explain how 12 \u00f7 4 can help you find 1,200 \u00f7 4<\/p>\n<p>Answer: 1,200 \u00f7 4 is 100 times the value of 12 \u00f7 4.<\/p>\n<p>Explanation:<\/p>\n<p>The value of 12 \u00f7 4 = 3<br \/>\nNow,<br \/>\nwe know that 1,200 times is 100 times the value of 12. ( From the place-value Concept)<br \/>\nSo,<br \/>\n1,200 \u00f7 4 = 120 tens \u00f7 4<br \/>\n=30 tens<br \/>\n= 300<br \/>\nHence, from the values of 3 and 300,<br \/>\nWe can conclude that the value of 300 is 100 times the value of 3.<\/p>\n<p><strong>Think and Grow: Divide Tens, Hundreds and Thousands<\/strong><\/p>\n<p>You can use place value and basic division facts to divide tens, hundreds, or thousands by one-digit numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 2\" width=\"294\" height=\"126\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind 270 \u00f7 9<br \/>\nThink: 27 \u00f7 9<br \/>\n270 \u00f7 9 = 27 tens \u00f7 9<br \/>\n= 3 tens<br \/>\n= 30<br \/>\nSo, 270 \u00f7 9 = 30<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 3\" width=\"212\" height=\"261\" \/><\/p>\n<p><strong>Example<br \/>\n<\/strong>Find 5,600 \u00f7 8.<br \/>\nThink: 56 \u00f7 8<br \/>\n5,600 \u00f7 8 = 56 hundreds \u00f7 8<br \/>\n= 7 hundreds<br \/>\n= 700<br \/>\nSo, 5,600 \u00f7 8 = 700<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nFind 2,400 \u00f7 6.<br \/>\nThink: 24 \u00f7 6 = 3<br \/>\n2,400 \u00f7 6 = 24 hundreds \u00f7 6<br \/>\n= 3 hundreds<br \/>\n=300<br \/>\nSo, 2,400 \u00f7 6 = 300.<\/p>\n<p>Question 2.<br \/>\nFind each quotient.<br \/>\n49 \u00f7 7 =_____<br \/>\n490 \u00f7 7 = ______<br \/>\n4,900 \u00f7 7 = ______<\/p>\n<p>Answer: Let the Expressions be A), B) and C)<br \/>\nSo,<br \/>\nThe quotients of A), B) and C) are:<br \/>\nA) 7<br \/>\nB) 70<br \/>\nC) 700<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A), B) and C)<br \/>\nSo, the given Expressions are:<br \/>\nA) 49 \u00f7 7<br \/>\nB) 490 \u00f7 7<br \/>\nC) 4,900 \u00f7 7<br \/>\nSo,<br \/>\nA) 49 \u00f7 7 = 7<\/p>\n<p>B) 490 \u00f7 7 = 49 tens \u00f7 7<br \/>\n= 7 tens<br \/>\n=70<br \/>\nSo, 490 \u00f7 7 = 70<\/p>\n<p>C) 4,900 \u00f7 7 = \u00a049 hundreds \u00f7 7<br \/>\n= 7 hundred<br \/>\n= 700<br \/>\nSo, 4,900 \u00f7 7 = 700<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Find the quotient<\/strong><br \/>\nQuestion 3.<br \/>\n50 \u00f7 5 = _____<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n50 \u00f7 5 = 5 tens \u00f7 5<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 50 \u00f7 5 = 10<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 4.<br \/>\n360 \u00f7 6 = _____<\/p>\n<p>Answer: 60<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n360 \u00f7 6 = 36 tens \u00f7 6<br \/>\n= 6 tens<br \/>\n=60<br \/>\nSo, 360 \u00f7 6 = 60<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 5.<br \/>\n7,200 \u00f7 8 = ______<\/p>\n<p>Answer: 900<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n7,200 \u00f7 8 = 72 hundreds \u00f7 8<br \/>\n= 9 hundred<br \/>\n=900<br \/>\nSo, 7,200 \u00f7 8 = 900<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 6.<br \/>\n180 \u00f7 2 = ______<\/p>\n<p>Answer: 90<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n180 \u00f7 2 = 18 tens \u00f7 2<br \/>\n= 9 tens<br \/>\n=90<br \/>\nSo, 180 \u00f7 2 = 90<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 7.<br \/>\n4,200 \u00f7 7 = _____<\/p>\n<p>Answer: 600<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n4,200 \u00f7 7 = 42 hundreds \u00f7 7<br \/>\n= 6 hundred<br \/>\n=600<br \/>\nSo, 4,200 \u00f7 7 = 600<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 8.<br \/>\n20 \u00f7 2 = ____<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n20 \u00f7 2 = 2 tens \u00f7 2<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 20 \u00f7 2 = 10<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 9.<br \/>\n2,000 \u00f7 5 = _____<\/p>\n<p>Answer: 400<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n2,000 \u00f7 5 = 20 hundreds \u00f7 5<br \/>\n= 4 hundred<br \/>\n=400<br \/>\nSo, 2,000 \u00f7 5 = 400<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 10.<br \/>\n30 \u00f7 3 = _____<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n30 \u00f7 3 = 3 tens \u00f7 3<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 30 \u00f7 3 = 10<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 11.<br \/>\n320 \u00f7 4 = ______<\/p>\n<p>Answer: 80<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n320 \u00f7 4 = 32 tens \u00f7 4<br \/>\n= 8 tens<br \/>\n=80<br \/>\nSo, 320 \u00f7 4 = 80<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 12.<br \/>\n140 \u00f7 2 = _____<\/p>\n<p>Answer: 70<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n140 \u00f7 2 = 14 tens \u00f7 2<br \/>\n= 7 tens<br \/>\n=70<br \/>\nSo, 140 \u00f7 2 = 70<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 13.<br \/>\n5,400 \u00f7 9 = ____<\/p>\n<p>Answer: 600<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n5,400 \u00f7 9 = 54 hundreds \u00f7 9<br \/>\n= 6 hundred<br \/>\n=600<br \/>\nSo, 5,400 \u00f7 9 = 600<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 14.<br \/>\n180 \u00f7 6 = _____<\/p>\n<p>Answer: 30<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n180 \u00f7 6 = 18 tens \u00f7 6<br \/>\n= 3 tens<br \/>\n=30<br \/>\nSo, 180 \u00f7 6 = 30<\/p>\n<p><strong>Note: <\/strong>The &#8220;Quotient&#8221; of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p><strong>DIG DEEPER!<\/strong><\/p>\n<p><strong>Find the missing number.<\/strong><br \/>\nQuestion 15.<br \/>\n70 \u00f7 ____ = 10<\/p>\n<p>Answer: The missing number is: 7<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\n70 \u00f7 X = 10<br \/>\nSo, X can be calculated by<br \/>\nX= 70 \u00f7 10 = 70<\/p>\n<p>Question 16.<br \/>\n4,000 \u00f7 _____ = 800<\/p>\n<p>Answer: The missing number is: 20<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\n4,000 \u00f7 X = 800<br \/>\nSo, X can be calculated by<br \/>\nX= 4,000 \u00f7 800 = 20<\/p>\n<p>Question 17.<br \/>\n160 \u00f7 _____ = 40<\/p>\n<p>Answer: The missing number is: 4<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\n160 \u00f7 X = 40<br \/>\nSo, X can be calculated by<br \/>\nX= 160 \u00f7 40 = 4<\/p>\n<p>Question 18.<br \/>\n_____ \u00f7 7 = 300<\/p>\n<p>Answer: The missing number is: 2,100<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\nX \u00f7 7 = 300<br \/>\nSo, X can be calculated by<br \/>\nX= 70 \u00d7 300 = 2,100<\/p>\n<p>Question 19.<br \/>\n_____ \u00f7 5 = 70<\/p>\n<p>Answer: The missing number is: 350<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\nX \u00f7 5 = 70<br \/>\nSo, X can be calculated by<br \/>\nX= 70 \u00d7 5 = 350<\/p>\n<p>Question 20.<br \/>\n_____ \u00f7 6 = 10<\/p>\n<p>Answer: The missing number is: 60<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\nX \u00f7 6 = 10<br \/>\nSo, X can be calculated by<br \/>\nX= 6 \u00d7 10 = 60<\/p>\n<p><strong>Compare<\/strong><br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 4\" width=\"156\" height=\"40\" \/><br \/>\nAnswer: 10 is equal to 10<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A) and B)<br \/>\nThe given Expressions are:<br \/>\nA) 40 \u00f7 4 = 4 tens \u00f7 4<br \/>\n= 1 ten<br \/>\n= 10<br \/>\nB) 1 \u00d7 10 = 10<strong><br \/>\n<\/strong>So, from the above,<br \/>\nWe can conclude that 10 is equal to 10<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 5\" width=\"171\" height=\"42\" \/><\/p>\n<p>Answer: 20 is less than 200<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A) and B)<br \/>\nThe given Expressions are:<br \/>\nA) 160 \u00f7 8 = 16 tens \u00f7 8<br \/>\n= 2 tens<br \/>\n= 20<br \/>\nB) 2 \u00d7 100 = 200<strong><br \/>\n<\/strong>So, from the above,<br \/>\nWe can conclude that 20 is less than 200<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 6\" width=\"168\" height=\"42\" \/><\/p>\n<p>Answer: 900 is greater than 90<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A) and B)<br \/>\nThe given Expressions are:<br \/>\nA) 8,100 \u00f7 9 = 81 hundreds \u00f7 9<br \/>\n= 9 hundreds<br \/>\n= 900<br \/>\nB) 9 \u00d7 10 = 90<strong><br \/>\n<\/strong>So, from the above,<br \/>\nWe can conclude that 900 is equal to 90<\/p>\n<p>Question 24.<br \/>\nThere are 240 students visiting a fair. They are divided equally among 8 barns. How many students are in each barn?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 7\" width=\"190\" height=\"177\" \/><br \/>\nAnswer: There are 30 students in each barn.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 240 students visiting a fair and these students are divided equally among 8 barns.<br \/>\nSo,<br \/>\nThe number of students in each barn can be calculated by dividing the number of students by the number of barns.<br \/>\nHence,<br \/>\nThe number of students in each barn is:<br \/>\n240 \u00f7 8 = 24 tens \u00f7 8<br \/>\n= 3 tens<br \/>\n= 30<br \/>\nSo, 240 \u00f7 8 = 30 students<\/p>\n<p>Question 25.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\nIs Descartes correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 8\" width=\"159\" height=\"162\" \/><\/p>\n<p>Answer: Descartes is not correct.<\/p>\n<p>Explanation:<br \/>\nGiven Expression is 2,500 \u00f7 5<br \/>\nThe value of 2,500 \u00f7 5 is:<br \/>\n2,500 \u00f7 5\u00a0 = 25 hundreds \u00f7 5<br \/>\n= 5 hundreds<br \/>\n= 500<br \/>\nSo, 2,500 \u00f7 5 = 500<br \/>\nBut, According to Descartes,<br \/>\n2,500 \u00f7 5 = 5,000<br \/>\nBut, up on calculation, we get the result as 500.<br \/>\nSo, Descartes is not correct.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<br \/>\n<\/strong><\/p>\n<p><strong>Example<br \/>\n<\/strong>A lobster lays 5,400 eggs. It lays 9 times as many eggs as a seahorse. How many eggs does the seahorse lay?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-9.1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 9.1\" width=\"205\" height=\"151\" \/><br \/>\nDraw a model.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-17285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-66.jpg\" alt=\"\" width=\"584\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-66.jpg 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-66-300x154.jpg 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 26.<br \/>\nA coach has 350 career wins. He has 7 times as many careers wins as wins this season. How many wins does the coach have this season?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 10\" width=\"178\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-10.png 178w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-10-162x300.png 162w\" sizes=\"(max-width: 178px) 100vw, 178px\" \/><\/p>\n<p>Answer: 50 wins<\/p>\n<p>Explanation:<br \/>\nGiven that a coach has 350 career wins and he has 7 times as many careers wins as this season.<br \/>\nSo,<br \/>\nThe number of wins that the coach has in this season can be calculated by dividing the total career wins by the number of times the career wins of this season.<br \/>\nHence,<br \/>\nThe number of career wins in this season is:<br \/>\n350 \u00f7 7 = 35 tens \u00f7 7<br \/>\n= 5 tens<br \/>\n= 50<br \/>\nSo, from the above,<br \/>\nWe can conclude that the career wins of this season are: 50<\/p>\n<p>Question 27.<br \/>\nThere are 160 shareable bicycles in a city. There are 8 bicycle-sharing stations. Each station has the same number of bicycles. How many bicycles are at each station?<\/p>\n<p>Answer: 20 bicycles are at each station.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 160 shareable bicycles in a city and there are 8 bicycle-sharing stations.<br \/>\nIt is also given that each station has the same number of bicycles.<br \/>\nSo, the number of bicycles in each station are:<br \/>\n160 \u00f7 8 = 16 tens \u00f7 8<br \/>\n= 2 tens<br \/>\n= 20<br \/>\nSo, 160 \u00f7 8 = 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 20 bicycles at each station.<\/p>\n<p>Question 28.<br \/>\nA charity has 637 adult volunteers and 563 teenage volunteers. All of the volunteers are divided, into 6 equal groups. How many volunteers are in each group?<\/p>\n<p>Answer: There are 200 volunteers in each group.<\/p>\n<p>Explanation;<br \/>\nGiven that a charity has 637 adult volunteers and 563 teenage volunteers.<br \/>\nSo,<br \/>\nThe total number of Volunteers = Number of adult volunteers + Number of teenage volunteers<br \/>\n= 637 + 563<br \/>\n= 1,200 volunteers<br \/>\nIt is also given that the volunteers are divided into 6 equal groups.<br \/>\nSo, the number of volunteers in each group are 1,200 \u00f7 6<strong>.<br \/>\n<\/strong>Now,<br \/>\n1,200 \u00f7 6 = 12 hundreds \u00f7 6<br \/>\n= 2 hundred<br \/>\n= 200<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 200 volunteers in each group.<\/p>\n<h3><a id=\" Divide_Tens,_Hundreds_and_Thousands_Homework_&amp;_Practice_5.1\"><\/a>Divide Tens, Hundreds and Thousands Homework &amp; Practice 5.1<\/h3>\n<p>Question 1.<br \/>\nFind 150 \u00f7 3.<br \/>\nThink: 15 \u00f7 3 = 5<br \/>\n150 \u00f7 3 = 15 tens \u00f7 3<br \/>\n= 5 tens<br \/>\n= 50<br \/>\nSo, 150 \u00f7 3 = 50<\/p>\n<p>Question 2.<br \/>\nFind 6,300 \u00f7 7<br \/>\nThink: 63 \u00f7 7 = 9<br \/>\n6,300 \u00f7 7 = 63 hundreds \u00f7 7<br \/>\n= 9\u00a0 hundreds<br \/>\n= 900<br \/>\nSo, 6300 \u00f7 7 = 900<\/p>\n<p><strong>Find the quotient.<\/strong><\/p>\n<p>Question 3.<br \/>\n12 \u00f7 2 = _____<br \/>\n120 \u00f7 2 = ______<br \/>\n1,200 \u00f7 2 = ______<br \/>\nAnswer:<br \/>\nLet the Expressions be A), B) and C)<br \/>\nSo,<br \/>\nThe quotients of A), B) and C) are:<br \/>\nA) 6<br \/>\nB) 60<br \/>\nC) 600<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A), B) and C)<br \/>\nSo, the given Expressions are:<br \/>\nA) 12 \u00f7 2<br \/>\nB) 120 \u00f7 2<br \/>\nC) 1,200 \u00f7 2<br \/>\nSo,<br \/>\nA) 12 \u00f7 2 = 6<\/p>\n<p>B) 120 \u00f7 2 = 12 tens \u00f7 2<br \/>\n= 6 tens<br \/>\n=60<br \/>\nSo, 120 \u00f7 2 = 60<\/p>\n<p>C) 1,200 \u00f7 2 = \u00a012 hundreds \u00f7 2<br \/>\n= 6 hundred<br \/>\n= 600<br \/>\nSo, 1,200 \u00f7 2 = 600<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 4.<br \/>\n40 \u00f7 8 = _____<br \/>\n400 \u00f7 8 = ______<br \/>\n4,000 \u00f7 8 = ______<\/p>\n<p>Answer:<br \/>\nLet the Expressions be A), B) and C)<br \/>\nSo,<br \/>\nThe quotients of A), B) and C) are:<br \/>\nA) 5<br \/>\nB) 50<br \/>\nC) 500<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A), B) and C)<br \/>\nSo, the given Expressions are:<br \/>\nA) 40 \u00f7 8<br \/>\nB) 400 \u00f7 8<br \/>\nC) 4,000 \u00f7 8<br \/>\nSo,<br \/>\nA) 40 \u00f7 8 = 5<\/p>\n<p>B) 400 \u00f7 8 = 40 tens \u00f7 8<br \/>\n= 5 tens<br \/>\n=50<br \/>\nSo, 400 \u00f7 8 = 50<\/p>\n<p>C) 4,000 \u00f7 8 = \u00a040 hundreds \u00f7 8<br \/>\n= 5 hundred<br \/>\n= 500<br \/>\nSo, 4,000 \u00f7 8 = 500<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p><strong>Find the quotient.<br \/>\n<\/strong>Question 5.<br \/>\n80 \u00f7 8 = ______<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n80 \u00f7 8 = 8 tens \u00f7 8<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 80 \u00f7 8 = 10<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 6.<br \/>\n300 \u00f7 6 = _____<\/p>\n<p>Answer: 50<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n300 \u00f7 6 = 30 tens \u00f7 6<br \/>\n= 5 tens<br \/>\n=50<br \/>\nSo, 300 \u00f7 6 = 50<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 7.<br \/>\n1,000 \u00f7 5 = _____<\/p>\n<p>Answer: 200<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n1,000 \u00f7 5 = 10 hundreds \u00f7 5<br \/>\n= 2 hundred<br \/>\n=200<br \/>\nSo, 1,000 \u00f7 5 = 200<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Find t<strong>he quotient.<\/strong><br \/>\nQuestion 8.<br \/>\n40 \u00f7 8 = ______<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n40 \u00f7 8 = 4 tens \u00f7 8<br \/>\n=5<br \/>\nSo, 40 \u00f7 8 = 5<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 9.<br \/>\n6,400 \u00f7 8 = _____<\/p>\n<p>Answer: 800<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n6,400 \u00f7 8 = 64 hundred \u00f7 8<br \/>\n= 8 hundred<br \/>\n=800<br \/>\nSo, 6,400 \u00f7 8 = 800<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 10.<br \/>\n350 \u00f7 5 = ______<\/p>\n<p>Answer: 70<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n350 \u00f7 5 = 35 tens \u00f7 5<br \/>\n= 7 tens<br \/>\n=70<br \/>\nSo, 350 \u00f7 5 = 70<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 11.<br \/>\n2,100 \u00f7 7 = ____<\/p>\n<p>Answer: 300<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n2,100 \u00f7 7 = 21 hundreds \u00f7 7<br \/>\n= 3 hundred<br \/>\n=300<br \/>\nSo, 2,100 \u00f7 7 = 300<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 12.<br \/>\n240 \u00f7 3 = ______<\/p>\n<p>Answer: 80<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n240 \u00f7 3 = 24 tens \u00f7 3<br \/>\n= 8 tens<br \/>\n=80<br \/>\nSo, 240 \u00f7 3 = 80<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 13.<br \/>\n90 \u00f7 9 = _____<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n90 \u00f7 9 = 9 tens \u00f7 9<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 90 \u00f7 9 = 10<\/p>\n<p><strong>Note: <\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p><strong>DIG DEEPER!<br \/>\n<\/strong><\/p>\n<p><strong>Find the missing number.<\/strong><\/p>\n<p>Question 14.<br \/>\n50 \u00f7 ______ = 10<\/p>\n<p>Answer: The missing number is:\u00a0 5<\/p>\n<p>Explanation:<br \/>\nLet the missing Expression be X.<br \/>\nThe given Expression is:<br \/>\n50 \u00f7 X = 10<br \/>\nSo, X can be calculated by<br \/>\nX= 160 \u00f7 40 = 4<\/p>\n<p>Question 15.<br \/>\n_____ \u00f7 7 = 600<\/p>\n<p>Answer: The missing number is: 4,200<\/p>\n<p>Explanation:<br \/>\nLet the missing Expression be X.<br \/>\nThe given Expression is:<br \/>\nX \u00f7 7 = 600<br \/>\nSo, X can be calculated by<br \/>\nX= 600 \u00d7 7 = 4,200<\/p>\n<p>Question 16.<br \/>\n320 \u00f7 ______ = 40<\/p>\n<p>Answer: The missing number is: 8<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\n320 \u00f7 X = 40<br \/>\nSo, X can be calculated by<br \/>\nX= 3200 \u00f7 40 = 8<\/p>\n<p><strong>Compare<br \/>\n<\/strong>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 11\" width=\"160\" height=\"45\" \/><\/p>\n<p>Answer: 10 is equal to 10<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A) and B)<br \/>\nThe given Expressions are:<br \/>\nA) 30 \u00f7 3 = 3 tens \u00f7 3<br \/>\n= 1 ten<br \/>\n= 10<br \/>\nB) 1 \u00d7 10 = 10<strong><br \/>\n<\/strong>So, from the above,<br \/>\nWe can conclude that 10 is equal to 10<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 12\" width=\"178\" height=\"58\" \/><br \/>\nAnswer: 70 is less than 700<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A) and B)<br \/>\nThe given Expressions are:<br \/>\nA)560 \u00f7 8 = 56 tens \u00f7 8<br \/>\n= 7 tens<br \/>\n= 70<br \/>\nB) 9 \u00d7 100 = 700<strong><br \/>\n<\/strong>So, from the above,<br \/>\nWe can conclude that 70 is less than 700<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 13\" width=\"190\" height=\"53\" \/><br \/>\nAnswer: 700 is less than 7,000<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be A) and B)<br \/>\nThe given Expressions are:<br \/>\nA) 4,900 \u00f7 7 = 49 hundreds \u00f7 7<br \/>\n= 7 hundreds<br \/>\n= 700<br \/>\nB) 7 \u00d7 1,000 = 7,000<strong><br \/>\n<\/strong>So, from the above,<br \/>\nWe can conclude that 700 is equal to 7,000<\/p>\n<p>Question 20.<br \/>\nA movie theater has 180 seats. The seats are divided into 9 equal rows. How many seats are in each row?<\/p>\n<p>Answer: There are 20 seats in each row.<\/p>\n<p>Explanation:<br \/>\nGiven that a model theater has 180 seats and the seats are divided into 9 equal rows.<br \/>\nNow, to find the number of seats in each row, we have to divide the total number of seats by the number of rows.<br \/>\nSo,<br \/>\n180 \u00f7 9 = 18 tens \u00f7 9<br \/>\n= 2 tens<br \/>\n= 20 seats<br \/>\nSo, from the above,<br \/>\nWe can conclude that the number of seats in each row is: 20 seats<\/p>\n<p>Question 21.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhat is Newton\u2019s number?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 14\" width=\"262\" height=\"178\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 22.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA gorilla understands 2,000 words. She understands 4 times as many words as a toddler. How many words does the toddler understand?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 15\" width=\"219\" height=\"171\" \/><\/p>\n<p>Answer: The toddler understands 500 words.<\/p>\n<p>Explanation:<br \/>\nGiven that a gorilla understands 2,000 words.<br \/>\nIt is also given that the gorilla understands 4 times as many words as a toddler.<br \/>\nSo,<br \/>\nThe words understand by a toddler = The words understand by a gorilla \u00f7 4<br \/>\nSo,<br \/>\n2,000 \u00f7 4 = 20 hundreds \u00f7 4<br \/>\n= 5 hundred<br \/>\n= 500<br \/>\nHence, from the above,<br \/>\nWe can conclude that the words understand by a toddler are: 500 words<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Compare<\/strong><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 16\" width=\"135\" height=\"44\" \/><br \/>\nAnswer: 1,834 is greater than 1,796<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 1,834 and 1,796.<br \/>\nHence, from these 2 numbers,<br \/>\nWe can conclude that 1,834 is greater than 1,796<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 17\" width=\"152\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-17.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-17-150x44.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer: 62,905 is greater than 62,081<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 62,905 and 62,081.<br \/>\nHence, from these 2 numbers,<br \/>\nWe can conclude that 62,905 is greater than 62,081<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 18\" width=\"149\" height=\"45\" \/><br \/>\nAnswer: 9,142 is less than 9,146<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 9,142 and 9,146<br \/>\nHence, from these 2 numbers,<br \/>\nWe can conclude that 9,142 is less than 9,146.<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 19\" width=\"140\" height=\"38\" \/><br \/>\nAnswer: 52,048 is less than 52,071<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 52,048 and 52,071<br \/>\nHence, from these 2 numbers,<br \/>\nWe can conclude that 52,048 is less than 52,071<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 20\" width=\"161\" height=\"39\" \/><br \/>\nAnswer: 402,157 is equal to 402,157<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 402,157 and 402,157<br \/>\nHence, from these 2 numbers,<br \/>\nWe can conclude that 402,157 is equal to 402,157<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.1 21\" width=\"161\" height=\"35\" \/><br \/>\nAnswer: 387,402 is less than 384,927<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 387,402 and 384,927<br \/>\nHence, from these 2 numbers,<br \/>\nWe can conclude that 387,402 is less than 384,927<\/p>\n<h3><a id=\"Lesson_5.2_Estimate_Quotients\"><\/a>Lesson 5.2 Estimate Quotients<\/h3>\n<h3><strong>Explore and Grow<\/strong><\/h3>\n<p>Explain how you can use the table to estimate 740 \u00f7 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-17524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-67.jpg\" alt=\"\" width=\"288\" height=\"249\" \/><\/p>\n<p>740 \u00f7 8 is about ______.<\/p>\n<p>Answer: 90<\/p>\n<p>Explanation:<br \/>\nLet 740 be Estimated to 720.<br \/>\nSo, now we have to find the value of 720 \u00f7 8<br \/>\nNow,<br \/>\n720 \u00f7 8 = 72 tens \u00f7 8<br \/>\n= 9 tens<br \/>\n= 90<br \/>\nHence, from the above,<br \/>\nWe can conclude that 740 \u00f7 8 is about 90.<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nWhy did you choose your estimate? Compare your results with your partner.<\/p>\n<p>Answer: We choose the Estimate to round off the Result because the quotient must be the Integer.<\/p>\n<p><strong>Think and Grow: Estimate Quotients<\/strong><\/p>\n<p>You can use division facts and compatible numbers to estimate a quotient.<br \/>\n<strong>Example<\/strong><br \/>\nEstimate 154 \u00f7 4.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 2\" width=\"221\" height=\"259\" \/><\/p>\n<p>Look at the first two digits of the dividend and use basic division facts. and are close to the actual numbers.<br \/>\nThink: What number close to 154 is easily divided by 4?<br \/>\nTry 120. 12 \u00f7 4 = 3, so 120 \u00f7 4 =30.<br \/>\nTry 160. 16 \u00f7 4 , = 4, so 160 \u00f7 4 = 140.<br \/>\nChoose 160 because 154 is closer to 160.<br \/>\nSo, 154 \u00f7 4 is about 40.<\/p>\n<p>When solving division problems, you can check whether an answer is reasonable by finding two numbers that a quotient is between.<br \/>\n<strong>Example<\/strong><br \/>\nFind two numbers that the quotient 6,427 \u00f7 7 is between.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 3\" width=\"212\" height=\"245\" \/><br \/>\nThink: What numbers close to 6,427 are easily divided by7?<br \/>\nUse 6,300. 63 \u00f7 7 = 9, so 6,300 \u00f7 7 = 900.<br \/>\nUse 7,000. 70 \u00f7 7 = 10, so 7,000 \u00f7 7 = 1,000 .<br \/>\n6,427 is between 6,300 and 7,000.<br \/>\nSo, the quotient 6,427 \u00f7 7 is between 900 and 1,000.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Estimate the quotient.<br \/>\n<\/strong>Question 1.<br \/>\n61 \u00f7 3<br \/>\nAnswer: 20<\/p>\n<p>Explanation;<br \/>\nLet 61 be rounded off to 60.<br \/>\nSo, now we have to find 60 \u00f7 3<br \/>\nNow,<br \/>\n60 \u00f7 3 = 6 tens \u00f7 3<br \/>\n= 2 tens<br \/>\n= 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that 61 \u00f7 3 can be rounded off to 20.<\/p>\n<p>Question 2.<br \/>\n465 \u00f7 9<br \/>\nAnswer: 50<\/p>\n<p>Explanation:<br \/>\nLet 465 be rounded off to 450.<br \/>\nSo, now we have to find 450 \u00f7 9<br \/>\nNow,<br \/>\n450 \u00f7 9 = 45 tens \u00f7 9<br \/>\n= 5 tens<br \/>\n= 50<br \/>\nHence, from the above,<br \/>\nWe can conclude that 465 \u00f7 9 can be rounded off to 50..<\/p>\n<p><strong>Find two numbers that the quotient is between.<br \/>\n<\/strong>Question 3.<br \/>\n477 \u00f7 8<br \/>\nAnswer: The Quotient of 477 \u00f7 8 is between 50 and 60.<\/p>\n<p>Explanation:<br \/>\nUse 400. 40 \u00f7 8 = 5, so 400 \u00f7 8 = 50.<br \/>\nUse 480. 48 \u00f7 8 = 6, so 480 \u00f7 8 = 60 .<br \/>\n477 is between 400 and 480.<br \/>\nSo, the quotient of 477 \u00f7 8 is between 50 and 60.<\/p>\n<p>Question 4.<br \/>\n5,194 \u00f7 6<br \/>\nAnswer: The Quotient of 5,194 \u00f7 6 is between 800 and 900<\/p>\n<p>Explanation:<br \/>\nUse 4,800. 48 \u00f7 6 = 8, so 4,800 \u00f7 6 = 800.<br \/>\nUse 5,400. 54 \u00f7 6 = 9, so 5,400 \u00f7 6 = 900 .<br \/>\n5,194 is between 4,800 and 5,400.<br \/>\nSo, the quotient of 5,194 \u00f7 6 is between 800 and 900<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Estimate the quotient<br \/>\n<\/strong>Question 5.<br \/>\n29 \u00f7 5<br \/>\nAnswer: 6<\/p>\n<p>Explanation;<br \/>\nLet 29 be rounded off to 30.<br \/>\nSo, now we have to find 30 \u00f7 5<br \/>\nNow,<br \/>\n30 \u00f7 5 = 3 tens \u00f7 5<br \/>\n= 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that 29 \u00f7 5 can be rounded off to 6.<\/p>\n<p>Question 6.<br \/>\n571 \u00f7 8<br \/>\nAnswer: 70<\/p>\n<p>Explanation;<br \/>\nLet 571 be rounded off to 560.<br \/>\nSo, now we have to find 560 \u00f7 8<br \/>\nNow,<br \/>\n560 \u00f7 8 = 56 tens \u00f7 8<br \/>\n= 7 tens<br \/>\n= 70<br \/>\nHence, from the above,<br \/>\nWe can conclude that 571 \u00f7 8 can be rounded off to 70.<\/p>\n<p>Question 7.<br \/>\n202 \u00f7 6<br \/>\nAnswer: 30<\/p>\n<p>Explanation;<br \/>\nLet 202 be rounded off to 180.<br \/>\nSo, now we have to find 180 \u00f7 6<br \/>\nNow,<br \/>\n180 \u00f7 6 = 18 tens \u00f7 6<br \/>\n= 3 tens<br \/>\n= 30<br \/>\nHence, from the above,<br \/>\nWe can conclude that 202 \u00f7 6 can be rounded off to 30.<\/p>\n<p>Question 8.<br \/>\n3,384 \u00f7 7<br \/>\nAnswer: 500<\/p>\n<p>Explanation;<br \/>\nLet 3,384 be rounded off to 3,500.<br \/>\nSo, now we have to find 3,500 \u00f7 7<br \/>\nNow,<br \/>\n3,500 \u00f7 7 = 35 hundreds \u00f7 7<br \/>\n= 5 hundred<br \/>\n= 500<br \/>\nHence, from the above,<br \/>\nWe can conclude that 3,384 \u00f7 7 can be rounded off to 500.<\/p>\n<p><strong>Find two estimates that the quotient is between.<br \/>\n<\/strong>Question 9.<br \/>\n22 \u00f7 3<br \/>\nAnswer: The Quotient of 22 \u00f7 3 is between 7 and 8.<\/p>\n<p>Explanation:<br \/>\nUse 21. , so 21 \u00f7 3 = 7.<br \/>\nUse 24.\u00a0 so 24 \u00f7 3 = 8 .<br \/>\n22 is between 21 and 24.<br \/>\nSo, the quotient of 22 \u00f7 3 is between 7 and 8.<\/p>\n<p>Question 10.<br \/>\n165 \u00f7 9<br \/>\nAnswer: The Quotient of 165 \u00f7 9 is between 10 and 20<\/p>\n<p>Explanation:<br \/>\nUse 90. 9 \u00f7 9 = 1, so 90 \u00f7 9 = 10.<br \/>\nUse 180. 18 \u00f7 9 = 2, so 180 \u00f7 9 = 20 .<br \/>\n165 is between 90 and 180.<br \/>\nSo, the quotient of 165 \u00f7 9 is between 10 and 20<\/p>\n<p>Question 11.<br \/>\n2,387 \u00f7 5<br \/>\nAnswer: The Quotient of 2,387 \u00f7 5 is between 400 and 500.<\/p>\n<p>Explanation:<br \/>\nUse 2,000. 20 \u00f7 5 = 4, so 2,000 \u00f7 5 = 400.<br \/>\nUse 2,500. 25 \u00f7 5 = 5, so 2,500 \u00f7 5 = 500 .<br \/>\n2,387 is between 2,000 and 2,500.<br \/>\nSo, the quotient of 2,387 \u00f7 5 is between 400 and 500.<\/p>\n<p>Question 12.<br \/>\n3,813 \u00f7 4<br \/>\nAnswer: The Quotient of 3,813 \u00f7 4 is between 900 and 1,000<\/p>\n<p>Explanation:<br \/>\nUse 3,600. 36 \u00f7 4 = 9, so 3,600 \u00f7 4 = 900.<br \/>\nUse 4,000. 40 \u00f7 4 = 10, so 4,000 \u00f7 4 = 1,000 .<br \/>\n3,813 is between 3,600 and 4,000.<br \/>\nSo, the quotient of 2,387 \u00f7 5 is between 400 and 500.<\/p>\n<p><strong>DIG DEEPER!<\/strong><br \/>\n<strong>Estimate to compare.<\/strong><br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-4.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 4\" width=\"112\" height=\"43\" \/><br \/>\nAnswer: 3 is greater than 2<\/p>\n<p>Explanation;<br \/>\nGiven Expressions are 26 \u00f7 9 and 2<br \/>\nLet 26 be rounded to 27.<br \/>\nNow,<br \/>\n27 \u00f7 9 = 3<br \/>\nHence, from the above values,<br \/>\nWe can conclude that 3 is greater than 2<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 5\" width=\"136\" height=\"44\" \/><br \/>\nAnswer: 50 is equal to 50.<\/p>\n<p>Explanation;<br \/>\nGiven Expressions are 142 \u00f7 3 and 50<br \/>\nLet 142 be rounded to 150.<br \/>\nNow,<br \/>\n150 \u00f7 3 = 15 tens \u00f7 3<br \/>\n= 5 tens<br \/>\n= 50<br \/>\nHence, from the above values,<br \/>\nWe can conclude that 50 is equal to 50.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 6\" width=\"165\" height=\"42\" \/><br \/>\nAnswer: 80 is less than 90<\/p>\n<p>Explanation;<br \/>\nGiven Expressions are 645 \u00f7 8 and 816 \u00f7 9<br \/>\nLet 645 be rounded to 640.<br \/>\nNow,<br \/>\n640 \u00f7 8 = 64 tens \u00f7 8<br \/>\n= 8 tens<br \/>\n= 80<br \/>\nLet 816 be rounded to 810.<br \/>\nNow,<br \/>\n810 \u00f7 9 = 81 tens \u00f7 9<br \/>\n= 9 tens<br \/>\n= 90<br \/>\nHence, from the above results,<br \/>\nWe can conclude that 80 is less than 90<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-7.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 7\" width=\"184\" height=\"47\" \/><br \/>\nAnswer: 200 is equal to 200<\/p>\n<p>Explanation;<br \/>\nGiven Expressions are 1,200 \u00f7 6 and 800 \u00f7 4<br \/>\nNow,<br \/>\n1,200 \u00f7 6 = 12 hundreds \u00f7 6<br \/>\n= 2 hundred<br \/>\n= 200<br \/>\nNow,<br \/>\n800 \u00f7 4 = 80 tens \u00f7 4<br \/>\n= 20 tens<br \/>\n= 200<br \/>\nHence, from the above results,<br \/>\nWe can conclude that 200 is equal to 200<\/p>\n<p>Question 17.<br \/>\nA pizza shop owner has 2,532 coupons in pamphlets of 4 coupons each. He wants to determine whether he has enough pamphlets to give one to each of his first 600 customers. Can he use an estimate, or is an exact answer required? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-8.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 8\" width=\"146\" height=\"153\" \/><\/p>\n<p>Answer: He has to use an Estimate.<\/p>\n<p>Explanation:<br \/>\nGiven that a pizza owner has 2,532 coupons in pamphlets of 4 coupons each and he wants to give one to each of his first 600 customers.<br \/>\nSo, we have to first find the total number of coupons he has.<br \/>\nBut, there are 2,532 coupons in pamphlets for 4 coupons each. The coupons are in such a way that we can cot divide all the coupons equally.<br \/>\nSo, we have to find the estimate of 2,532<br \/>\nLet 2,532 be rounded to 2,400 ( Since the coupons are to be divided into 4 coupons each)<br \/>\nHence,<br \/>\n2,400 \u00f7 4 = 24 hundreds \u00f7 4<br \/>\n= 6 hundred<br \/>\n= 600<br \/>\nFrom this,<br \/>\nWe can conclude that the pizza owner has to use an Estimate.<\/p>\n<p><strong>YOU BE THE TEACHER<br \/>\n<\/strong>Your friend finds a quotient. Is his answer reasonable? Estimate to check.<br \/>\nQuestion 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 9\" width=\"114\" height=\"50\" \/><br \/>\nAnswer: His answer is reasonable<\/p>\n<p>Explanation:<br \/>\nGiven Expression is 273 \u00f7 3<br \/>\nLet 273 be rounded to 270<br \/>\nNow,<br \/>\n270 \u00f7 3 = 27 tens \u00f7 3<br \/>\n= 9 tens<br \/>\n= 90<br \/>\nSince there is not much difference between the Estimate quotient and the quotient of your friend, his answer is reasonable.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-10.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 10\" width=\"145\" height=\"53\" \/><br \/>\nAnswer: His answer is not reasonable.<\/p>\n<p>Explanation:<br \/>\nGiven Expression is 4,290 \u00f7 6<br \/>\nLet 4,290 be rounded to 4,200<br \/>\nNow,<br \/>\n4,200 \u00f7 6 = 42 hundreds \u00f7 6<br \/>\n= 7 hundred<br \/>\n= 700<br \/>\nSince the Estimate quotient and the quotient of your friend has large difference, the answer of your friend is not reasonable.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<br \/>\n<\/strong>Mount Nantai is 2,486 meters above sea level. It is about 8 times as many meters above sea level as the Taal Volcano. About how many meters above sea level is the Taal Volcano?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-11.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 11\" width=\"204\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-11.png 204w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-11-150x150.png 150w\" sizes=\"(max-width: 204px) 100vw, 204px\" \/><\/p>\n<p>Mount Nantai is about 8 times as many meters above sea level as the Taal Volcano, so estimate 2,486 \u00f7 8.<br \/>\nThink: What number close to 2,486 is easily divided by 8?<br \/>\nTry 2,400. 24 \u00f7 8 = 3, so 2,400 \u00f7 8 = 300.<br \/>\nTry 3,200. 32 \u00f7 8 = 4, so 3,200 \u00f7 8 = 400.<br \/>\nChoose 2,400 because 2,486 is closer to 2,400.<br \/>\nSo, the Taal Volcano is about 400 meters above sea level.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 20.<br \/>\nThere are about 3,785 milliliters in 1 gallon. There are 4 times as many milliliters in 1 gallon as there are in 1 quart. About how many milliliters are in 1 quart?<br \/>\nAnswer: 900 milliliters<\/p>\n<p>Explanation:<br \/>\nGiven that there are about 3,785 milliliters in 1 gallon and there are 4 times as many milliliters in 1 gallon as there are in 1 quart.<br \/>\nSo,<br \/>\nThe number of milliliters in 1 gallon = the number of milliliters in 1 quant<br \/>\nSo, we have to find 3,785 \u00f7 4<br \/>\nNow,<br \/>\nLet 3,785 be rounded to 3,600<br \/>\nSo,<br \/>\n3,600 \u00f7 4 = 36 hundreds \u00f7 4<br \/>\n= 9 hundred<br \/>\n= 900<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of milliliters in 1 quant is: 900 milliliters.<\/p>\n<p>Question 21.<br \/>\nA teenager works at an amusement park for 3 months and earns $2,178. She earns the same amount each month. About how much money does she earn each month?<\/p>\n<p>Answer: $700<\/p>\n<p>Explanation:<br \/>\nGiven that a teenager works at an amusement park for 3 months ad earns $2,178 and she earns the same amount each month.<br \/>\nSo, the amount of money she earns each month = $2,178 \u00f7 3<br \/>\nNow,<br \/>\nLet 2,178 be rounded to 2,100 (Since the amount of money is the same each month)<br \/>\nNow,<br \/>\n2,100 \u00f7 3 = 21 hundreds \u00f7 3<br \/>\n= 7 hundred<br \/>\n=700<br \/>\nHence, from the above,<br \/>\nWe can conclude that she earns $700 each month.<\/p>\n<p>Question 22.<br \/>\nAn animal shelter has a bin filled with 456 pounds of dog food. There are 4 large dogs at the shelter who each eat 2 pounds of dog food each day. For about how many days can the dogs eat from the bin of food?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-12.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 12\" width=\"300\" height=\"150\" \/><\/p>\n<p>Answer: The dogs eat food from the bin of food for about 60 days.<\/p>\n<p>Explanation:<br \/>\nGiven that an animal shelter has a bin filled with 456 pounds of dog food.<br \/>\nIt is also given that there are 4 large dogs at the shelter who each eat 2 pounds of dog food each day.<br \/>\nSo,<br \/>\nThe total amount of food dogs eat = 4 \u00d7 2 = 8 pounds<br \/>\nSo,<br \/>\nThe number of days the total amount of food the dogs eat = Total amount of food \u00f7 Total amount of food dogs eat per each day<br \/>\n= 456 \u00f7 8<br \/>\nLet,<br \/>\n456 be rounded to 480<br \/>\nNow,<br \/>\n480 \u00f7 8 = 48 tens \u00f7 8<br \/>\n= 6 tens<br \/>\n= 60<br \/>\nHence, from the above,<br \/>\nWe can conclude that the dogs complete the total food in about 60 days.<\/p>\n<h3><a id=\"Estimate_Quotients_Practice_5.2\"><\/a>Estimate Quotients Homework &amp; Practice 5.2<\/h3>\n<p><strong>Estimate the quotient.<\/strong><\/p>\n<p>Question 1.<br \/>\n33 \u00f7 4.<br \/>\nAnswer: 8<\/p>\n<p>Explanation;<br \/>\nLet 33 be rounded off to 32.<br \/>\nSo, now we have to find 32 \u00f7 4<br \/>\nNow,<br \/>\n32 \u00f7 4 = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that 33 \u00f7 4 can be rounded off to 8.<\/p>\n<p>Question 2.<br \/>\n527 \u00f7 9<br \/>\nAnswer: 60<\/p>\n<p>Explanation;<br \/>\nLet 527 be rounded off to 540.<br \/>\nSo, now we have to find 540 \u00f7 9<br \/>\nNow,<br \/>\n540 \u00f7 9 = 54 tens \u00f7 9<br \/>\n= 6 tens<br \/>\n= 60<br \/>\nHence, from the above,<br \/>\nWe can conclude that 527 \u00f7 9 can be rounded off to 60.<\/p>\n<p><strong>Find two estimates that the quotient is between.<\/strong><\/p>\n<p>Question 3.<br \/>\n308 \u00f7 7<br \/>\nAnswer: The Quotient of 308 \u00f7 7 is between 40 and 50<\/p>\n<p>Explanation:<br \/>\nUse 280. 28 \u00f7 7 = 4, so 280 \u00f7 7 = 40.<br \/>\nUse 350. 35 \u00f7 7 = 5, so 350 \u00f7 7 = 50 .<br \/>\n308 is between 280 and 350.<br \/>\nSo, the quotient of 308\u00f7 7 is between 40 and 50.<\/p>\n<p>Question 4.<br \/>\n3,421 \u00f7 6<br \/>\nAnswer: The Quotient of 3,421 \u00f7 6 is between 500 and 600<\/p>\n<p>Explanation:<br \/>\nUse 3,000. 30 \u00f7 6 = 5, so 3,000 \u00f7 6 = 500.<br \/>\nUse 3,600. 36 \u00f7 6 = 6, so 3,600 \u00f7 6 = 600 .<br \/>\n3,421 is between 3,000 and 3,600.<br \/>\nSo, the quotient of 3,421 \u00f7 6 is between 500 and 600.<\/p>\n<p><strong>DIG DEEPER!<\/strong><br \/>\n<strong>Estimate to compare<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-13.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 13\" width=\"126\" height=\"43\" \/><br \/>\nAnswer: 30 is less than 40<\/p>\n<p>Explanation;<br \/>\nGiven Expressions are 97 \u00f7 3 and 40<br \/>\nLet 97 be rounded to 90.<br \/>\nNow,<br \/>\n90 \u00f7 3 = 30<br \/>\nHence, from the above values,<br \/>\nWe can conclude that 30 is greater than 40<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-14.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 14\" width=\"161\" height=\"41\" \/><br \/>\nAnswer: 80 is greater than 20<\/p>\n<p>Explanation;<br \/>\nGiven Expressions are 425 \u00f7 5 and 182 \u00f77<br \/>\nLet 425 be rounded to 400.<br \/>\nNow,<br \/>\n400 \u00f7 5 = 40 tens \u00f7 5<br \/>\n= 8 tens<br \/>\n= 80<br \/>\nLet 182 be rounded to 140.<br \/>\nNow,<br \/>\n140 \u00f7 7 =14 tens \u00f7 7<br \/>\n= 2 tens<br \/>\n= 20<br \/>\nHence, from the above results,<br \/>\nWe can conclude that 80 is greater than 20<\/p>\n<p>Question 7.<br \/>\nThree friends want to share 261 tickets equally. They want to determine whether they can each have at least 87 tickets. Can they use an estimate, or is an exact answer required? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-15.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 15\" width=\"308\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-15.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-15-300x55.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p>Answer: The three friends don&#8217;t have to use an Estimate and they needed an exact answer.<\/p>\n<p>Explanation:<br \/>\nGiven that 3 friends want to share 261 tickets equally and they want to determine whether they each have at least 87 tickets.<br \/>\nBy using Estimate:<br \/>\nLet 261 be rounded to 270.<br \/>\nSo, 270 tickets have to be shared among 3 friends.<br \/>\nNow,<br \/>\n270 \u00f7 3 = 27 tens \u00f7 3<br \/>\n= 9 tens<br \/>\n= 90<br \/>\nSo, each friend have 90 tickets.<br \/>\nNow,<br \/>\nThe given actual value is 261 tickets.<br \/>\nSo,<br \/>\n261 \u00f7 3 = ( 240 + 21 ) \u00f7 3 ( Divide 261 into multiples of 3 so that all the partitioned numbers can be divided exactly)<br \/>\n= ( 240 \u00f7 3) + ( 21 \u00f7 3)<br \/>\n= 80 + 7<br \/>\n= 87 tickets.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 3 friends required an exact number.<\/p>\n<p>Question 8.<br \/>\n<strong>Reasoning<\/strong><br \/>\nExplain how to find a better estimate for 462 \u00f7 5 than the one shown.<\/p>\n<p>Round 462 to 500. Estimate 500 \u00f7 5. 500 \u00f7 5 = 100, so 462 \u00f7 5 is about 100.<\/p>\n<p>Answer: The better estimate to find 462 \u00f7 5 is to round off 462 to 450.<\/p>\n<p>Explanation:<br \/>\nGiven Expression is 462 \u00f7 5<br \/>\nLet 462 be rounded to 450<br \/>\nSo,<br \/>\n450 \u00f7 5 = 45 tens \u00f7 5<br \/>\n= 9 tens<br \/>\n= 90<br \/>\nNow,<br \/>\nLet 462 be rounded to 500.<br \/>\nSo,<br \/>\n500 \u00f7 5 = 5 hundreds \u00f7 5<br \/>\n= 1 hundred<br \/>\n=100<br \/>\nBut, 462 is near to 450 when compared to 450.<br \/>\nSo,<br \/>\nWe can conclude that<br \/>\n462 \u00f7 5 = 90<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA machine that makes toy spinners is in operation for 8 hours each day. The machine makes 7,829 toy spinners in 1 day. About how many toy spinners does the machine make each hour?<\/p>\n<p>Answer: About 1,000 toy spinners the machine make each hour.<\/p>\n<p>Explanation:<br \/>\nGiven that a machine that makes toy spinners is in operation for 8 hours each day and the machine makes 7,829 toy spinners in 1 day.<br \/>\nSo, to find the number of toy spinners the machine make each hour, we have to find the value of 7,829 \u00f7 8<br \/>\nNow,<br \/>\nLet 7,829 be rounded to 8,000<br \/>\nSo, 8,000 \u00f7 8 = 80 hundreds \u00f7 8<br \/>\n= 10 hundred<br \/>\n=1,000<br \/>\nSo, from the above<br \/>\nWe can conclude that about 1,000 toy spinners the machine make each hour.<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA little penguin has 10,235 feathers. The penguin has about 3 times as many feathers as a blue jay. About how many feathers does the blue jay have?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.2-16.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.2 16\" width=\"297\" height=\"171\" \/><br \/>\nAnswer: The blue jay have about 3,412 feathers.<\/p>\n<p>Explanation;<br \/>\nGiven that a penguin has 10,235 feathers and it has about 3 times as many feathers as a blue jay.<br \/>\nSo,<br \/>\nThe feathers of a blue jay = 10,235 \u00f7 3<br \/>\nNow,<br \/>\nLet 10,235 be rounded to 10,236<br \/>\nSo,<br \/>\n10,236 \u00f7 3 = ( 9,000 + 1,236) \u00f7 3<br \/>\n=( 9,000 \u00f7 3 )+ ( 1,236 \u00f7 3)<br \/>\n= 3,000 + 412<br \/>\n= 3,412 feathers<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are about 3,412 feathers in a blue jay.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write an equation for the comparison sentence.<\/strong><\/p>\n<p>Question 11.<br \/>\n15 is 9 more than 6.<\/p>\n<p>Answer:<\/p>\n<p>Question 12.<br \/>\n56 is 7 times as many as 8.<\/p>\n<p>Answer: 7 \u00d78 = 56<\/p>\n<p>Explanation:<br \/>\nGiven that 56 is 7 times as many as 8<br \/>\nThat means 8 + 8 + 8+ 8 + 8 +8 + 8 = 56<br \/>\n= 7 \u00d78 = 56<\/p>\n<h3><a id=\"Lesson_5.3_Understand_Division_and_Remainder\"><\/a>Lesson 5.3 Understand Division and Remainder<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use base ten blocks to determine whether 14 can be divided equally among 2, 3, 4, or 5 groups. Draw and describe your models.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 1\" width=\"162\" height=\"119\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 2\" width=\"583\" height=\"316\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-2.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-2-300x163.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-17761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-68.jpg\" alt=\"\" width=\"592\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-68.jpg 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-68-300x164.jpg 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p><strong>Structure<\/strong><br \/>\nExplain why the units that are leftover cannot be put into a group.<\/p>\n<p>Answer: The leftover units of the above group can not be put into a group because it is clearly mentioned that the blocks will have to be divided into equal parts.<\/p>\n<p><strong>Think and Grow: Find and Interpret Remainder<\/strong><\/p>\n<p>Sometimes you cannot divide a number evenly and there is an amount left over.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 3\" width=\"251\" height=\"176\" \/><br \/>\nThe amount left over is called the remainder. Use an R to represent the remainder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-17764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-69.jpg\" alt=\"\" width=\"647\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-69.jpg 647w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-4-69-300x157.jpg 300w\" sizes=\"(max-width: 647px) 100vw, 647px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Use a model to find the quotient and the remainder.<\/strong><\/p>\n<p>Question 1.<br \/>\n19 \u00f7 6 = _____ R _____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-5.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 5\" width=\"253\" height=\"94\" \/><\/p>\n<p>Answer: 6 R 1<\/p>\n<p>Explanation:<br \/>\nNumber of Units in each group = 6<br \/>\nNumber of units leftover = 1<br \/>\nSo,<br \/>\n19 \u00f7 6 = 6 R 1<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 2.<br \/>\n34 \u00f7 5 = _____ R ______<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-6.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 6\" width=\"382\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-6.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-6-300x76.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\nAnswer: 6 R 4<\/p>\n<p>Explanation:<br \/>\nNumber of Units in each group = 6<br \/>\nNumber of units leftover = 4<br \/>\nSo,<br \/>\n34 \u00f7 5 = 6 R 4<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 3.<br \/>\n26 \u00f7 3 = _____ R _____<br \/>\nAnswer: 8 R 2<\/p>\n<p>Explanation:<br \/>\nDivide 26 into 3 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 8<br \/>\nNumber of units leftover = 2<br \/>\nHence,<br \/>\n26 \u00f7 3 = 8 R 2<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 4.<br \/>\n20 \u00f7 7 = ______ R _____<br \/>\nAnswer: 14 R 6<\/p>\n<p>Explanation:<br \/>\nDivide 20 into 7 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 2<br \/>\nNumber of units leftover = 6<br \/>\nHence,<br \/>\n20 \u00f7 7 = 14 R 6<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Use a model to find the quotient and the remainder.<\/strong><br \/>\nQuestion 5.<br \/>\n13 \u00f7 2 = _____ R _____<br \/>\nAnswer: 6 R 1<\/p>\n<p>Explanation:<br \/>\nDivide 13 into 2 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 6<br \/>\nNumber of units leftover = 1<br \/>\nHence,<br \/>\n13 \u00f7 2 = 6 R 1<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 6.<br \/>\n25 \u00f7 9 = ____ R ____<br \/>\nAnswer: 2 R 7<\/p>\n<p>Explanation:<br \/>\nDivide 25 into 9 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 2<br \/>\nNumber of units leftover = 7<br \/>\nHence,<br \/>\n25 \u00f7 9 = 2 R 7<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 7.<br \/>\n28 \u00f7 8 = _______ R _____<br \/>\nAnswer: 3 R 4<\/p>\n<p>Explanation:<br \/>\nDivide 28 into 8 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 3<br \/>\nNumber of units leftover = 4<br \/>\nHence,<br \/>\n28 \u00f7 8 = 3 R 4<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 8.<br \/>\n15 \u00f7 4 = _____ R _____<br \/>\nAnswer: 3 R 3<\/p>\n<p>Explanation:<br \/>\nDivide 15 into 4 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 3<br \/>\nNumber of units leftover = 3<br \/>\nHence,<br \/>\n15 \u00f7 4 = 3 R 3<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 9.<br \/>\n29 \u00f7 6 = _____ R ______<br \/>\nAnswer: 4 R 5<\/p>\n<p>Explanation:<br \/>\nDivide 29 into 6 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 4<br \/>\nNumber of units leftover = 5<br \/>\nHence,<br \/>\n29 \u00f7 6 = 4 R 5<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 10.<br \/>\n11 \u00f7 5 = ______ R ______<br \/>\nAnswer: 2 R 1<\/p>\n<p>Explanation:<br \/>\nDivide 11 into 5 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 2<br \/>\nNumber of units leftover = 1<br \/>\nHence,<br \/>\n11 \u00f7 5 = 2 R 1<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 11.<br \/>\nDescartes has 23 cat treats to divide equally among 4 friends. How many treats does he give each friend? How many treats are left over?<br \/>\nAnswer:<br \/>\nThe number of treats he gives to each friend = 5<br \/>\nThe number of treats leftover = 3<\/p>\n<p>Explanation:<br \/>\nGiven that Descartes has 23 cat treats to divide equally among 4 friends.<br \/>\nSo,<br \/>\nWe have to find 23 \u00f7 4 to find the number of treats he gives to each friend and the number of treats leftover<br \/>\nNow,<br \/>\nDivide 23 into 4 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 5<br \/>\nNumber of units leftover = 3<br \/>\nSo,<br \/>\n23 \u00f7 4 = 5 R 3<br \/>\nWhere R is the Remainder (or) the number of units leftover<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\nThe number of treats he gives to each friend = 5<br \/>\nThe number of treats leftover = 3<\/p>\n<p>Question 12.<br \/>\nYou have 26 markers. How many groups of 3 markers can you make? How many markers are left over?<br \/>\nAnswer:<\/p>\n<p>The number of markers can you make = 8<br \/>\nThe number of markers leftover = 2<\/p>\n<p>Explanation:<br \/>\nGiven that you have 26 markers and you have to make a group of 3 markers each.<br \/>\nSo, we have to find 26 \u00f7 3 so that we can find the number of markers that you make and the number of markers leftover.<br \/>\nNow,<br \/>\nDivide 26 into 3 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 8<br \/>\nNumber of units leftover = 2<br \/>\nSo,<br \/>\n26 \u00f7 3 = 8 R 2<br \/>\nWhere R is the Remainder (or) the number of units leftover<br \/>\nHence, from the above,<br \/>\nWe can conclude that,<br \/>\nThe number of markers can you make = 8<br \/>\nThe number of markers leftover = 2<\/p>\n<p>Question 13.<br \/>\n<strong>Structure<\/strong><br \/>\nWrite a division equation represented by the model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-7.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 7\" width=\"279\" height=\"87\" \/><br \/>\nAnswer: 19 \u00f7 3 = 5 R 4<\/p>\n<p>Explanation:<br \/>\nGiven model is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-7.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 7\" width=\"279\" height=\"87\" \/><br \/>\nSo, from the above model, we can see that<br \/>\nThe number of groups = 3<br \/>\nThe number of units in each group = 5<br \/>\nThe number of units leftover = 4<br \/>\nSo, to find the total number of units,<br \/>\nTotal number of units = (The number of groups \u00d7 The number of units in each group ) + ( The number of units leftover)<br \/>\n= (5 \u00d7 3) + 4 = 15 + 4 = 19<br \/>\nHence, from the above, the division equation represented by the model is:<br \/>\n19 \u00f7 3 = 5 R 4<\/p>\n<p>Question 14.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nIs Newton correct? Draw a model to support your answer.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-8.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 8\" width=\"140\" height=\"161\" \/><\/p>\n<p>Answer: Yes, Newton is correct.<\/p>\n<p>Explanation:<br \/>\nThe given\u00a0 division equation is:<br \/>\n30 \u00f7 4<br \/>\nFrom the division equation, we can see that<br \/>\nThe number of units in each group = 6<br \/>\nThe number of units leftover = 6<br \/>\nSo, we can write<br \/>\n30 \u00f7 4 = 6 R 6<br \/>\nNewton has also given the same division equation as we got above.<br \/>\nHence, Newton is correct.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<br \/>\n<\/strong><strong>Example<\/strong><br \/>\nA water taxi transports passengers to an island. The taxi holds no more than 8 passengers at a time. There are 53 people in line to ride the water taxi.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-9.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 9\" width=\"205\" height=\"167\" \/><br \/>\n\u2022 How many trips to the island are full?<br \/>\n\u2022 How many trips to the island are needed?<br \/>\n\u2022 How many passengers are on the last trip?<br \/>\nUse a model to find 53 \u00f7 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-10.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 10\" width=\"538\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-10.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-10-300x37.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><br \/>\nThe quotient is 6. The remainder is 5.<br \/>\nInterpret the quotient and the remainder.<\/p>\n<p>How many trips to the island are full?<br \/>\n&#8220;6&#8221;\u00a0 is the number of trips that have 8 passengers.<br \/>\nSo, 6 trips to the island are full.<\/p>\n<p>How many trips to the island are needed?<br \/>\n6 trips are full and 1 trip is not full.<br \/>\nSo, 7 trips are needed.<\/p>\n<p>How many passengers are on the last trip?<br \/>\n&#8220;5&#8221;\u00a0 is the number of passengers that are on the last trip.<br \/>\nSo, 5 passengers are on their last trip.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nTours of a crayon factory have no more than 9 guests. There are 87 guests in line to tour the factory.<br \/>\n\u2022 How many tours are full?<br \/>\n\u2022 How many tours are needed?<br \/>\n\u2022 How many guests are on the last tour?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-11.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 11\" width=\"296\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\na) 9 Tours are full.<br \/>\nb) 10 Tours are needed.<br \/>\nc) 6 guests are on the last tour.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 87 guests in line to tour a crayon factory It is also given that there are no more than 9 guests in the tours of a crayon factory.<br \/>\nWe have to observe that to make all the guests full on all the trips without leftovers, we will need 10 trips. i.e.., 90 guests.<br \/>\nSo, now we have to find the number of guests in each tour of a crayon factory by finding the quotient and remainder of 87 \u00f7 9.<br \/>\nNow,<br \/>\n87 \u00f7 9<br \/>\nFrom this, we can see<br \/>\nThe number of guests in each tour that are full = 9<br \/>\nThe number of guests leftover on the last trip = 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\na) 9 Tours are full.<br \/>\nb) 10 Tours are needed.<br \/>\nc) 6 guests are on the last tour.<\/p>\n<h3><a id=\"Understand_Division_and_Remainder_Practice_5.3\"><\/a>Understand Division and Remainder Homework &amp; Practice 5.3<\/h3>\n<p><strong>Use a model to find the quotient and the remainder.<\/strong><br \/>\nQuestion 1.<br \/>\n25 \u00f7 7 = _____ R _____<br \/>\nAnswer: 3 R 4<\/p>\n<p>Explanation:<br \/>\nDivide 25 into 7 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 3<br \/>\nNumber of units leftover = 4<br \/>\nHence,<br \/>\n25 \u00f7 7 = 3 R 4<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 2.<br \/>\n19 \u00f7 2 = ______ R ______<br \/>\nAnswer: 9 R 1<\/p>\n<p>Explanation:<br \/>\nDivide 19 into 2 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 9<br \/>\nNumber of units leftover = 1<br \/>\nHence,<br \/>\n19 \u00f7 2 = 9 R 1<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 3.<br \/>\n27 \u00f7 6 = _____ R ______<br \/>\nAnswer: 4 R 3<\/p>\n<p>Explanation:<br \/>\nDivide 27 into 6 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 4<br \/>\nNumber of units leftover = 3<br \/>\nHence,<br \/>\n27 \u00f7 6 = 4 R 3<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 4.<br \/>\n26 \u00f7 4 = ______ R ______<br \/>\nAnswer: 6 R 2<\/p>\n<p>Explanation:<br \/>\nDivide 26 into 4 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 6<br \/>\nNumber of units leftover = 2<br \/>\nHence,<br \/>\n26 \u00f7 4 = 6 R 2<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p><strong>Use a model to find the quotient and the remainder.<\/strong><br \/>\nQuestion 5.<br \/>\n29 \u00f7 8 = _____ R _____<br \/>\nAnswer: 3 R 5<\/p>\n<p>Explanation:<br \/>\nDivide 29 into 8 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 3<br \/>\nNumber of units leftover = 5<br \/>\nHence,<br \/>\n29 \u00f7 8 = 3 R 5<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 6.<br \/>\n11 \u00f7 2 = _____ R ______<br \/>\nAnswer: 5 R 1<\/p>\n<p>Explanation:<br \/>\nDivide 11 into 2 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 5<br \/>\nNumber of units leftover = 1<br \/>\nHence,<br \/>\n11 \u00f7 2 = 5 R 1<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA number divided by 4 has a remainder. What numbers might the remainder be? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nTours of a space center can have no more than 7 guests. There are 31 guests in line to tour the space center.<br \/>\n\u2022 How many tours are full?<br \/>\n\u2022 How many tours are needed?<br \/>\n\u2022 How many guests are on the last tour?<br \/>\nAnswer:<br \/>\na) 4 Tours are full.<br \/>\nb) 5 Tours are needed.<br \/>\nc) 3 guests are on the last tour.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 31 guests in line to tour the space center. It is also given that there are no more than 7 guests in the tours of a space center.<br \/>\nWe have to observe that to make all the guests full on all the trips without leftovers, we will need 5 trips. i.e.., 35 guests.<br \/>\nSo, now we have to find the number of guests in each tour of a crayon factory by finding the quotient and remainder of 31 \u00f7 7.<br \/>\nNow,<br \/>\n31 \u00f7 7<br \/>\nFrom this, we can see<br \/>\nThe number of guests in each tour that are full = 4<br \/>\nThe number of guests leftover on the last trip = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\na) 4 Tours are full.<br \/>\nb) 5 Tours are needed.<br \/>\nc) 3 guests are on the last tour.<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou need 3 googly eyes to make one monster puppet. You have 28 googly eyes. How many monster puppets can you make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.3-12.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.3 12\" width=\"149\" height=\"105\" \/><br \/>\nAnswer: You can make 9 monster puppets.<\/p>\n<p>Explanation:<br \/>\nGiven that you need 3\u00a0 googly eyes to make 1 monster puppet.<br \/>\nIt is also given that you have 28 googly eyes.<br \/>\nSo, to find the number of monster puppets that you can make with the given googly eyes, we have to find the quotient and remainder of 28 \u00f7 3.<br \/>\nThe quotient of 28 \u00f7 3.is the number of monster puppets that you can make with the help of given googly eyes.<br \/>\nNow,<br \/>\n28 \u00f7 3<br \/>\nFrom this, we can find<br \/>\nThe number of units in each group = 9<br \/>\nThe number of units leftover = 1<br \/>\nNow, we have to observe that &#8220;The number of units in each group&#8221; is the &#8220;Quotient&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that You can make 9 monster puppets with 1 leftover.<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nForty-one students attend tryouts for a debate league. Each team can have 6 students. How many students will not be on a team?<br \/>\nAnswer: 5 students will not be on a team<\/p>\n<p>Explanation:<br \/>\nGiven that 41 students attend tryouts for a debate league and each team can have 6 students.<br \/>\nSo, to find the number of students that can not form a team, we have to find the quotient and remainder of 41 \u00f76<br \/>\nNow,<br \/>\n41 \u00f7 6<br \/>\nFrom this, we can observe that<br \/>\nThe number of students in each team = 6<br \/>\nThe number of students that can not form a team = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that 5 students will not be on a team.<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA book has 37 pages. You read 7 pages each day. How many days will it take you to finish the book?<br \/>\nAnswer: About 5 days<\/p>\n<p>Explanation:<br \/>\nGiven that a book has 37 pages and you read 7 pages each day.<br \/>\nTo find the number of days it will take to finish the book, we have to find the quotient of 37 \u00f7 7.<br \/>\nNow,<br \/>\n37 \u00f7 7<br \/>\nFrom this,<br \/>\nThe number of groups that can be filled = 5<br \/>\nThe number of groups that are leftover = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the book will be finished in about 5 days.<\/p>\n<p><strong style=\"font-size: 16px;\">Review &amp; Refresh<\/strong><\/p>\n<p><strong>Estimate the sum or difference.<\/strong><br \/>\nQuestion 12.<br \/>\n50,917 &#8211; 23,846 = _____<br \/>\nAnswer: 27,071<\/p>\n<p>Question 13.<br \/>\n499,042 + 181,765 = ______<br \/>\nAnswer: 680,807<\/p>\n<h3><a id=\"Lesson_5.4_Use_Partial_Quotients\"><\/a>5.4 Use Partial Quotients<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use the area models to find 3 \u00d7 12 and 36 \u00f7 3.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 1\" width=\"293\" height=\"393\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-1.png 293w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-1-224x300.png 224w\" sizes=\"(max-width: 293px) 100vw, 293px\" \/><br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-17856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5.jpg\" alt=\"\" width=\"276\" height=\"194\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-17858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-1.jpg\" alt=\"\" width=\"295\" height=\"184\" \/><\/p>\n<p><strong>Reasoning<\/strong><br \/>\nHow does the Distributive Property relate to each of the area models? Explain.<\/p>\n<p>Answer: The &#8220;Distributive Property for Partial Quotients&#8221; works in a similar way to &#8221; The Distributive Property of Partial Products&#8221;<\/p>\n<p>Explanation:<br \/>\nTake the above 2 Area models as examples.<br \/>\nIn the 1st Area model, we have to find 3 \u00d7 12.<br \/>\nNow, by using the Distributive Property of Partial Products,<br \/>\n3 \u00d7 12 = 3 \u00d7 (10 + 2)<br \/>\n= ( 3 \u00d710 ) + ( 3 \u00d7 2 )<br \/>\n= 30 + 6<br \/>\n= 36<br \/>\nHence, 3 \u00d7 12 = 36<br \/>\nIn the 2ndArea model, we have to find 36 \u00f7 3<br \/>\nNow, by using the Distributive Property for Partial Quotients,<br \/>\n36 \u00f7 3 = ( 30 + 6 ) \u00f7 3<br \/>\n= ( 30 \u00f7 3 ) + ( 6 \u00f7 3 )<br \/>\n= 10 + 2<br \/>\n= 12<br \/>\nHence, 36 \u00f7 3 = 12<\/p>\n<p><strong>Note:\u00a0\u00a0<\/strong>When the quotient has to divide into Partial quotients, the partial quotients has to be the multiples of the number that has to\u00a0 divide the quotient.<\/p>\n<p><strong>Think and Grow: Use Partial Quotients to Divide<\/strong><\/p>\n<p>To divide using partial quotients, subtract a multiple of the divisor that is less than the dividend. Continue to subtract multiples until the remainder is less than the divisor. The factors that are multiplied by the divisor are called partial quotients. Their sum is the quotient.<br \/>\n<strong>Example<\/strong><br \/>\nUse an area model and partial quotients to find 235 \u00f7 5.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-17860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-2.jpg\" alt=\"\" width=\"564\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-2.jpg 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-2-300x191.jpg 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Use an area model and partial quotients to divide.<br \/>\n<\/strong>Question 1.<br \/>\n60 \u00f7 4 = _____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-3.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 3\" width=\"246\" height=\"214\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-17861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-3.jpg\" alt=\"\" width=\"232\" height=\"198\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n60 \u00f7 4 = ( 40 + 20 ) \u00f7 4<br \/>\n= ( 40 \u00f7 4 ) + ( 20 \u00f7 4 )<br \/>\n= 10 + 5<br \/>\n= 15<br \/>\nHence, 60 \u00f7 4 = 15<\/p>\n<p>Question 2.<br \/>\n192 \u00f7 3 = _____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-4.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 4\" width=\"291\" height=\"223\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-17862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-4.jpg\" alt=\"\" width=\"268\" height=\"208\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n192 \u00f7 3 = ( 180 + 12 ) \u00f7 3<br \/>\n= ( 180 \u00f7 3 ) + ( 12 \u00f7 3 )<br \/>\n= 60 + 4<br \/>\n= 64<br \/>\nHence, 192 \u00f7 3 = 64<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Question 3.<br \/>\nUse an area model and partial quotients to find 264 \u00f7 8.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-5.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 5\" width=\"641\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-5.png 641w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-5-300x68.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-17863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-5.jpg\" alt=\"\" width=\"653\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-5.jpg 653w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-5-300x68.jpg 300w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n264 \u00f7 8 = ( 240 + 24 ) \u00f7 8<br \/>\n= ( 240 \u00f7 8 ) + ( 24 \u00f7 8 )<br \/>\n= 30 + 3<br \/>\n= 33<br \/>\nHence, 264 \u00f7 8 = 33<\/p>\n<p><strong>Use partial quotients to divide<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\sqrt [ 4 ]{ 96 } \\)<\/p>\n<p>Answer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-18176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-26.jpg\" alt=\"\" width=\"287\" height=\"204\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n96 \u00f7 4 = ( 80 + 16 ) \u00f7 4<br \/>\n= ( 80 \u00f7 4 ) + ( 16 \u00f7 4 )<br \/>\n= 20 + 4<br \/>\n= 24<br \/>\nHence, 96 \u00f7 4 = 24<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 9 ]{ 405 } \\)<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-18177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-27.jpg\" alt=\"\" width=\"645\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-27.jpg 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-27-300x59.jpg 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n405 \u00f7 9 = ( 360 + 45 ) \u00f7 9<br \/>\n= ( 360 \u00f7 9 ) + ( 45 \u00f7 9 )<br \/>\n= 40 + 5<br \/>\n= 45<br \/>\nHence, 405 \u00f7 9 = 45<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 6 ]{ 378 } \\)<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-18183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-28.jpg\" alt=\"\" width=\"681\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-28.jpg 681w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-28-300x55.jpg 300w\" sizes=\"(max-width: 681px) 100vw, 681px\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n378 \u00f7 6 = ( 360 + 18 ) \u00f7 6<br \/>\n= ( 360 \u00f7 6 ) + ( 18 \u00f7 6 )<br \/>\n= 60 + 3<br \/>\n= 63<br \/>\nHence, 378 \u00f7 6 = 63<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 7 ]{ 84 } \\)<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-18235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-29.jpg\" alt=\"\" width=\"656\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-29.jpg 656w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-29-300x59.jpg 300w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n84 \u00f7 7 = ( 70 + 14 ) \u00f7 7<br \/>\n= ( 70 \u00f7 7 ) + ( 14 \u00f7 7 )<br \/>\n= 10 +2<br \/>\n= 12<br \/>\nHence, 84 \u00f7 7 = 12<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 5 ]{ 735 } \\)<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-18307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-30.jpg\" alt=\"\" width=\"288\" height=\"202\" \/><\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n735 \u00f7 5 = ( 700 + 35 ) \u00f7 5<br \/>\n= ( 700 \u00f7 5 ) + ( 35 \u00f7 5 )<br \/>\n= 140 + 7<br \/>\n= 147<br \/>\nHence, 735 \u00f7 5 = 147<\/p>\n<p>Question 9.<br \/>\n<strong>Structure<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-6.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 6\" width=\"208\" height=\"166\" \/><br \/>\nAnswer: The missing numbers are: 60, 20, and 3.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-31.jpg\" alt=\"\" width=\"228\" height=\"142\" \/><br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n332 \u00f7 4 = ( 240 + 80 + 12 ) \u00f7 4<br \/>\n= ( 240 \u00f7 4 ) + ( 80 \u00f7 4 ) + ( 12 \u00f7 4 )<br \/>\n= 60 + 20 + 3<br \/>\n= 83<br \/>\nHence, 332 \u00f7 4 = 63<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThere are 8 students on each tug-of-war team. How many tug-of-war teams are there?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-7.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 7\" width=\"320\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-7.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-7-300x225.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nUse an area model and partial quotients to find 128 \u00f7 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-32.jpg\" alt=\"\" width=\"639\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-32.jpg 639w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-32-300x153.jpg 300w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Use the table above.<br \/>\n<\/strong>Question 10.<br \/>\nThere are 5 students on each relay race team. How many relay race teams are there?<br \/>\nAnswer: 18 relay race teams<\/p>\n<p>Explanation:<br \/>\nThe given number of students in relay race = 90<br \/>\nGiven that there are 5 students on each relay race team.<br \/>\nSO, to find the number of relay race teams, we have to find the value of 90 \u00f7 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-33.jpg\" alt=\"\" width=\"641\" height=\"316\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-33.jpg 641w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-33-300x148.jpg 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 18 relay race teams.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThere are 6 students on beach volleyball team. There are 4 fewer students on each water balloon toss team than each volleyball team. How many of each team are there?<\/p>\n<p>Answer: There are 78 teams of water balloon toss team.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe total number of students in the volleyball team = 96<br \/>\nThe total number of students in the water balloon toss team = 156<br \/>\nIt is also given that,<br \/>\nThere are 6 students on each volleyball team and there are 4 fewer students on each water balloon toss team.<br \/>\nSo,<br \/>\nThe number of students on\u00a0 water balloon toss team = 6 &#8211; 4 = 2 students.<br \/>\nHence, to find the number of students on each water balloon toss team, we have to find the value of 156 \u00f7 2 by using the Distributive Property of Partial quotients.<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n156 \u00f7 2 = ( 140 + 16 ) \u00f7 2<br \/>\n= ( 140 \u00f7 2 ) + ( 16 \u00f7 2 )<br \/>\n= 70 + 8<br \/>\n= 78<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 78 students on each water balloon toss team.<\/p>\n<p>Question 12.<br \/>\nTwenty-seven students were absent on the day of sign-ups. They all decide to play kickball. There are 9 students on each kickball team. How many kickball teams are there?<\/p>\n<p>Answer:\u00a0 There are 3 kickball teams<\/p>\n<p>Explanation:<br \/>\nGiven that there are 27 students who were absent on the day of sign-ups and they all decide to play kickball. It is also given that there are 9 students on each kickball team.<br \/>\nSo, to find the number of kickball teams, we have to find the value of 27 \u00f7 9<br \/>\nNow, by using the Distributive Property of partial quotients,<br \/>\n27 \u00f7 9 = ( 18 + 9 ) \u00f7 9<br \/>\n= ( 18 \u00f7 9 ) + ( 9 \u00f7 9 )<br \/>\n= 2 + 1<br \/>\n= 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 3 kickball teams.<\/p>\n<h3><a id=\"Use_Partial_Quotients_Practice_5.4\"><\/a>Use Partial Quotients Homework &amp; Practice 5.4<\/h3>\n<p>Question 1.<br \/>\nUse an area model and partial quotients to find 345 \u00f7 5.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-9.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 9\" width=\"644\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-9.png 644w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-9-300x68.png 300w\" sizes=\"(max-width: 644px) 100vw, 644px\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-18407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-34.jpg\" alt=\"\" width=\"635\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-34.jpg 635w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-34-300x60.jpg 300w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n345 \u00f7 5 = ( 300 + 45 ) \u00f7 5<br \/>\n= ( 300 \u00f7 5 ) + ( 45 \u00f7 5 )<br \/>\n= 60 + 9<br \/>\n= 69<br \/>\nHence, 345 \u00f7 5 = 63<\/p>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 2.<br \/>\n\\(\\sqrt [ 6 ]{ 90 } \\)<br \/>\nAnswer: 15<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n90 \u00f7 6 = ( 60 + 30 ) \u00f7 6<br \/>\n= ( 60 \u00f7 6 ) + ( 30 \u00f7 6 )<br \/>\n= 10 + 5<br \/>\n= 15<br \/>\nHence, 90 \u00f7 6 = 15<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt [ 3 ]{ 48 } \\)<br \/>\nAnswer: 16<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n48 \u00f7 3 = ( 18 + 30 ) \u00f7 3<br \/>\n= ( 30 \u00f7 3 ) + ( 18 \u00f7 3 )<br \/>\n= 10 + 6<br \/>\n= 16<br \/>\nHence, 48 \u00f7 3 = 16<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt [ 8 ]{ 200 } \\)<br \/>\nAnswer: 25<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n200 \u00f7 8 = ( 160 + 40 ) \u00f7 8<br \/>\n= ( 160 \u00f7 8 ) + ( 40 \u00f7 8 )<br \/>\n= 20 + 5<br \/>\n= 25<br \/>\nHence, 200 \u00f7 8 = 25<\/p>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\sqrt [ 4 ]{ 56 } \\)<br \/>\nAnswer: 14<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n56 \u00f7 4 = ( 40 + 16 ) \u00f7 4<br \/>\n= ( 40 \u00f7 4 ) + ( 16 \u00f7 4 )<br \/>\n= 10 + 4<br \/>\n= 14<br \/>\nHence, 56 \u00f7 4 = 14<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 7 ]{ 511 } \\)<br \/>\nAnswer: 73<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n511 \u00f7 7 = ( 490 + 21 ) \u00f7 7<br \/>\n= ( 490 \u00f7 7 ) + ( 21 \u00f7 7 )<br \/>\n= 70 + 3<br \/>\n= 73<br \/>\nHence, 511 \u00f7 7 = 73<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 9 ]{ 423 } \\)<br \/>\nAnswer: 47<\/p>\n<p>Explanation;<br \/>\nUsing the Distributive Property of Partial quotients,<br \/>\n423 \u00f7 9 = ( 360 + 63 ) \u00f7 9<br \/>\n= ( 360 \u00f7 9 ) + ( 63 \u00f7 9 )<br \/>\n= 40 + 7<br \/>\n= 47<br \/>\nHence, 423 \u00f7 9 = 47<\/p>\n<p>Question 8.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nDescartes finds 952 \u00f7 8. Is he correct? Explain.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-10.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 10\" width=\"239\" height=\"163\" \/><\/p>\n<p>Answer: Descartes is correct.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-16.jpg\" alt=\"\" width=\"236\" height=\"161\" \/><br \/>\nBy using the Distributive Property for Partial Quotients,<br \/>\n952 \u00f7 8 = ( 800 + 80 + 72 ) \u00f7 8<br \/>\n= ( 800 \u00f7 8 ) + ( 80 \u00f7 8 ) + ( 72 \u00f7 8 )<br \/>\n= 100 + 10 + 9<br \/>\n= 119<br \/>\nHence, 952 \u00f7 8 = 119<\/p>\n<p>Question 9.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how you can solve a division problem in more than one-way using partial quotients.<br \/>\nAnswer: We can solve partial quotients in more than one-way by dividing the partial quotients in more than 2 multiples.<\/p>\n<p>Explanation:<br \/>\nTake an example of 952 \u00f7 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-17.jpg\" alt=\"\" width=\"236\" height=\"161\" \/><br \/>\nFrom the above, we can see that the partial quotients are divided in to 3 quotients which are the multiples of 8.<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nEach shelter animal gets 3 toys. How many shelter animals are there?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-11.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.4 11\" width=\"502\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-11.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.4-11-300x145.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Answer: There are 56 shelter animals.<\/p>\n<p>Explanation:<br \/>\nFrom the given table,<br \/>\nThe number of toys donated = 168<br \/>\nIt is also given that each shelter animal gets 3 toys.<br \/>\nSo,<br \/>\nThe number of shelter animals = The number of toys donated \u00f7 The number of toys that each shelter animal gets<br \/>\n= 168 \u00f7 3<br \/>\nBy using the Distributive property of quotients,<br \/>\n168 \u00f7 3 = ( 150 + 18 ) \u00f7 3<br \/>\n= ( 150 \u00f7 3 ) + ( 18 \u00f7 3 )<br \/>\n= 50 + 6<br \/>\n= 56<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 56 shelter animals.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 11.<br \/>\n40 \u00d7 70 = _____<br \/>\nAnswer: 2,800<\/p>\n<p>Explanation:<br \/>\nUsing the Place-value method,<br \/>\n40 \u00d7 70 = 40 \u00d7 7 tens<br \/>\n= 4 tens \u00d7 7 tens<br \/>\n= 28 \u00d7 1 ten \u00d7 1 ten<br \/>\n= 28 \u00d7 10 \u00d7 10<br \/>\n= 2,800<br \/>\nHence, 40 \u00d7 70 = 2,800<\/p>\n<p>Question 12.<br \/>\n30 \u00d7 58 = ______<br \/>\nAnswer: 1740<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of partial products,<br \/>\n30 \u00d7 58 = 30 \u00d7 ( 50 + 8 )<br \/>\n= ( 30 \u00d7 50 ) + ( 30 \u00d7 8 )<br \/>\n= 1,500 + 240<br \/>\n= 1,740<br \/>\nHence, 30 \u00d7 58 = 1,740<\/p>\n<p>Question 13.<br \/>\n62 \u00d7 90 = ______<br \/>\nAnswer: 5580<\/p>\n<p>Explanation:<br \/>\nUsing the place-value method,<br \/>\n62 \u00d7 90 = 62 \u00d7 9 tens<br \/>\n= 558 tens<br \/>\n= 558 \u00d7 10<br \/>\n= 5,580<br \/>\nHence,62 \u00d7 90 = 5,580<\/p>\n<h3><a id=\"Lesson_5.5_Use_Partial_Quotients_with_a_Remainder\"><\/a>Lesson 5.5 Use Partial Quotients with a Remainder<\/h3>\n<h3><\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use an area model to find 125 \u00f7 5.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 1\" width=\"469\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-1.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-1-300x99.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-18065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-18.jpg\" alt=\"\" width=\"276\" height=\"147\" \/><\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of partial quotients,<br \/>\n125 \u00f7 5 = ( 100 + 25 ) \u00f7 5<br \/>\n= ( 100 \u00f7 5 ) + ( 25 \u00f7 5 )<br \/>\n= 20 + 5<br \/>\n= 25<br \/>\nHence, 125 \u00f7 5 = 25<\/p>\n<p>Can you use an area model to find 128 \u00f7 5? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 2\" width=\"471\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-2.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-2-300x101.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p>Answer: We can&#8217;t use an area model to find 128 \u00f7 5 because 128 can&#8217;t be divided by 5 as 128 leaves a remainder.<\/p>\n<p>Explanation:<br \/>\nGiven division Expression is 128 \u00f7 5<br \/>\nFrom this Expression, we can say that 128 can&#8217;t be divided by 5<br \/>\nWhen 128 is divided by 5, it leaves a remainder of 3.<br \/>\nSo,<br \/>\n128 \u00f7 5<br \/>\nFrom this,<br \/>\nThe number of units in each group = 25<br \/>\nThe number of units that are leftover = 3<br \/>\nHence,<br \/>\n128 \u00f7 5 = 25 R 3<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nExplain to your partner how your model shows that 5 does not divide evenly into 128.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-18067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-20.jpg\" alt=\"\" width=\"53\" height=\"21\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-18066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-19.jpg\" alt=\"\" width=\"83\" height=\"17\" \/><br \/>\nLike the above arrangement, do the remaining 20 times.<br \/>\nHence, we arranged 125 models in to a group and there are 3 models that are not fit in the group.<br \/>\nIn this way, 128 will not be divided by 5 evenly.<\/p>\n<p><strong>Think and Grow: Practice<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nUse partial quotients to find 2,918 \u00f7 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-21.jpg\" alt=\"\" width=\"591\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-21.jpg 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-21-300x136.jpg 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\nSo, 2,918 \u00f7 4 = 2,916 R 2.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 1.<br \/>\n82 \u00f7 3 = _____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 5\" width=\"278\" height=\"145\" \/><br \/>\nAnswer: 27 R 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-22.jpg\" alt=\"\" width=\"282\" height=\"127\" \/><br \/>\nUsing Distributive property of partial quotients,<br \/>\n82 \u00f7 3 = ( 60 + 21 ) \u00f7 3<br \/>\n= ( 60 \u00f7 3 ) + ( 21 \u00f7 3)<br \/>\n= 20 + 7<br \/>\n= 27 R 1<br \/>\nHence, 82 \u00f7 3 = 27 R 1<\/p>\n<p>Question 2.<br \/>\n754 \u00f7 9 = _____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 6\" width=\"296\" height=\"138\" \/><br \/>\nAnswer: 83 R 7<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-23.jpg\" alt=\"\" width=\"300\" height=\"119\" \/><br \/>\nUsing Distributive property of partial quotients,<br \/>\n754 \u00f7 9 = ( 720 + 27 ) \u00f7 9<br \/>\n= ( 720 \u00f7 9 ) + ( 27 \u00f7 9 )<br \/>\n= 80 + 3<br \/>\n= 83 R 7<br \/>\nHence, 754 \u00f7 9 = 83 R 7<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt [ 8 ]{ 460 } \\)<br \/>\nAnswer:\u00a0 57 R 4<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n460 \u00f7 8 = ( 400 + 56 ) \u00f7 8<br \/>\n= ( 400 \u00f7 8 ) + ( 56 \u00f7 8 )<br \/>\n= 50 + 7<br \/>\n= 57 R 4<br \/>\nHence, 460 \u00f7 8 = 57 R 4<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt [ 5 ]{ 3,242 } \\)<br \/>\nAnswer: 648 R 2<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n3,242 \u00f7 5 = ( 3,000 + 200 + 40 ) \u00f7 5<br \/>\n= ( 3,000 \u00f7 5 ) + ( 200 \u00f7 5 ) + ( 40 \u00f7 5 )<br \/>\n= 600 + 40 + 8<br \/>\n= 648 R 2<br \/>\nHence, 3,242 \u00f7 5 = 648 R 2<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 6 ]{ 5,850 } \\)<br \/>\nAnswer: 975 R 0<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n5,850 \u00f7 6 = ( 5,400 + 420 + 30 ) \u00f7 6<br \/>\n= ( 5,400 \u00f7 6 ) + ( 420 \u00f7 6 ) + ( 30 \u00f7 6 )<br \/>\n= 900 + 70 + 5<br \/>\nHence, 5,850 \u00f7 6 = 975 R 0<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Use partial quotients to divide.<br \/>\n<\/strong>Question 6.<br \/>\n\\(\\sqrt [ 5 ]{ 63 } \\)<br \/>\nAnswer: 12 R 3<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n63 \u00f7 5 = ( 50 + 10 ) \u00f7 5<br \/>\n= ( 50 \u00f7 5 ) + ( 10 \u00f7 5 )<br \/>\n= 10 + 2<br \/>\n= 12 R 3<br \/>\nHence, 63 \u00f7 5 = 12 R 3<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 7 ]{ 401 } \\)<br \/>\nAnswer: 57 R 2<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n401 \u00f7 7 = ( 350 + 49 ) \u00f7 7<br \/>\n= ( 350 \u00f7 7 ) + ( 49 \u00f7 7 )<br \/>\n= 50 + 7<br \/>\n= 57 R 2<br \/>\nHence, 401 \u00f7 7 = 57 R 2<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 4 ]{ 5,237 } \\)<br \/>\nAnswer: 1,309 R 1<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n5,237 \u00f7 4 = ( 5,200 + 36 ) \u00f7 4<br \/>\n= ( 5,200 \u00f7 4 ) + ( 36 \u00f7 4 )<br \/>\n= 1,300 + 9<br \/>\n= 1,309 R 1<br \/>\nHence, 5,237 \u00f7 4 = 1,309 R 1<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 9 ]{ 256 } \\)<br \/>\nAnswer: 28 R 4<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n256 \u00f7 9 = ( 180 + 72 ) \u00f7 9<br \/>\n= ( 180 \u00f7 9 ) + ( 72 \u00f7 9 )<br \/>\n= 20 + 8<br \/>\n= 28 R 4<br \/>\nHence, 256 \u00f7 9 = 28 R 4<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 8 ]{ 945 } \\)<br \/>\nAnswer: 118 R 1<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n945 \u00f7 8 = ( 880 + 64 ) \u00f7 8<br \/>\n= ( 880 \u00f7 8 ) + ( 64 \u00f7 8 )<br \/>\n= 110 + 8<br \/>\n= 118 R 1<br \/>\nHence, 945 \u00f7 8 = 118 R 1<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 2 ]{ 7,043 } \\)<br \/>\nAnswer: 3521 R 1<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n7,043 \u00f7 2 = ( 7,000 + 42 ) \u00f7 2<br \/>\n= ( 7,000 \u00f7 2 ) + ( 42 \u00f7 2 )<br \/>\n= 3,500 + 21<br \/>\n= 3,521 R 1<br \/>\nHence, 7,043 \u00f7 2 = 3,521 R 1<\/p>\n<p>Question 12.<br \/>\nThe third, fourth, and fifth grades make 146 science projects for a fair. Did each grade make the same number of projects? Explain.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 7\" width=\"167\" height=\"124\" \/><\/p>\n<p>Answer:\u00a0 No, each grade did not make the same number of projects.<\/p>\n<p>Explanation:<br \/>\nIt is given that the third, fourth, and fifth grades make 146 science projects for a fair.<br \/>\nFrom this,<br \/>\nThe total number of grades = 3<br \/>\nNow, to find whether each grade makes the same number of projects or not, we can find out by knowing the value of 146 \u00f7 3.<br \/>\nNow,<br \/>\nUsing Distributive property of partial quotients,<br \/>\n146 \u00f7 3 = ( 120 + 24 ) \u00f7 3<br \/>\n= ( 120 \u00f7 3 ) + ( 24 \u00f7 3 )<br \/>\n= 40 + 8<br \/>\n= 48 R 2<br \/>\nHence, 146 \u00f7 3 = 48 R 2<\/p>\n<p>Question 13.<br \/>\n<strong>Structure<\/strong><br \/>\nNewton found 315 \u00f7 6. Explain how the steps would be different if he had used 50 as the first partial quotient?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 8\" width=\"252\" height=\"196\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-24.jpg\" alt=\"\" width=\"250\" height=\"182\" \/><br \/>\nBy changing the first partial quotient to 50, the number of partial quotients reduced to 2, and hence the calculation of the division becomes easy.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThere are 1,862 people attending a mud run. Each wave of runners can have8 people. How many waves of runners are needed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 9\" width=\"208\" height=\"150\" \/><br \/>\nUse partial quotients to find 1,862 \u00f7 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-25.jpg\" alt=\"\" width=\"321\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-25.jpg 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-25-300x153.jpg 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\n1,862 \u00f7 8 = 232 R 6<br \/>\nInterpret the quotient and the remainder.<br \/>\nThe quotient is 232. This means that 232 waves of runners will have 8 people.<br \/>\nThe remainder is 6. This means that 1 wave of runners will have 6 people.<br \/>\nSo, 1864\u00a0 waves of runners are needed.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nA juice factory has 768 fluid ounces of juice for guests to sample. A worker pours the juice into 5-fluid ounce cups. How many cups does the worker fill?<br \/>\nAnswer: The number of cups that the worker fill = 153 cups<\/p>\n<p>Explanation:<br \/>\nGiven that a juice factory has 78 fluid ounces of juice for guests to sample and a worker pours the juice into 5- fluid ounce cups.<br \/>\nTo find the number of cups that the worker\u00a0fill, we have to find the quotient of 768 \u00f7 5<br \/>\nNow,<br \/>\n768 \u00f7 5 = ( 700 + 60 + 5 ) \u00f7 5<br \/>\n= ( 700 \u00f7 5 ) + ( 60 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 140 + 12 + 1<br \/>\n= 153 R 3<br \/>\nHence,<br \/>\nThe number of cups that the worker fill = 153 cups<\/p>\n<p>Question 15.<br \/>\nA toy company designs 214 collectible figures. The company releases 6 of the figures each month. How many months will it take the company to release all of the collectible figures? How many years will it take?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 11\" width=\"136\" height=\"157\" \/><br \/>\nAnswer:<br \/>\nThe number of months that the company released all the toys = About 35 years<br \/>\nThe number of years that the company released all the toys = About 3 years<\/p>\n<p>Explanation:<br \/>\nGiven that a toy company designs 214 collectible figures and the company releases 6 of the figures each month.<br \/>\nNow,<br \/>\nThe number of months that the company released all toys = 214 \u00f7 6<br \/>\nNow,<br \/>\n214 \u00f7 6 = ( 180 + 30 ) \u00f7 6<br \/>\n= ( 180 \u00f7 6 ) + ( 30 \u00f7 6 )<br \/>\n= 30 + 5<br \/>\n= 35 R 4<br \/>\nWe know that,<br \/>\n1 year = 12 months<br \/>\nIt is given that 6 figures released each month.<br \/>\nSo, for 1 year, 72 toys will be released.<br \/>\nNow,<br \/>\nThe number of years that the company released all the toys = 214 \u00f7 72<br \/>\nNow,<br \/>\n214 \u00f7 72 = 2 R 70<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe number of months that the company released all the toys = About 35 years<br \/>\nThe number of years that the company released all the toys = About 3 years<\/p>\n<h3><a id=\"Use_Partial_Quotients_with_a_Remainder_Practice_5.5\"><\/a>Use Partial Quotients with a Remainder Homework &amp; Practice 5.5<\/h3>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sqrt [ 4 ]{ 67 } \\)<br \/>\nAnswer: 16 R 3<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n67 \u00f7 4 = ( 60 + 4 ) \u00f7 4<br \/>\n= ( 60 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 15 + 1<br \/>\n= 16 R 3<br \/>\nHence, 67 \u00f7 4 = 16 R 3<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt [ 2 ]{ 715 } \\)<br \/>\nAnswer: 357 R 1<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n715 \u00f7 2 = ( 700 + 14 ) \u00f7 2<br \/>\n= ( 700 \u00f7 2 ) + ( 14 \u00f7 2 )<br \/>\n= 350 + 7<br \/>\n= 357 R 1<br \/>\nHence, 715 \u00f7 2 = 357 R 1<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt [ 5 ]{ 1,308 } \\)<br \/>\nAnswer: 261 R 3<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n1,308 \u00f7 5 = ( 1,000 + 300 + 5 ) \u00f7 5<br \/>\n= ( 1,000 \u00f7 5 ) + ( 300 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 200 + 60 + 1<br \/>\n= 261 R 3<br \/>\nHence, 1,308 \u00f7 5 = 261 R 3<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt [ 3 ]{ 516 } \\)<br \/>\nAnswer: 172 R 0<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n516 \u00f7 3 = ( 510 + 6 ) \u00f7 3<br \/>\n= ( 510 \u00f7 3 ) + ( 6 \u00f7 3 )<br \/>\n= 170 + 2<br \/>\n= 172 R 0<br \/>\nHence, 516 \u00f7 3 = 172 R 0<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 9 ]{ 2,497 } \\)<br \/>\nAnswer: 277 R 4<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n2,497 \u00f7 9 = ( 1,800 + 630 + 36 + 27 )\u00a0 \u00f7 9<br \/>\n= ( 1,800 \u00f7 9 ) + ( 630 \u00f7 9 ) + ( 36 \u00f7 9 ) + ( 27 \u00f7 9 )<br \/>\n= 200 + 70 + 4 + 3<br \/>\n= 277 R 4<br \/>\nHence, 2,497 \u00f7 9 = 277 R 4<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 6 ]{ 831 } \\)<br \/>\nAnswer: 138 R 3<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n831 \u00f7 6 = ( 780 + 48 ) \u00f7 6<br \/>\n= (780 \u00f7 6 ) + ( 48 \u00f7 6 )<br \/>\n= 130 + 8<br \/>\n= 138 R 3<br \/>\nHence, 831 \u00f7 6 = 138 R 3<\/p>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\sqrt [ 9 ]{ 476 } \\)<br \/>\nAnswer: 52 R 8<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n476 \u00f7 9 = ( 450 + 18 ) \u00f7 9<br \/>\n= ( 450 \u00f7 9 ) + ( 18 \u00f7 9 )<br \/>\n= 50 + 2<br \/>\n= 52 R 8<br \/>\nHence, 476 \u00f7 9 = 52 R 8<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 7 ]{ 2,254 } \\)<br \/>\nAnswer: 322 R 0<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n2,254 \u00f7 7 = ( 2,100 + 140 + 14 ) \u00f7 7<br \/>\n= ( 2,100 \u00f7 7 ) + ( 140 \u00f7 7 ) + ( 14 \u00f7 7 )<br \/>\n= 300 + 20 + 2<br \/>\n= 322 R 0<br \/>\nHence, 2,254 \u00f7 7 = 322 R 0<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 4 ]{ 3,018 } \\)<br \/>\nAnswer: 754 R 2<\/p>\n<p>Explanation:<br \/>\nUsing Distributive property of partial quotients,<br \/>\n3,018 \u00f7 4 = ( 2,800 + 200 + 16 ) \u00f7 4<br \/>\n= ( 2,800 \u00f7 4 ) + ( 200 \u00f7 4 ) + ( 16 \u00f7 4 )<br \/>\n= 700 + 50 + 4<br \/>\n= 754 R 2<br \/>\nHence, 3,018 \u00f7 4 = 754 R 2<\/p>\n<p>Question 10.<br \/>\n<strong>Reasoning<\/strong><br \/>\nShow how to use the least number of partial quotients to find 3,526 \u00f7 4<\/p>\n<p>Answer:<br \/>\nBy using the Distributive property of partial quotients,<br \/>\n3,526 \u00f7 4 = ( 3,520 + 4) \u00f7 4<br \/>\n= ( 3,520 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 880 + 1<br \/>\n= 881 R 2<br \/>\nHence, 3,526 \u00f7 4 = 881 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the least number of partial quotients are &#8220;2&#8221; in 3,526 \u00f7 4<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA gardening center has 1,582 pots to fill. Each bag of soil can fill 4 pots. How many bags of soil are needed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.5 12\" width=\"139\" height=\"203\" \/><\/p>\n<p>Answer: The number of bags of soil needed = 395 R 2<\/p>\n<p>Explanation:<br \/>\nGiven that a gardening center has 1,582 pots to fill and each bag of soil can fill 4 pots.<br \/>\nSo, the number of bags of soil needed = Number of pots \u00f7 Number of pots that each bag of soil fill<br \/>\n= 1,582 \u00f7 4<br \/>\nBy using the Distributive property of quotients,<br \/>\n1,582 \u00f7 4 = ( 1,200 + 360 + 20 ) \u00f7 4<br \/>\n= ( 1,200 \u00f7 4 ) + ( 360 \u00f7 4 ) + ( 20 \u00f7 4 )<br \/>\n= 300 + 90 + 5<br \/>\n= 395 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of bags of soil needed are: 395 R 2<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 178 photos. You put 3 photos on each page of an album. Your friend has 354 photos. She puts 6 photos on each page of an album. Who uses more pages? Explain.<br \/>\nAnswer: The one who has 178 photos uses more pages.<\/p>\n<p>Explanation:<br \/>\nGiven that you 178 photos and you put 3 photos on each page of an album.<br \/>\nHence, The number of pages used by you = The number of photos \u00f7 The number of photos on each page of an album<br \/>\n= 178 \u00f7 3<br \/>\nBy using the Distributive property of quotients,<br \/>\n178 \u00f7 3 = ( 150 + 27 ) \u00f7 3<br \/>\n= ( 150 \u00f7 3 ) + ( 27 \u00f7 3 )<br \/>\n= 50 + 9<br \/>\n= 59 R 1 pages<br \/>\nIt is also given that your friend has 354 photos and she puts 6 photos on each page of an album.<br \/>\nHence, The number of pages used by your friend = The number of photos \u00f7 The number of photos on each page of an album<br \/>\n= 354 \u00f7 6<br \/>\nBy using the Distributie property of quotients,<br \/>\n354 \u00f7 6 = ( 300 + 48 + 6 ) \u00f7 6<br \/>\n= ( 300 \u00f7 6 ) + ( 48 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 50 + 8 + 1<br \/>\n= 59 pages<br \/>\nHence, from the above,<br \/>\nwe can conclude that you have more pages wh0 have 60 pages.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 13.<br \/>\nAn Olympic swimmer wants to eat 10,000 calories each day. He eats 3,142 calories at breakfast and 3,269 calories at lunch. How many more calories must the swimmer eat to reach his goal?<br \/>\nAnswer: The swimmer must eat 3,589 calories to reach his goal.<\/p>\n<p>Explanation:<br \/>\nGiven that an Olympic swimmer wants to eat 10,000 calories each day.<br \/>\nIt is also given that he eats 3,142 calories at breakfast and 3,269 calories at lunch.<br \/>\nSo,<br \/>\nThe total calories he eat = 3,142 + 3,269 = 6,411 calories<br \/>\nHence,<br \/>\nThe number of calories he wants to eat more to reach his goal = Total number of calories &#8211; The number of calories he eats<br \/>\n= 10,000 &#8211; 6,411<br \/>\n= 3,589 calories<br \/>\nHence, from the above,<br \/>\nWe can conclude that the swimmer must eat 3,589 calories to reach his goal.<\/p>\n<h3><a id=\"Lesson_5.6_Divide_Two_Digit_Numbers_by_One_Digit_Numbers\"><\/a>Lesson 5.6 Divide Two-Digit Numbers by One-Digit Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use a model to find each quotient. Draw each model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 1\" width=\"170\" height=\"124\" \/><br \/>\n84 \u00f7 4<\/p>\n<p>85 \u00f7 5<br \/>\nAnswer:<br \/>\n84 \u00f7 4 = 21<br \/>\n85 \u00f7 5 = 17<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be marked as A) and B)<br \/>\nSo,<br \/>\nA) 84 \u00f74\u00a0 B) 85 \u00f7 5<br \/>\nNow,<br \/>\nBy using the Distributive property of partial quotients,<br \/>\n84 \u00f7 4 = ( 80 + 4 ) \u00f7 4<br \/>\n= ( 80 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 20 + 1<br \/>\n= 21<br \/>\nHence, 84 \u00f7 4 = 21<br \/>\nBy using the Distributive property of partial quotients,<br \/>\n85 \u00f7 5 = ( 80 + 5 0 \u00f7 5<br \/>\n= ( 80 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 16 + 1<br \/>\n= 17<br \/>\nHence, 85 \u00f7 5 = 17<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nExplain to your partner how your methods for finding the quotients above are the same. Then explain how they are different.<br \/>\nAnswer: Let you and your partner are finding the value of 70 \u00f7 5.<br \/>\nYou want to use the Partial quotients method and your partner wants to use the area model method.<br \/>\nEven though the methods of your&#8217;s and your partner are different, the answer will be the same.<br \/>\nNow,<br \/>\nBy using the Distributive Property of partial quotients,<br \/>\n70 \u00f7 5 = ( 65 + 5) \u00f7 5<br \/>\n= ( 65 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 13 + 1<br \/>\n= 14<br \/>\nSo, 70 \u00f7 5 = 14<br \/>\nNow,<br \/>\nBy using the Area Model,<br \/>\n70 \u00f7 5<br \/>\nFrom this,<br \/>\nThe number of units that are grouped together = 14<br \/>\nThe number of units that are leftover = 0<br \/>\nSo, 70 \u00f7 5 = 14 R 0<\/p>\n<p><strong>Think and Grow: Use Regrouping to Divide<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-18602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-35.jpg\" alt=\"\" width=\"697\" height=\"595\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-35.jpg 697w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-35-300x256.jpg 300w\" sizes=\"(max-width: 697px) 100vw, 697px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 3\" width=\"79\" height=\"153\" \/><br \/>\nAnswer: 96 \u00f7 6 = 16<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-36.jpg\" alt=\"\" width=\"55\" height=\"153\" \/><br \/>\nBy using the partial quotients method,<br \/>\n96 \u00f7 6 = ( 90 + 6 ) \u00f7 6<br \/>\n= ( 90 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 15 + 1<br \/>\n= 16<br \/>\nHence, 96 \u00f7 6 = 16<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-4.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 4\" width=\"59\" height=\"58\" \/><br \/>\nAnswer: 88 \u00f7 2 = 44<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-37.jpg\" alt=\"\" width=\"51\" height=\"92\" \/><br \/>\nBy using the partial quotients method,<br \/>\n88 \u00f7 2 = ( 80 + 8 ) \u00f7 2<br \/>\n= ( 80 \u00f7 2 ) + ( 8 \u00f7 2 )<br \/>\n= 40 + 4<br \/>\n= 44<br \/>\nSo, 88 \u00f7 2 = 44<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 5\" width=\"111\" height=\"58\" \/><br \/>\nAnswer: 74 \u00f7 5 = 14 R 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-38.jpg\" alt=\"\" width=\"120\" height=\"121\" \/><br \/>\nBy using the partial quotients method,<br \/>\n74 \u00f7 5 = ( 65 + 5 ) \u00f7 5<br \/>\n= ( 65 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 13 + 1<br \/>\n= 14<br \/>\nSo, 74 \u00f7 5 = 14 R 4<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<br \/>\n<\/strong>Question 4.<br \/>\n\\(\\sqrt [ 5 ]{ 60 } \\)<br \/>\nAnswer: 60 \u00f7 5 = 12<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n60 \u00f7 5 = ( 55 + 5 ) \u00f7 5<br \/>\n= ( 55 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 11 + 1<br \/>\n= 12<br \/>\nHence, 60 \u00f7 5 = 12<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 6 ]{ 70 } \\)<br \/>\nAnswer: 70 \u00f7 6 = 11 R 4<\/p>\n<p>Explanation:<br \/>\n70 \u00f7 6 = ( 60 + 6 ) \u00f7 6<br \/>\n= ( 60 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 10 + 1<br \/>\n= 11<br \/>\nHence, 70 \u00f7 6 = 11 R 4<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 8 ]{ 90 } \\)<br \/>\nAnswer: 90 \u00f7 8 = 11 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n90 \u00f7 8 = ( 80 + 8 ) \u00f7 8<br \/>\n= ( 80 \u00f7 8 ) + ( 8 \u00f7 8 )<br \/>\n= 10 + 1<br \/>\n= 11<br \/>\nHence, 90 \u00f7 8 = 11 R 2<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 3 ]{ 93 } \\)<br \/>\nAnswer: 93 \u00f7 3 = 31 R 0<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n93 \u00f7 3 = ( 90 + 3 ) \u00f7 3<br \/>\n= ( 90 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 30 + 1<br \/>\n= 31<br \/>\nHence, 93 \u00f7 3 = 31 R 0<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 2 ]{ 45 } \\)<br \/>\nAnswer: 45 \u00f7 2 = 22 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partila quotients method,<br \/>\n45 \u00f7 2 = ( 40 + 4 ) \u00f7 2<br \/>\n= ( 40 \u00f7 2 ) + ( 4 \u00f7 2 )<br \/>\n= 20 + 2<br \/>\n= 22<br \/>\nHence, 45 \u00f7 2 = 22 R 1<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 3 ]{ 64 } \\)<br \/>\nAnswer: 64 \u00f7 3 = 21 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n64 \u00f7 3 = ( 60 + 3 ) \u00f7 3<br \/>\n= ( 60 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 20 + 1<br \/>\n= 21<br \/>\nHence, 64 \u00f7 3 = 21 R 1<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 6 ]{ 42} \\)<br \/>\nAnswer: 42 \u00f7 6 = 7<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n42 \u00f7 6 = ( 36 + 6 ) \u00f7 6<br \/>\n= ( 36 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 6 + 1<br \/>\n= 7<br \/>\nHence, 42 \u00f7 6 = 7<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 8 ]{ 36 } \\)<br \/>\nAnswer: 36 \u00f7 8 = 4 R 4<\/p>\n<p>Explanantion:<br \/>\nBy using the partial quotients method,<br \/>\n36 \u00f7 8 = ( 24 + 8 ) \u00f7 8<br \/>\n= ( 24 \u00f7 8 ) + ( 8 \u00f7 8 )<br \/>\n= 3 + 1<br \/>\n= 4 R 4<br \/>\nHence, 36 \u00f7 8 = 4 R 4<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt [ 7 ]{ 50 } \\)<br \/>\nAnswer: 50 \u00f7 7 = 7 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n50 \u00f7 7 = ( 42 + 7 ) \u00f7 7<br \/>\n= ( 42 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 6 + 1<br \/>\n= 7<br \/>\nHence, 50 \u00f7 7 = 7 R 1<\/p>\n<p>Question 13.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how you can use estimation to check the reasonableness of your answer when dividing a two-digit number by a one-digit number.<br \/>\nAnswer:\u00a0 We can check the estimation to check the reasonableness of the answer when dividing a two-digit number by a one-digit number by 2 methods. They are:<br \/>\nA) The partial quotients method\u00a0 B) Regrouping\u00a0 C) Area model method<\/p>\n<p>Question 14.<br \/>\n<strong>Structure<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 6\" width=\"131\" height=\"158\" \/><br \/>\nAnswer: The missing numbers are: 4, 2, 5, 2, and 2 ( The order of numbers is from top to bottom)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-39.jpg\" alt=\"\" width=\"111\" height=\"153\" \/><br \/>\nBy using the partial quotients method,<br \/>\n72 \u00f7 5 = ( 65 + 5 ) \u00f7 5<br \/>\n= ( 65 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 13 + 1<br \/>\n= 14<br \/>\nHence, 72 \u00f7 5 = 14 R 2<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA house cat has 64 muscles in its ears. It has the same number of muscles in each ear. How many muscles does the house cat have in each ear?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-7.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 7\" width=\"183\" height=\"144\" \/><br \/>\nThe house cat has 2 ears, so find 64 \u00f7 2.<br \/>\nThink: 64 is 6 tens and 4 ones.<br \/>\nDivide the tens.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-18607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-40.jpg\" alt=\"\" width=\"803\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-40.jpg 803w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-40-300x154.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-40-768x394.jpg 768w\" sizes=\"(max-width: 803px) 100vw, 803px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nYou earn 5 cents for each plastic bottle you recycle. You recycle some bottles and earn 75 cents. How many bottles did you recycle?<br \/>\nAnswer:\u00a0 75 \u00f7 5 = 15 bottles<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe cost of each plastic bottle you recycle = 5 cents<br \/>\nThe total money earned by recycling plastic bottles = 75 cents<br \/>\nSo,<br \/>\nThe number of plastic bottles = The total money earned by recycling plastic bottles \u00f7 The cost of each plastic bottle you recycle<br \/>\n=75 \u00f7 5<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n75 \u00f7 5 = ( 70 + 5 ) \u00f7 5<br \/>\n= ( 70 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 14 + 1<br \/>\n= 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 15 plastic bottles that are recycled.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA cross-country runner must run 80 miles in 1 week. He wants to run about the same number of miles each day. How many miles should he run each day? How can you interpret the remainder?<br \/>\nAnswer: 80 \u00f7 7 = 11 R 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-41.jpg\" alt=\"\" width=\"55\" height=\"153\" \/><br \/>\nBy using the partial quotients method,<br \/>\n80 \u00f7 7 = ( 70 + 7 ) \u00f7 7<br \/>\n= ( 70 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 10 + 1<br \/>\n= 11<br \/>\nHence, 80 \u00f7 7 = 11 R 3<\/p>\n<p>Question 17.<br \/>\nAdmission to a go-kart park costs a total of $78 for 3 adults and 3 children. The price is the same for all ages. What is the cost of admission for each person?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 9\" width=\"203\" height=\"137\" \/><br \/>\nAnswer: 78 \u00f7 6 = $13<\/p>\n<p>Explanation:<br \/>\nGiven that admission to a go-kart, park costs a total of $78 for 3 adults and 3 children and it is also given that the price is the same for all ages.<br \/>\nHence, the price for children and adults are the same.<br \/>\nHence, total number of people = 3 adults + 3 children = 6 people<br \/>\nTo find the cost of admission for each person, we have to find the value of 78 \u00f7 6<br \/>\nNow,<br \/>\nBy using the partial products method,<br \/>\n78 \u00f7 6 = ( 60 + 18 ) \u00f7 6<br \/>\n= ( 60 \u00f7 6 ) + ( 18 \u00f7 6 )<br \/>\n= 10 + 3<br \/>\n= 13<br \/>\nHence, from the above,<br \/>\nWe can conclude that the cost of admission for each person is: $13.<\/p>\n<h3><a id=\"Divide_Two_Digit_Numbers_by_One_Digit_Numbers_Practice_5.6\"><\/a>Divide Two-Digit Numbers by One-Digit Numbers Homework &amp; Practice 5.6<\/h3>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-10.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 10\" width=\"84\" height=\"152\" \/><br \/>\nAnswer: 85 \u00f7 5 = 17<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-42.jpg\" alt=\"\" width=\"58\" height=\"144\" \/><br \/>\nBy using the partial quotients method,<br \/>\n85 \u00f7 5 = ( 80 + 5 ) \u00f7 5<br \/>\n= ( 80 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 16 + 1<br \/>\n= 17<br \/>\nHence, 85 \u00f7 5 = 17<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-11.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 11\" width=\"60\" height=\"72\" \/><br \/>\nAnswer: 63 \u00f7 3 = 21<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-43.jpg\" alt=\"\" width=\"49\" height=\"96\" \/><br \/>\nBy using the partial quotients method,<br \/>\n63 \u00f7 3 = ( 60 + 3 ) \u00f7 3<br \/>\n= ( 60 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n=20 + 1<br \/>\n= 21<br \/>\nHence, 63 \u00f7 3 = 21<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-12.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 12\" width=\"130\" height=\"58\" \/><br \/>\nAnswer: 94 \u00f7 7 =13 R 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-44.jpg\" alt=\"\" width=\"113\" height=\"100\" \/><br \/>\nBy using the partial quotients method,<br \/>\n94 \u00f77 = ( 84 + 7 ) \u00f7 7<br \/>\n= ( 84 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 12 + 1<br \/>\n= 13 R 3<br \/>\nHence, 94 \u00f7 7 = 13 R 3<\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\sqrt [ 6 ]{ 74 } \\)<br \/>\nAnswer: 74 \u00f7 6 = 12 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n74 \u00f7 6 = ( 60 + 12 ) \u00f7 6<br \/>\n= ( 60 \u00f7 6 ) + ( 12 \u00f7 6 )<br \/>\n= 10 + 2<br \/>\n= 12 R 2<br \/>\nHence, 74 \u00f7 6 = 12 R 2<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 8 ]{ 92 } \\)<br \/>\nAnswer: 92 \u00f7 8 = 11 R 4<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n92 \u00f7 8 = ( 80 + 8 ) \u00f7 8<br \/>\n= ( 80 \u00f7 8 ) + ( 8 \u00f7 8 )<br \/>\n= 10 + 1<br \/>\n= 11 R 4<br \/>\nHence, 92 \u00f7 8 = 11 R 4<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 3 ]{ 50 } \\)<br \/>\nAnswer: 50 \u00f7 3 = 16 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n50 \u00f7 3 = ( 42 + 6 ) \u00f7 3<br \/>\n= ( 42 \u00f7 3 ) + ( 6 \u00f7 3 )<br \/>\n= 14 + 2<br \/>\n= 16 R 2<br \/>\nHence, 50 \u00f7 3 = 16 R 2<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 2 ]{ 83 } \\)<br \/>\nAnswer: 83 \u00f7 2 = 41 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n83 \u00f7 2 = ( 80 + 2 ) \u00f7 2<br \/>\n= ( 80 \u00f7 2 ) + ( 2 \u00f7 2 )<br \/>\n= 40 + 1<br \/>\n= 41 R 1<br \/>\nHence, 83 \u00f7 2 = 41 R 1<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 9 ]{ 72 } \\)<br \/>\nAnswer: 72 \u00f7 9 = 8 R 0<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n72 \u00f7 9 = ( 63 + 9 ) \u00f7 9<br \/>\n= ( 63 \u00f7 9 ) + ( 9 \u00f7 9 )<br \/>\n= 7 + 1<br \/>\n= 8 R 0<br \/>\nHence, 72 \u00f7 9 = 8 R 0<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 7 ]{ 65 } \\)<br \/>\nAnswer: 65 \u00f7 7 = 9 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the artial products method,<br \/>\n65 \u00f7 7 = ( 56 + 7 ) \u00f7 7<br \/>\n= ( 56 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 8 + 1<br \/>\n= 9 R 2<br \/>\nHence, 65 \u00f7 7 = 9 R 2<\/p>\n<p>Question 10.<br \/>\n<strong>Which One Doesn\u2019t Belong?<\/strong><br \/>\nWhich problem does not require regrouping not to solve?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-13.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 13\" width=\"279\" height=\"55\" \/><br \/>\nAnswer: Let the given Expressions be named as A), B), C), and D)<br \/>\nHence,<br \/>\nA) 36 \u00f7 2<br \/>\nB) 55 \u00f7 2<br \/>\nC) 47 \u00f7 2<br \/>\nD) 92 \u00f7 2<br \/>\nFrom the above Expressions, we can conclude that Expression A) does not require Regrouping to solve.<\/p>\n<p>Explanation:<br \/>\nLet the given Expressions be named as A), B), C), and D)<br \/>\nHence,<br \/>\nA) 36 \u00f7 2<br \/>\nB) 55 \u00f7 2<br \/>\nC) 47 \u00f7 2<br \/>\nD) 92 \u00f7 2<br \/>\nA) 36 \u00f7 2 = ( 3 tens + 6 ones ) \u00f7 2<br \/>\n= ( 3 tens \u00f7 2 ) + ( 6 ones \u00f7 2 )<br \/>\n= 15 + 3<br \/>\n= 18<br \/>\nHere, as there are no tens left to regroup, there is no need for Regrouping again.<br \/>\nB) 55 \u00f7 2 = ( 5 tens + 5 ones ) \u00f7 2<br \/>\n= ( 5 tens \u00f7 2 ) + ( 5 ones \u00f7 2 )<br \/>\nIt can&#8217;t be solved further and there is need for us for further Regrouping.<br \/>\nHence, the remaining two will also be the same.<br \/>\nHence, from the above,<br \/>\nWe can conclude that Expression A) does not require Regrouping.<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA team of 6 students finishes an obstacle course in 66 minutes. Each student spends the same number of minutes on the course. How many minutes is each student on the course?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-14.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 14\" width=\"151\" height=\"153\" \/><\/p>\n<p>Answer: Each student takes 11 minutes to finish an obstacle course.<\/p>\n<p>Explanation:<br \/>\nGiven that a team of 6 students finishes an obstacle course in 66 minutes and it is also given that each student spends the same number of minutes on the course.<br \/>\nSo,<br \/>\nThe number of minutes each student takes on the course = The number of total minutes taken to complete an obstacle course \u00f7 The number of members on each team<br \/>\n= 66 \u00f7 6<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n66 \u00f7 6 = ( 60 + 6 ) \u00f7 6<br \/>\n= ( 60 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 10 + 1<br \/>\n= 11 minutes<br \/>\nHence, from the above,<br \/>\nWe can conclude that each student takes 11 minutes to finish an obstacle race.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou want to make 40 origami animals in 3 days. You want to make about the same number of animals each day. How many animals should you make each day? How can you interpret the remainder?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.6-15.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.6 15\" width=\"207\" height=\"125\" \/><\/p>\n<p>Answer: You should make 13 animals each day.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-18613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-45.jpg\" alt=\"\" width=\"58\" height=\"144\" \/><br \/>\nGiven that you want to make 40 origami animals in 3 days and you want to make about the same number of animals each day.<br \/>\nSo,<br \/>\nThe number of animals you want to make on each day = Total number of animals \u00f7 3<br \/>\n= 40 \u00f7 3<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n40 \u00f7 3 = ( 30 + 9 ) \u00f7 3<br \/>\n= ( 30 \u00f7 3 ) + ( 9 \u00f7 3 )<br \/>\n= 10 + 3<br \/>\n= 13 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that you have to make 13 animals each day with one remaining at last.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Estimate the product.<\/strong><br \/>\nQuestion 13.<br \/>\n32 \u00d7 67<br \/>\nAnswer:\u00a0 32 \u00d7 67 = 2,144<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n32 \u00d7 6 = ( 30 + 2 ) \u00d7 ( 60 + 7 )<br \/>\n= ( 30 \u00d7 60 ) + ( 2 \u00d7 60 ) + ( 30 \u00d7 7 ) + ( 2 \u00d7 7 )<br \/>\n= 1,800 + 120 + 210 + 14<br \/>\n= 2,144<br \/>\nHence, 32 \u00d7 67 = 2,144<\/p>\n<p>Question 14.<br \/>\n24 \u00d7 51<br \/>\nAnswer: 24 \u00d7 51 = 1,224<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n24 \u00d7 51 = ( 20 + 4 ) \u00d7 ( 50 + 1 )<br \/>\n= ( 20 \u00d7 50 ) + ( 20 \u00d7 1 ) + ( 4 \u00d7 50 ) + ( 4 \u00d7 1 )<br \/>\n= 1,000 + 20 + 200 + 4<br \/>\n= 1,244<br \/>\nHence, 24 \u00d7 51 = 1,244<\/p>\n<p>Question 15.<br \/>\n96 \u00d7 75<br \/>\nAnswer: 96 \u00d7 75 = 7,200<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n96 \u00d7 75 = ( 90 + 6 ) \u00d7 ( 70 + 5 )<br \/>\n= ( 90 \u00d7 70 ) + ( 90 \u00d7 5 ) + ( 6 \u00d7 70 ) + ( 6 \u00d7 5 )<br \/>\n= 6,300 + 450 + 420 + 30<br \/>\n= 7,200<br \/>\nHence, 96 \u00d7 75 = 7,200<\/p>\n<h3><a id=\"Lesson_5.7_Divide_Multi_Digit_Numbers_by_One_Digit_Numbers\"><\/a>Lesson 5.7 Divide Multi-Digit Numbers by One-Digit Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use a model to divide. Draw each model.<br \/>\n348 \u00f7 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 1\" width=\"280\" height=\"143\" \/><br \/>\n148 \u00f7 3<br \/>\nAnswer:<br \/>\n348 \u00f7 3 = 116<br \/>\n148 \u00f7 3 = 49 R 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-46.jpg\" alt=\"\" width=\"113\" height=\"142\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-19005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-47.jpg\" alt=\"\" width=\"113\" height=\"142\" \/><br \/>\nBy using the partial quotients method,<br \/>\n348 \u00f7 3 = ( 330+ 18 ) \u00f7 3<br \/>\n= ( 330 \u00f7 3 ) + ( 18 \u00f7 3 )<br \/>\n= 110 + 6<br \/>\n= 116<br \/>\nHence, 348 \u00f7 3 = 116<br \/>\n148 \u00f7 3 = ( 120 + 27 ) \u00f7 3<br \/>\n= ( 120 \u00f7 3 ) + ( 27 \u00f7 3 )<br \/>\n= 40 + 9<br \/>\n= 49 R 1<br \/>\nHence, 148 \u00f7 3 = 49 R 1<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nExplain why the quotient of 148 \u00f7 3 does not have a digit in the hundreds place.<br \/>\nAnswer:<br \/>\nWhen 148 is divided by 3, the hundreds place in 148 won&#8217;t be divided by 3. This is the reason why the\u00a0quotient of 148 \u00f7 3 does not have the hundreds place.<\/p>\n<p><strong>Think and Grow: Practice<\/strong><\/p>\n<p><strong>Example<br \/>\n<\/strong>Find 907 \u00f7 5.<br \/>\nEstimate: 1,000 \u00f7 5 = 200 R 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 2\" width=\"610\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-2.png 610w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-2-300x257.png 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><br \/>\nSo, 907 \u00f7 5 = 181 R 2.<br \/>\nCheck: Because 181 R 2 is close to the estimate, the answer is reasonable.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<br \/>\n<\/strong>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 3\" width=\"138\" height=\"61\" \/><br \/>\nAnswer: 531 \u00f7 4 = 132 R 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-48.jpg\" alt=\"\" width=\"122\" height=\"190\" \/><br \/>\nBy using the partial quotients method,<br \/>\n531 \u00f7 4 = ( 480 +48 ) \u00f7 4<br \/>\n= ( 480 \u00f7 4 ) + ( 48 \u00f7 4 )<br \/>\n= 120 + 12<br \/>\n= 132 R 3<br \/>\nHence, 531 \u00f7 4 = 132 R 3<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-4.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 4\" width=\"73\" height=\"61\" \/><br \/>\nAnswer: 7,180 \u00f7 5 = 1,436<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-49.jpg\" alt=\"\" width=\"81\" height=\"272\" \/><br \/>\nBy using the partial quotients method,<br \/>\n7,180 \u00f7 5 = ( 7,000 + 150 + 30 ) \u00f7 5<br \/>\n= ( 7,000 \u00f7 5 ) + ( 150 \u00f7 5 ) + ( 30 \u00f7 5 )<br \/>\n= 1,400 + 10 + 30 + 6<br \/>\n= 1,436<br \/>\nHence, 7,180 \u00f7 5 = 1,436<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-5.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 5\" width=\"139\" height=\"63\" \/><br \/>\nAnswer: 8,385 \u00f7 7 = 1,197 R 6<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-50.jpg\" alt=\"\" width=\"127\" height=\"272\" \/><br \/>\nBy using the partial quotients method,<br \/>\n8,385 \u00f7 7 = ( 7,700 + 630 + 49 ) \u00f7 7<br \/>\n= ( 7,700 \u00f7 7 ) + ( 630 \u00f7 7 ) + ( 49 \u00f7 7 )<br \/>\n= 1,100 + 90 + 7<br \/>\n=1,197 R 6<br \/>\nHence, 8,385 \u00f7 7 = 1,197 R 6<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\sqrt [ 5 ]{ 6,381 } \\)<br \/>\nAnswer: 6,381 \u00f7 5 = 1,276 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n6,381 \u00f7 5 = ( 6,000 + 350 + 30 ) \u00f7 5<br \/>\n= ( 6,000 \u00f7 5 ) + ( 350 \u00f7 5 ) + ( 30 \u00f7 5 )<br \/>\n=1,200 + 70 + 6<br \/>\n=1,276 R 1<br \/>\nHence, 6,381 \u00f7 5 = 1,276 R 1<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 3 ]{ 4,605 } \\)<br \/>\nAnswer: 4,605 \u00f7 3 = 1,535 R 0<\/p>\n<p>Explanation:<br \/>\n4,605 \u00f7 3 = ( 4,500 + 105 ) \u00f7 3<br \/>\n= ( 4,500 \u00f7 3 ) + ( 105 \u00f7 3 )<br \/>\n= 1,500 + 35<br \/>\n= 1,535 R 0<br \/>\nHence, 4,605 \u00f7 3 = 1,535 R 0<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 6 ]{ 820 } \\)<br \/>\nAnswer: 820 \u00f7 6 = 136 R 4<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n820 \u00f7 6 = ( 720 + 90 + 6 ) \u00f7 6<br \/>\n= ( 720 \u00f7 6 ) + ( 90 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 120 + 15 + 1<br \/>\n= 136 R 4<br \/>\nHence, 820 \u00f7 6 = 136 R 4<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 6 ]{ 7,039 } \\)<br \/>\nAnswer: 7,039 \u00f7 6 = 1,173 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n7,039 \u00f7 6 = ( 6,600 + 420 + 18 ) \u00f7 6<br \/>\n= ( 6,600 \u00f7 6 ) + ( 420 \u00f7 6 ) + ( 18 \u00f7 6 )<br \/>\n= 1,100 + 70 + 3<br \/>\n= 1,173 R 1<br \/>\nHence,<br \/>\n7,039 \u00f7 6 = 1,173 R 1<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 4 ]{ 855 } \\)<br \/>\nAnswer: 855 \u00f7 4 = 213 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n855 \u00f7 4 = ( 800 + 52 ) \u00f7 4<br \/>\n= ( 800 \u00f7 4 ) + ( 52 \u00f7 4 )<br \/>\n= 200 + 13<br \/>\n= 213 R 3<br \/>\nHence, 855 \u00f7 4 = 213 R 3<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 2 ]{ 367 } \\)<br \/>\nAnswer: 367 \u00f7 2 = 183 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n367 \u00f7 2 = ( 360 + 6 ) \u00f7 2<br \/>\n= ( 360 \u00f7 2 ) + ( 6 \u00f7 2 )<br \/>\n= 180 + 3<br \/>\n= 183 R 1<br \/>\nHence, 367 \u00f7 2 = 183 R 1<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 8 ]{ 9,692 } \\)<br \/>\nAnswer: 9,692 \u00f7 8 = 1,211 R 4<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n9,692 \u00f7 8 = ( 9,600 + 88 ) \u00f7 8<br \/>\n= ( 9,600 \u00f7 8 ) + ( 88 \u00f7 8 )<br \/>\n= 1,200 + 11<br \/>\n= 1,211 R 4<br \/>\nHence, 9,692 \u00f7 8 = 1,211 R 4<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 7 ]{ 8,345 } \\)<br \/>\nAnswer: 8,345 \u00f7 7 = 1,192 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n8,345 \u00f7 7 = ( 7,700 +630 +14 ) \u00f7 7<br \/>\n= ( 7,700 \u00f7 7 ) + ( 630 \u00f7 7 ) + ( 14 \u00f7 7 )<br \/>\n= 1,100 + 90 + 2<br \/>\n=1,192 R 1<br \/>\nHence, 8,345 \u00f7 7 = 1,192 R 1<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt [ 7 ]{ 971 } \\)<br \/>\nAnswer: 971 \u00f7 7 = 138 R 5<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n971 \u00f7 7 = ( 910 + 56 ) \u00f7 7<br \/>\n= ( 910 \u00f7 7 ) + ( 56 \u00f7 7 )<br \/>\n= 130 + 8<br \/>\n= 138 R 5<br \/>\nHence, 971 \u00f7 7 = 138 R 5<\/p>\n<p>Question 13.<br \/>\nThere are 8,274 people at an air show. The people are divided into equally 6 sections. How many people are in each section?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-6.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 6\" width=\"243\" height=\"157\" \/><\/p>\n<p>Answer: There are 1,379 people in each section.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 8,274 people at an air show and the people are divided equally into 6 sections.<br \/>\nSo,<br \/>\nThe number of people in each section = Total number of people \u00f7 Number of sections<br \/>\n= 8,274 \u00f7 6<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n8,274 \u00f7 6 = ( 7,800 + 420 + 54 ) \u00f7 6<br \/>\n= ( 7,800 \u00f7 6 ) + ( 420 \u00f7 6 ) + ( 54 \u00f7 6 )<br \/>\n= 1,300 + 70 + 9<br \/>\n= 1,379<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 1,379 people in each section.<\/p>\n<p>Question 14.<br \/>\n<strong>YOU BE THE TEACHER<br \/>\n<\/strong>Newton finds 120 \u00f7 5. Is he correct? Explain.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-7.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 7\" width=\"84\" height=\"181\" \/><\/p>\n<p>Answer: Newton is not correct.<\/p>\n<p>Explanation:<br \/>\nAccording to Newton,<br \/>\nFor 120 \u00f7 5,<br \/>\nQuotient = 114 and Remainder = 0<br \/>\nBut,<br \/>\nBy using the partial quotients method,<br \/>\n120 \u00f7 5 = ( 100 + 20 ) \u00f7 5<br \/>\n= ( 100 \u00f7 5 ) + ( 20 \u00f7 5 )<br \/>\n= 20 + 4 )<br \/>\n= 24<br \/>\nHence,<br \/>\nAccording to the partial quotients method,<br \/>\nFor 120 \u00f7 5,<br \/>\nQuotient = 24 and Remainder = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton is not correct.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThere are 1,014 toy car tires at a factory. Each car needs 4 tires. How many toy cars can the factory workers make with the tires?<br \/>\nEach car needs 4 tires, so find 1,014 \u00f7 4.<br \/>\n1 thousand cannot be shared among 4 groups without regrouping. So, regroup 1 thousand as 10 hundreds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-51.jpg\" alt=\"\" width=\"350\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-51.jpg 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-51-271x300.jpg 271w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\nInterpret the quotient and the remainder.<br \/>\nThe quotient is 253. The factory workers can make 253 toy cars.<br \/>\nThe remainder is 2. There are 2 tires left over.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nA principal orders 750 tablets. The distributor can fit 8 tablets in each box. How many boxes are needed to ship all of the tablets?<br \/>\nAnswer:<br \/>\nThe number of boxes needed to ship all of the tablets= 93 boxes with 6 leftovers = 93 R 6<\/p>\n<p>Explanation:<br \/>\nGiven that a principal orders 750 tablets and the distributor can fit 8 tablets in each box.<br \/>\nSo,<br \/>\nThe number of boxes needed to ship all of the tablets = The number of tablets ordered \u00f7 The number of tablets that fits into each box<br \/>\n= 750 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n750 \u00f7 8 = ( 720 + 24 ) \u00f7 8<br \/>\n= ( 720 \u00f7 8 ) + ( 24 \u00f7 8 )<br \/>\n= 90 + 3<br \/>\n= 93 R 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe number of boxes needed to ship all the tablets = 93 boxes with 6 leftovers<\/p>\n<p>Question 16.<br \/>\nAn athlete\u2019s heart rate after a 5-mile run is 171 beats per minute, which is 3 times as fast as her resting heart rate. What is the athlete\u2019s resting heart rate?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-9.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 9\" width=\"200\" height=\"86\" \/><br \/>\nAnswer: The athlete&#8217;s resting heart rate is 57 beats per minute.<\/p>\n<p>Explanation:<br \/>\nGiven that an athlete&#8217;s heart rate after a 5-mile run is 171 beats per minute. It is also given that 171 beats per minute which are 3 times as fast as her resting heart rate.<br \/>\nSo,<br \/>\nThe athlete&#8217;s heart rating rate = Athlete&#8217;s heart rate after a 5-mile run \u00f7 3<br \/>\n= 171 \u00f7 3<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n171 \u00f7 3 = ( 150 + 21 ) \u00f7 3<br \/>\n= ( 150 \u00f7 3 ) + ( 21 \u00f7 3 )<br \/>\n= 50 + 7<br \/>\n= 57 beats per minute.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the athlete&#8217;s resting heart rate is 57 beats per minute.<\/p>\n<p>Question 17.<br \/>\nA car costs $5,749. The taxes and fees for the car cost an additional $496. A customer uses a 5-year\u00a0 interest-free loan to buy the car. How much money will the customer pay for the car each year?<br \/>\nAnswer:\u00a0 The customer will pay $1,249 for the car each year<\/p>\n<p>Explanation:<br \/>\nGiven that a car costs $5,749 and the taxes and fees for the car cost an additional $496.<br \/>\nSo,<br \/>\nThe total cost of the car = 5,749 + 496 = $6,245<br \/>\nIt is also given that the customer uses a 5-year interest &#8211; free loan to buy the car.<br \/>\nSo,<br \/>\nThe money that the customer will pay each year = The total cost of the car \u00f7 5<br \/>\n= 6,245 \u00f7 5<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n6,245 \u00f7 5 = ( 6,000 +\u00a0 200 + 45 ) \u00f7 5<br \/>\n= ( 6,000 \u00f7 5 )\u00a0+ ( 200 \u00f7 5 ) + ( 45 \u00f7 5 )<br \/>\n= 1,200 +\u00a0 40 + 9<br \/>\n= $1,249<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe money that the customer pay each year = $1,249<\/p>\n<h3><a id=\"Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Practice_5.7\"><\/a>Divide Multi-Digit Numbers by One-Digit Numbers Homework &amp; Practice 5.7<\/h3>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-10.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 10\" width=\"126\" height=\"63\" \/><br \/>\nAnswer: 473 \u00f7 9 = 52 R 5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-52.jpg\" alt=\"\" width=\"115\" height=\"183\" \/><br \/>\nBy using the partial quotients method,<br \/>\n473 \u00f7 9 = ( 450 \u00f7 9) + ( 18 \u00f7 9)<br \/>\n= 50 + 2<br \/>\n= 52 R 5<br \/>\nHence, 473 \u00f7 9 = 52 R 5<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-11.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 11\" width=\"81\" height=\"74\" \/><br \/>\nAnswer: 3,904 \u00f7 2 = 1,952<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-53.jpg\" alt=\"\" width=\"78\" height=\"202\" \/><br \/>\nBy using the partial quotients method,<br \/>\n3,904 \u00f7 2 = ( 3,000 + 900 + 4 ) \u00f7 2<br \/>\n= ( 3,000 \u00f7 2 ) + ( 900 \u00f7 2 ) + ( 4 \u00f7 2 )<br \/>\n= 1,500 + 450 +2<br \/>\n= 1,902<br \/>\nHence, 3,904 \u00f7 2 = 1,902<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-12.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 12\" width=\"152\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-12.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-12-150x70.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer: 2,531 \u00f76 = 421 R 5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-54.jpg\" alt=\"\" width=\"140\" height=\"232\" \/><br \/>\nBy using the partial quotients method,<br \/>\n2,531 \u00f7 6 = ( 2,400 + 120 + 6 ) \u00f7 6<br \/>\n= ( 2,400 \u00f7 6 ) + ( 120 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 400 + 20 + 1<br \/>\n= 421 R 5<br \/>\nHence, 2,531 \u00f7 6 = 421 R 5<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt [ 5 ]{ 8,271 } \\)<br \/>\nAnswer: 8,271 \u00f7 5 = 1,654 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n8,271 \u00f7 5 = ( 8,000 + 250 + 20 ) \u00f7 5<br \/>\n= ( 8,000 \u00f7 5 ) + ( 250 \u00f7 5 ) + (20 \u00f7 5 )<br \/>\n= 1,600 + 50 + 4<br \/>\n= 1,654 R 1<br \/>\nHence, 8,271 \u00f7 5 = 1,654 R 1<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 7 ]{ 952 } \\)<br \/>\nAnswer: 952 \u00f7 7 = 136<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n952 \u00f7 7 = ( 910 + 42 ) \u00f7 7<br \/>\n= (910 \u00f7 7 ) + ( 42 \u00f7 7 )<br \/>\n= 130 + 6<br \/>\n= 136<br \/>\nHence, 952 \u00f7 7 = 136<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 8 ]{ 9,107 } \\)<br \/>\nAnswer: 9,107 \u00f7 8 = 1,138 R 3<\/p>\n<p>Explanation:<br \/>\n9,107 \u00f7 8 = ( 8,800 + 240 + 56 +8 ) \u00f7 8<br \/>\n= ( 8,800 \u00f7 8 ) + ( 240 \u00f7 8 ) + ( 56 \u00f7 8 ) + ( 8 \u00f7 8 )<br \/>\n= 1,100 + 30 + 7 + 1<br \/>\n= 1,138 R 3<br \/>\nHence, 9,107 \u00f7 8 = 1,138 R 3<\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\sqrt [ 3 ]{ 509 } \\)<br \/>\nAnswer: 509 \u00f7 3 = 169 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n509 \u00f7 3 = ( 480 + 27 ) \u00f7 3<br \/>\n= ( 480 \u00f7 3 ) + ( 27 \u00f7 3 )<br \/>\n= 160 + 9<br \/>\n= 169 R 2<br \/>\nHence, 509 \u00f7 3 = 169 R 2<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 4 ]{ 7,150 } \\)<br \/>\nAnswer: 7,150 \u00f7 4 = 1,787 R 2<\/p>\n<p>Explanation:<br \/>\n7,150 \u00f7 4 = ( 6,800 + 320 + 28 ) \u00f7 4<br \/>\n= ( 6,800 \u00f7 4 ) + ( 320 \u00f7 4 ) + ( 28 \u00f7 4 )<br \/>\n= 1,700 + 80 + 7<br \/>\n= 1,787 R 2<br \/>\nHence, 7,150 \u00f7 4 = 1,787 R 2<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 2 ]{ 5,547 } \\)<br \/>\nAnswer: 5,547 \u00f7 2 = 2,773 R 1<\/p>\n<p>Explanation:<br \/>\n5,547 \u00f7 2 = ( 5,000 + 500 +46 ) \u00f7 2<br \/>\n= ( 5,000 \u00f7 2 ) + ( 500 \u00f7 2 ) + ( 46 \u00f7 2 )<br \/>\n= 2,500 + 250 + 23<br \/>\n= 2,273 R 1<br \/>\nHence, 5,547 \u00f7 2 = 2,273 R 1<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 3 ]{ 756 } \\)<br \/>\nAnswer: 756 \u00f7 3 = 252 R 0<\/p>\n<p>Explanation:<br \/>\n756 \u00f7 3 = ( 720 +36 ) \u00f7 3<br \/>\n= ( 720 \u00f7 3 ) + ( 36 \u00f7 3 )<br \/>\n= 240 + 12<br \/>\n= 252<br \/>\nHence, 756 \u00f7 3 = 252 R 0<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 4 ]{ 6,871 } \\)<br \/>\nAnswer: 6,871 \u00f7 4 = 1,717 R 3<\/p>\n<p>Explanation:<br \/>\n6,871 \u00f7 4 = ( 6,000 + 800 + 64 + 4 ) \u00f7 4<br \/>\n= ( 6,000 \u00f7 4 ) + ( 800 \u00f7 4 ) + ( 64 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 1,500 + 200 + 16 +1<br \/>\n= 1,717 R 3<br \/>\nHence, 6,871 \u00f7 4 = 1,717 R 3<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt [ 5 ]{ 108 } \\)<br \/>\nAnswer: 108 \u00f7 5 = 21 R 3<\/p>\n<p>Explanation:<br \/>\n108 \u00f7 5 = ( 100 +5 ) \u00f7 5<br \/>\n= ( 100 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 20 + 1<br \/>\n= 21 R 3<br \/>\nHence, 108 \u00f7 5 = 21 R 3<\/p>\n<p>Question 13.<br \/>\nA deli sells 203 pretzel roll sandwiches. Each bag has 7 pretzel rolls. How many bags of pretzel rolls are used?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-13.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 13\" width=\"157\" height=\"174\" \/><\/p>\n<p>Answer: The number of pretzel rolls is used = 29 rolls<\/p>\n<p>Explanation:<br \/>\nGiven that a deli sells 203 pretzel roll sandwiches and each bag has 7 pretzel rolls.<br \/>\nSo,<br \/>\nThe number of pretzel rolls used = Total number of pretzel roll sandwiches \u00f7 7<br \/>\n= 203 \u00f7 7<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n203 \u00f7 7 = ( 140 + 63 ) \u00f7 7<br \/>\n= ( 140 \u00f7 7 ) + ( 63 \u00f7 7 )<br \/>\n= 20 + 9<br \/>\n= 29 bags<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 29 bags of pretzel rolls of sandwiches<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhich expression does have a 4-digit quotient? Explain not how you know without solving.<br \/>\n6,197 \u00f7 2<br \/>\n3, 261 \u00f7 5<br \/>\n5,240 \u00f7 4<br \/>\n9,045 \u00f7 8<br \/>\nAnswer:<br \/>\nLet the Expressions be named as A), B), C), and D)<br \/>\nSo,<br \/>\nA) 6,197 \u00f7 2<br \/>\nB) 3, 261 \u00f7 5<br \/>\nC) 5,240 \u00f7 4<br \/>\nD) 9,045 \u00f7 8<br \/>\nFrom the above,<br \/>\nExpression C) does have a 4- digit quotient without leaving a remainder.<\/p>\n<p>Explanation;<br \/>\nLet the Expressions be named as A), B), C), and D)<br \/>\nSo,<br \/>\nA) 6,197 \u00f7 2<br \/>\nB) 3, 261 \u00f7 5<br \/>\nC) 5,240 \u00f7 4<br \/>\nD) 9,045 \u00f7 8<br \/>\nA) 6,197 \u00f7 2<br \/>\nBy using the partial quotients method,<br \/>\n6,197 \u00f7 2 = ( 6,000 + 196 ) \u00f7 2<br \/>\n= ( 6,000 + 196 ) \u00f7 2<br \/>\n= 3,000 + 98<br \/>\n=3,098 R 1<br \/>\nHence, 6,197 \u00f7 2 = 3,098 R 1<br \/>\nB) 3,261 \u00f7 5 = ( 3,000 + 250 + 10 ) \u00f7 5<br \/>\n= ( 3,000 \u00f7 5 ) + ( 250 \u00f7 5 ) + ( 10 \u00f7 5 )<br \/>\n= 600 + 50 + 2<br \/>\n= 652 R 1<br \/>\nHence, 3,261 \u00f7 5 = 652 R 1<br \/>\nC) 5,240 \u00f7 4 = ( 5,200 + 40 ) \u00f7 4<br \/>\n= ( 5,200 \u00f7 4 ) + ( 40 \u00f7 4 )<br \/>\n= 1,300 + 10<br \/>\n= 1,310 R 0<br \/>\nHence, 5,240 \u00f7 4 = 1,310<br \/>\nD) 9,045 \u00f7 8 = ( 9,000 + 40 ) \u00f7 8<br \/>\n= ( 9,000 \u00f7 8 ) + ( 40 \u00f7 8 )<br \/>\n= 1,125 + 5<br \/>\n= 1,130 R 5<br \/>\nHence, from all the 4 Expressions,<br \/>\nWe can conclude that the Expression C)\u00a0 has 4-digit quotient having remainder 0<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThere are 505 pieces of chalk donated for a community event. The chalk is bundled into groups of 7 pieces. How many bundles can be made?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.7-14.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.7 14\" width=\"231\" height=\"153\" \/><\/p>\n<p>Answer: The number of bundles that can be made = 72 R 1<\/p>\n<p>Explanation:<br \/>\nGiven that there are 505 pieces of chalk donated for a community event and the chalk is bundled into groups of 7 pieces.<br \/>\nSo,<br \/>\nThe number of bundles that can be made = 505 \u00f7 7<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n505 \u00f7 7 = ( 490 + 14 ) \u00f7 7<br \/>\n= ( 490 \u00f7 7 ) + ( 14 \u00f7 7 )<br \/>\n= 70 + 2<br \/>\n= 72 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe number of bundles that can be made = 72 bundles with 1 leftover<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product. Check whether your answer is reasonable.<\/strong><br \/>\nQuestion 16.<br \/>\nEstimate: _____<br \/>\n61 \u00d7 3 = _____<br \/>\nAnswer: 61 \u00d7 3 =183<\/p>\n<p>Explanation:<br \/>\nBy using theDistributive Property,<br \/>\n61 \u00d7 3 = ( 60 + 1 ) \u00d7 3<br \/>\n= ( 60 \u00d7 3 ) + ( 1 \u00d7 3 )<br \/>\n= 180 + 3<br \/>\n= 183<br \/>\nSo, 61 \u00d7 3 = 183<br \/>\nEstimate:<br \/>\nLet 61 be rounded to 60.<br \/>\nSo, by using the place-value method,<br \/>\n60 \u00d7 3 = 6 tens \u00d7 3<br \/>\n= 18 tens<br \/>\n= 18 \u00d7 10<br \/>\n= 180<br \/>\nSo, 60 \u00d7 3 = 180<br \/>\nHence, from the above,<br \/>\nWe can conclude that the actual answer is near to the Estimate. So, the answer is reasonable.<\/p>\n<p>Question 17.<br \/>\nEstimate: ______<br \/>\n54 \u00d7 9 = ______<br \/>\nAnswer: 54 \u00d7 9 = 486<\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property,<br \/>\n54 \u00d7 9 = ( 50 + 4 ) \u00d7 9<br \/>\n= ( 50 \u00d7 9 ) + ( 4 \u00d7 9 )<br \/>\n= 450 + 36<br \/>\n= 486<br \/>\nSo, 54 \u00d7 9 = 486<br \/>\nEstimate:<br \/>\nLet 54 be rounded to 55.<br \/>\nLet 9 be rounded to 10<br \/>\nSo, by using the place-value method,<br \/>\n10 \u00d7 55 = 1 ten \u00d7 55<br \/>\n= 55 tens<br \/>\n= 55 \u00d7 10<br \/>\n= 550<br \/>\nSo, 55 \u00d7 10 = 550<br \/>\nHence, from the above,<br \/>\nWe can conclude that the actual answer is not near to the Estimate. So, the answer is not reasonable.<\/p>\n<p>Question 18.<br \/>\nEstimate: _______<br \/>\n82 \u00d7 7 = ______<br \/>\nAnswer: 82 \u00d7 7 = 574<\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property,<br \/>\n82 \u00d7 7 = ( 80 + 2 ) \u00d7 7<br \/>\n= ( 80 \u00d7 7 ) + ( 2 \u00d7 7 )<br \/>\n= 560 + 14<br \/>\n= 574<br \/>\nSo, 82 \u00d7 7 = 574<br \/>\nEstimate:<br \/>\nLet 82 be rounded to 80.<br \/>\nLet 7 be rounded to 5.<br \/>\nSo, by using the place-value method,<br \/>\n80 \u00d7 5 = 8 tens \u00d7 5<br \/>\n= 40 tens<br \/>\n= 40 \u00d7 10<br \/>\n= 400<br \/>\nSo, 80 \u00d7 5 = 400<br \/>\nHence, from the above,<br \/>\nWe can conclude that the actual answer is not near to the Estimate. So, the answer is not reasonable.<\/p>\n<h3><a id=\"Lesson_5.8_Divide_by_One_Digit_Numbers\"><\/a>Lesson 5.8 Divide by One-Digit Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use a model to find each quotient. Draw each model.<br \/>\n312 \u00f7 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 1\" width=\"235\" height=\"130\" \/><br \/>\n312 \u00f7 4<br \/>\nAnswer:<br \/>\n312 \u00f7 3 = 104<br \/>\n312 \u00f7 4 = 78<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-55.jpg\" alt=\"\" width=\"78\" height=\"202\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-19477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-56.jpg\" alt=\"\" width=\"115\" height=\"183\" \/><br \/>\nBy using the partial quotients method,<br \/>\n312 \u00f7 3 = ( 300 + 12 )\u00f7 3<br \/>\n= ( 300 \u00f7 3 ) + ( 12 \u00f7 3 )<br \/>\n= 100 + 4<br \/>\n= 104<br \/>\nHence, 312 \u00f7 3 = 104<br \/>\nBy using the partial quotients method,<br \/>\n312 \u00f7 4 = ( 280 + 20 + 12 ) \u00f7 4<br \/>\n= ( 280 \u00f7 4 ) + ( 20 \u00f7 4 ) + ( 12 \u00f7 4 )<br \/>\n= 70 + 5 + 3<br \/>\n= 78<br \/>\nHence, 312 \u00f7 4 = 78<\/p>\n<p><strong>Structure<\/strong><br \/>\nCompare your models for each quotient. What is the same? What is different? What do you think this means when using regrouping to divide?<br \/>\nAnswer: The Divisor for both the models is the same and the quotient is different for both Expressions.<\/p>\n<p><strong>Think and Grow: Divide by One-Digit Numbers<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nFind 4,829 \u00f7 8.<br \/>\n4 thousand cannot be shared among 8 groups without regrouping. So, regroup 4 thousands as 40 hundred and combine with 8 hundred.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-57.jpg\" alt=\"\" width=\"658\" height=\"546\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-57.jpg 658w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-57-300x249.jpg 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-3.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 3\" width=\"71\" height=\"67\" \/><br \/>\nAnswer: 756 \u00f7 7 = 108<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-58.jpg\" alt=\"\" width=\"60\" height=\"209\" \/><br \/>\nBy using the partial quotients method,<br \/>\n756 \u00f7 7 = ( 700 + 56 ) \u00f7 7<br \/>\n= ( 700 \u00f7 7 ) + ( 56 v 7 )<br \/>\n= 100 + 8<br \/>\n= 108<br \/>\nHence, 756 \u00f7 7 = 108<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-4.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 4\" width=\"120\" height=\"65\" \/><br \/>\nAnswer: 364 \u00f7 6 = 6 R 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-59.jpg\" alt=\"\" width=\"123\" height=\"119\" \/><br \/>\nBy using the partial quotients method,<br \/>\n364 \u00f7 6 = ( 300 + 60 ) \u00f7 6<br \/>\n= ( 300 \u00f7 6 ) + ( 60 \u00f7 6 )<br \/>\n= 50 + 10<br \/>\n= 60 R 4<br \/>\nHence, 364 \u00f7 6 = 60 R 4<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-5.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 5\" width=\"149\" height=\"67\" \/><br \/>\nAnswer: 3,190 \u00f7 3 = 1,063 R 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-60.jpg\" alt=\"\" width=\"140\" height=\"265\" \/><br \/>\nBy using the partial quotients method,<br \/>\n3,190 \u00f7 3 = ( 3,000 + 180 + 9 ) \u00f7 3<br \/>\n= ( 3,000 \u00f7 3 ) + ( 180 \u00f7 3 ) + ( 9 \u00f7 3 )<br \/>\n= 1,000 + 60 + 3<br \/>\n= 1,063 R 1<br \/>\nHence, 3,190 \u00f7 3 = 1,063 R 1<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\sqrt [ 2 ]{ 81 } \\)<br \/>\nAnswer: 81 \u00f7 2 = 40 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n81 \u00f7 2 = ( 60 + 20 ) \u00f7 2<br \/>\n= ( 60 \u00f7 2 ) + ( 20 \u00f7 2 )<br \/>\n= 30 + 10<br \/>\n= 40 R 1<br \/>\nHence, 81 \u00f7 2 = 40 R 1<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 4 ]{ 428 } \\)<br \/>\nAnswer: 428 \u00f7 4 = 107<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n428 \u00f7 4 = ( 400 + 28 ) \u00f7 4<br \/>\n= ( 400 \u00f7 4 ) + ( 28 \u00f7 4 )<br \/>\n= 100 + 7<br \/>\n= 107<br \/>\nHence, 428 \u00f7 4 = 107<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 6 ]{ 842 } \\)<br \/>\nAnswer: 842 \u00f7 6 = 140 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n842 \u00f7 6 = ( 780 + 60 ) \u00f7 6<br \/>\n= ( 780 \u00f7 6 ) + ( 60 \u00f7 6 )<br \/>\n= 130 + 10<br \/>\n= 140 R 2<br \/>\nHence, 842 \u00f7 6 = 140 R 2<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 3 ]{ 2,724 } \\)<br \/>\nAnswer: 2,724 \u00f7 3 = 908<\/p>\n<p>Explanation:<br \/>\nBy using partial quotients method,<br \/>\n2,724 \u00f7 3 = ( 2,700 + 24 ) \u00f7 3<br \/>\n= ( 2,700 \u00f7 3 ) + ( 24 \u00f7 3 )<br \/>\n= 900 + 8<br \/>\n= 908<br \/>\nHence, 2,724 \u00f7 3 = 908<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 9 ]{ 635 } \\)<br \/>\nAnswer: 635 \u00f7 9 = 70 R 5<\/p>\n<p>Explanation:<br \/>\nBy using partial products method,<br \/>\n635 \u00f7 9 = ( 540 + 90 ) \u00f7 9<br \/>\n= ( 540 \u00f7 9 ) + ( 90 \u00f7 9 )<br \/>\n= 60 + 10<br \/>\n= 70 R 5<br \/>\nHence, 635 \u00f7 9 = 70 R 5<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 6 ]{ 1,442 } \\)<br \/>\nAnswer: 1,442 \u00f7 6 = 240 R 2<\/p>\n<p>Explanation:<br \/>\nBy using partial quotients method,<br \/>\n1,442 \u00f7 6 = ( 1,200 +240 ) \u00f7 6<br \/>\n= ( 1,200 \u00f7 6 ) + ( 240 \u00f7 6 )<br \/>\n= 200 +40<br \/>\n= 240 R 2<br \/>\nHence, 1,442 \u00f7 6 = 240 R 2<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt [ 6 ]{ 303 } \\)<br \/>\nAnswer: 303 \u00f7 6 = 50 R 3<\/p>\n<p>Explanation:<br \/>\nBy using partial quotients method,<br \/>\n303 \u00f7 6 = ( 240 + 60 ) \u00f7 6<br \/>\n= ( 240 \u00f7 6 ) + ( 60 \u00f7 6 )<br \/>\n= 40 + 10<br \/>\n= 50 R 3<br \/>\nHence, 303 \u00f7 6 = 50 R 3<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 5 ]{ 2,530 } \\)<br \/>\nAnswer: 2,530 \u00f7 5 = 506<\/p>\n<p>Explanation:<br \/>\nBy using partial quotients method,<br \/>\n2,530 \u00f7 5 = ( 2,500 + 30 ) \u00f7 5<br \/>\n= ( 2,500 \u00f7 5 ) + ( 30 \u00f7 5 )<br \/>\n= 500 + 6<br \/>\n= 506<br \/>\nHence, 2,530 \u00f7 5 = 506<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt [ 8 ]{ 7,209 } \\)<br \/>\nAnswer: 7,209 \u00f7 8 = 900 R 9<\/p>\n<p>Explanation:<br \/>\nBy using partial quotients method,<br \/>\n7,209 \u00f7 8 = ( 6,400 + 800 ) \u00f7 8<br \/>\n= ( 6,400 \u00f7 8 ) + ( 800 \u00f7 8 )<br \/>\n= 800 + 100<br \/>\n= 900 R 9<br \/>\nHence, 7,209 \u00f7 8 = 900 R\u00a0 9<\/p>\n<p>Question 13.<br \/>\nThe 5 developers of a phone app earn a profit of $4,535 this month. They divide the profit equally. How much money does each developer get?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-6.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 6\" width=\"203\" height=\"158\" \/><br \/>\nAnswer: Each developer gets the money of $907<\/p>\n<p>Explanation:<br \/>\nGiven that the 5 developers of a phone app earn a profit of $4,535 this month and it is also given that they divide the profit equally.<br \/>\nSo,<br \/>\nThe money each developer get = The total profit earned by 5 developers \u00f7 5<br \/>\n= $4,535 \u00f7 5<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n4,535 \u00f7 5 = ( 4,500 + 35 ) \u00f7 5<br \/>\n= ( 4,500 \u00f7 5 ) + ( 35 \u00f7 5 )<br \/>\n= 900 + 7<br \/>\n= 907<br \/>\nHence, from the above,<br \/>\nWe can conclude that the money got by each developer is $907.<\/p>\n<p>Question 14.<br \/>\nNewton finds 817 \u00f7 4. Is he correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-7.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 7\" width=\"118\" height=\"134\" \/><br \/>\nAnswer: Newton is not correct.<\/p>\n<p>Explanation;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-61.jpg\" alt=\"\" width=\"92\" height=\"125\" \/><br \/>\nBy using the partial quotients method,<br \/>\n817 \u00f7 4 = ( 800 + 16 ) \u00f7 4<br \/>\n= ( 800 \u00f7 4 ) + ( 16 \u00f7 4 )<br \/>\n= 200 + 4<br \/>\n= 204 R 1<br \/>\nAccording to Newton,<br \/>\n817 \u00f7 4 = 24 R 1<br \/>\nBut according to the partial quotients method,<br \/>\n817 \u00f7 4 = 204 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton is not correct.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nSeven players are placed on each basketball team. Remaining basketball players are added to the teams, so some of the teams have 8 players. How many basketball teams have 7 players? 8 players?<br \/>\nThere are 1,839 players signed up for basketball, so find 1,839 \u00f7 7.<br \/>\n1 thousand be shared cannot among 7 groups without regrouping. So, regroup 1 thousand as 10 hundreds and combine with 8 hundreds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-62.jpg\" alt=\"\" width=\"414\" height=\"399\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-62.jpg 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-62-300x289.jpg 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><br \/>\nInterpret the quotient and the remainder.<br \/>\nThe quotient is262. So, there are 262 basketball teams in all.<br \/>\nThe remainder is 5. So, 5 basketball teams have 8 players.<br \/>\nSubtract to \ufb01nd how many teams have 7 players. 262 \u22125 = 257<br \/>\nSo, 257 basketball teams have 7 players and 5 have 8 players.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Use the table above.<\/strong><br \/>\nQuestion 15.<br \/>\nNine players are placed on each ball hockey team. Remaining players are added to the teams, so some of the teams have 10 players. How many ball hockey teams have9 players? 10 players?<br \/>\nAnswer:<br \/>\nGiven that there are 9 players on each ball hockey team.<br \/>\nSo, the quotient represents the ball hockey teams who have 9 players and the remainder represents the ball hockey teams who have 10 players.<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n952 \u00f7 9 = ( 900 + 45 ) \u00f7 9<br \/>\n= ( 900 \u00f7 9 ) + ( 45 \u00f7 9 )<br \/>\n= 100 + 5<br \/>\n= 105 R 7<br \/>\nThe quotient is 105. So, there are 105 ball hockey teams in all.<br \/>\nThe remainder is 7. So, 7 ball hockey teams have 10 players.<br \/>\nSubtract to \ufb01nd the number of teams has 9 players. 105 \u22127 = 98<br \/>\nSo, 98 basketball teams have 9 players and 7 have 10 players.<\/p>\n<p>Question 16.<br \/>\nEighty-four players who signed up to play soccer decide not to play. Eight players are placed on each soccer team. How many soccer teams are there?<br \/>\nAnswer: There are 299 soccer teams<\/p>\n<p>Explanation:<br \/>\nGiven that 84 players who signed up to play soccer decide not to play and it is also given that 8 players are placed on each soccer team.<br \/>\nIt is also given that,<br \/>\nThe total number of players who play soccer = 2,476 players<br \/>\nSo,<br \/>\nThe number of players who played soccer = 2,476 &#8211; 84 = 2,392 players<br \/>\nNow,<br \/>\nThe number of soccer teams = 2,392 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n2,392 \u00f7 8 = ( 1,600 + 720 + 72 ) \u00f7 8<br \/>\n= ( 1,600\u00a0 \u00f7 8 ) + ( 720 \u00f7 8 ) + ( 72 \u00f7 8 )<br \/>\n= 200 + 90 + 9<br \/>\n= 299<br \/>\nHence, from the above,<br \/>\nwe can conclude that there are 299 soccer teams.<\/p>\n<h3><a id=\"Divide_by_One_Digit_Numbers_Practice_5.8\"><\/a>Divide by One-Digit Numbers Homework &amp; Practice 5.8<\/h3>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-9.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 9\" width=\"72\" height=\"63\" \/><br \/>\nAnswer: 832 \u00f7 8 = 104<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-63.jpg\" alt=\"\" width=\"71\" height=\"177\" \/><br \/>\nBy using the partial quotients method,<br \/>\n832 \u00f7 8 = ( 800 + 32 ) \u00f7 8<br \/>\n= ( 800 \u00f7 8 ) + ( 32 \u00f7 8 )<br \/>\n= 100 + 4<br \/>\n= 104<br \/>\nHence, 832 \u00f7 8 = 104<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-10.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 10\" width=\"132\" height=\"61\" \/><br \/>\nAnswer: 215 \u00f7 7 = 30 R 5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-64.jpg\" alt=\"\" width=\"109\" height=\"119\" \/><br \/>\nBy using the partial quotients method,<br \/>\n215 \u00f7 7 = ( 140 + 70 ) \u00f77<br \/>\n( 140 \u00f7 7 ) + ( 70 \u00f7 7 )<br \/>\n= 20 + 10<br \/>\n= 30 R 5<br \/>\nHence, 215 \u00f77 = 30 R 5<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-11.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 11\" width=\"139\" height=\"59\" \/><br \/>\nAnswer: 5,078 \u00f7 5 = 1,015 R 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-65.jpg\" alt=\"\" width=\"139\" height=\"285\" \/><br \/>\nBy using the partial quotients method,<br \/>\n5,078 \u00f7 5 = ( 5,000 + 75 ) \u00f7 5<br \/>\n= ( 5,000 \u00f75 ) + ( 75 \u00f7 5 )<br \/>\n= 1,000 + 15<br \/>\n= 1,015 R 3<br \/>\nHence, 5,078 \u00f7 5 = 1,015 R 3<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt [ 7 ]{ 94 } \\)<br \/>\nAnswer: 94 \u00f7 7 = 13 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n94 \u00f7 7 = ( 84 + 7 ) \u00f7 7<br \/>\n= ( 84 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 12 + 1<br \/>\n= 13 R 1<br \/>\nHence, 94 \u00f7 7 = 13 R 1<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt [ 6 ]{ 731 } \\)<br \/>\nAnswer: 731 \u00f7 6 = 121 R 5<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n731 \u00f7 6 = ( 720 + 6 ) \u00f7 6<br \/>\n= ( 720 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 120 + 1<br \/>\n= 121 R 5<br \/>\nHence, 731 \u00f7 6 = 121 R 5<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt [ 4 ]{ 6,514 } \\)<br \/>\nAnswer: 6,514 \u00f7 4 = 1,628 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n6,514 \u00f7 4 = ( 6,000 + 480 + 32 ) \u00f7 4<br \/>\n= ( 6,000 \u00f7 4 ) + ( 480 \u00f7 4 ) + ( 32 \u00f7 4 )<br \/>\n= 1,500 + 120 + 8<br \/>\n= 1,628 R 2<br \/>\nHence, 6,514 \u00f7 4 = 1,628 R 2<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt [ 3 ]{ 62 } \\)<br \/>\nAnswer: 62 \u00f7 3 = 20 R 2<br \/>\nExplanation:<br \/>\nBy using the partial quotients method,<br \/>\n62 \u00f73 = ( 33 + 27 ) \u00f7 3<br \/>\n= ( 33 \u00f7 3 ) + ( 27 \u00f7 3 )<br \/>\n= 11 + 9<br \/>\n= 20 R 2<br \/>\nHence, 62 \u00f7 3 = 20 R 2<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt [ 5 ]{ 548 } \\)<br \/>\nAnswer: 548 \u00f7 5 = 109 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n548 \u00f7 5 = ( 500 + 45 ) \u00f7 5<br \/>\n= ( 500 \u00f7 5 ) + ( 45 \u00f7 5 )<br \/>\n= 100 + 9<br \/>\n= 109 R 3<br \/>\nHence, 548 \u00f7 5 = 109 R 3<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt [ 2 ]{ 4,136 } \\)<br \/>\nAnswer: 4,136 \u00f7 2 = 2,068<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n4,136 \u00f7 2 = ( 4,000 + 100 + 36 ) \u00f7 2<br \/>\n= ( 4,000 \u00f7 2 ) + ( 100 \u00f7 2 ) + ( 36 \u00f7 2 )<br \/>\n= 2,000 + 50 + 18<br \/>\n= 2,068<br \/>\nHence, 4,136 \u00f7 2 = 2,068<\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 10.<br \/>\n\\(\\sqrt [ 7 ]{ 214 } \\)<br \/>\nAnswer: 214 \u00f7 7 = 30 R 4<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n214 \u00f7 7 = ( 140 + 70 ) \u00f7 7<br \/>\n= ( 140 \u00f7 7 ) + ( 70 \u00f7 7 )<br \/>\n= 20 + 10<br \/>\n= 30 R 4<br \/>\nHence, 214 \u00f7 7 = 30 R 4<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt [ 4 ]{ 321 } \\)<br \/>\nAnswer: 321 \u00f7 4 = 80 R 1<\/p>\n<p>Explanation:<br \/>\nBy usng the partial quotients method,<br \/>\n321 \u00f7 4 = ( 280 + 40 ) \u00f7 4<br \/>\n= ( 280 \u00f7 4 ) + ( 40 \u00f7 4 )<br \/>\n= 70 + 10<br \/>\n= 80 R 1<br \/>\nHence, 321 \u00f7 4 = 80 R 1<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt [ 6 ]{ 5,162 } \\)<br \/>\nAnswer: 5,162 \u00f76 = 860 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n5,162 \u00f7 6 = ( 4,800 + 300 + 60 ) \u00f7 6<br \/>\n= ( 4,800 \u00f7 6 ) + ( 300 \u00f7 6 ) + ( 60 \u00f7 6 )<br \/>\n= 800 + 50 + 10<br \/>\n= 860 R 2<br \/>\nHence, 5,162 \u00f7 6 = 860 R 2<\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt [ 2 ]{ 7,301 } \\)<br \/>\nAnswer: 7,301 \u00f7 2 = 3,650 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n7,301 \u00f7 2 = ( 7,000 + 300 ) \u00f7 2<br \/>\n= ( 7,000 \u00f7 2 ) + ( 300 \u00f7 2 )<br \/>\n= 3,500 + 150<br \/>\n= 3,650 R 1<br \/>\nHence, 7,301 \u00f7 2 = 3,650 R 1<\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt [ 5 ]{ 603 } \\)<br \/>\nAnswer: 603 \u00f7 5 = 120 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n603 \u00f7 5 = ( 550 + 50 ) \u00f7 5<br \/>\n= ( 550 \u00f7 5 ) + ( 50 \u00f7 5 )<br \/>\n= 110 + 10<br \/>\n= 120 R 3<br \/>\nHence, 603 \u00f7 5 = 120 R 3<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt [ 3 ]{ 6,082 } \\)<br \/>\nAnswer: 6,082 \u00f7 3 = 2,027 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n6,082 \u00f7 3 = ( 6,000 + 81 ) \u00f7 3<br \/>\n= ( 6,000 \u00f7 3 ) + ( 81 \u00f7 3 )<br \/>\n= 2,000 + 27<br \/>\n= 2,027 R 1<br \/>\nHence, 6,082 \u00f7 3 = 2,027 R 1<\/p>\n<p>Question 16.<br \/>\nThere are 450 pounds of grapes for a grape stomping contest. They are divided equally into 5 barrels. How many pounds of grapes are in each barrel?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-12.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 12\" width=\"202\" height=\"128\" \/><\/p>\n<p>Answer: There are 90 pounds of grapes in each barrel.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 450 pounds of grapes for a grape stomping contest and they are divided equally into 5 barrels.<br \/>\nSo,<br \/>\nThe number of pounds of grapes in each barrel = Total number of pounds of groups \u00f7 5<br \/>\n= 450 \u00f7 5<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n450 \u00f7 5 = ( 400 + 50 ) \u00f7 5<br \/>\n= ( 400 \u00f7 5 ) + ( 50 \u00f7 5 )<br \/>\n= 80 + 10<br \/>\n= 90 pounds<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 90 pounds of grapes in each barrel.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nHow could you change the dividend in Exercise 11 so that there would be no remainder? Explain.<br \/>\nAnswer: The dividend given in Exercise 11 is 321 and leaves the remainder 1 when the dividend is divided by 4.<br \/>\nSo, to make the dividend a number in such a way that it is divisible by 4 and leaves the remainder 0<br \/>\nBy observing the given number 321, we can say that it is close to 320 which is divisible by 4 and leaves the remainder 0.<br \/>\nHence, the number which we have to change so that the remainder will be 0 is: 320<\/p>\n<p>Question 18.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nFive actresses are placed on each team. Remaining actresses are added to the teams, so some of the teams have 6 actresses. How many teams have 5 actresses? 6 actresses?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-13739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.8-13.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.8 13\" width=\"266\" height=\"207\" \/><\/p>\n<p>Answer:<br \/>\nThe number of teams that have 5 actresses = 40<br \/>\nThe number of teams that have 6 actresses = 2<\/p>\n<p>Explanation:<br \/>\nGiven that actresses are placed on each team and the remaining actresses are added to the teams.<br \/>\nSo, from the table, we can see that<br \/>\nThe total number of actresses = 202<br \/>\nNow, to find the number of teams that have 5 actresses, we have to find the value of 202 \u00f7 5<br \/>\nThe remainder of 202 \u00f7 5 gives the number of teams that have 6 actresses<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n202 \u00f7 5 = ( 150 + 50 ) \u00f7 5<br \/>\n= ( 150 \u00f7 5 ) + ( 50 \u00f7 5 )<br \/>\n= 30 + 10<br \/>\n= 40 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe number of teams that have 5 actresses = 40 teams<br \/>\nThe number of teams that have 6 actresses = 2 teams<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write the value of the underlined digit.<\/strong><br \/>\nQuestion 19.<br \/>\n8<span style=\"text-decoration: underline;\">6<\/span>,109<br \/>\nAnswer: The place- value of 6 in 86,109 is: 6,000<\/p>\n<p>Explanation:<br \/>\nWe know that the position of a given digit in any number depends on the place-value of that number.<br \/>\nSo,<br \/>\nThe place-value of 6 in 86,109 is: 6,000<\/p>\n<p>Question 20.<br \/>\n<span style=\"text-decoration: underline;\">1<\/span>5,327<br \/>\nAnswer: The place-value of 1 in 15,327 is: 10,000<\/p>\n<p>Explanation:<br \/>\nWe know that the position of a given digit in any number depends on the place-value of that number.<br \/>\nSo,<br \/>\nThe place-value of 1 in 15,327 is: 10,000<\/p>\n<p>Question 21.<br \/>\n<span style=\"text-decoration: underline;\">9<\/span>14,263<br \/>\nAnswer: The place-value of 9 in\u00a0 914,263 is: 900,000<\/p>\n<p>Explanation:<br \/>\nWe know that the position of a given digit in any number depends on the place-value of that number.<br \/>\nSo,<br \/>\nThe place-value of 9 in\u00a0 914,263 is: 900,000<\/p>\n<p>Question 22.<br \/>\n284,5<span style=\"text-decoration: underline;\">0<\/span>5<br \/>\nAnswer: The place-value of 0 in 284,505 is: 0 ( Since 0 \u00d7 10 = 0 )<\/p>\n<p>Explanation:<br \/>\nWe know that the position of a given digit in any number depends on the place-value of that number.<br \/>\nSo,<br \/>\nThe place-value of 0 in 284,505 is: 0 ( Since 0 \u00d7 10 = 0 )<\/p>\n<h3><a id=\"Lesson_5.9_Problem_Solving:_Division\"><\/a>Lesson 5.9 Problem Solving: Division<\/h3>\n<p><strong>Explore &amp; Grow<\/strong><\/p>\n<p>Make a plan to solve the problem.<br \/>\nA fruit vendor has 352 green apples and 424 red apples. The vendor uses all of the apples to make fruit baskets. He puts 8 apples in each basket. How many fruit baskets does the vendor make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 1\" width=\"209\" height=\"159\" \/><\/p>\n<p>Answer: The fruit vendor makes 97 fruit baskets<\/p>\n<p>Explanation:<br \/>\nGiven that a fruit vendor has 352 green apples and 424 red apples.<br \/>\nSo,<br \/>\nTotal number of apples = Number of red apples + Number of green apples<br \/>\n= 352 + 424<br \/>\n= 776 apples.<br \/>\nIt is also given that the vendor uses all of the apples to make fruit baskets and he puts 8 apples in each basket.<br \/>\nHence,<br \/>\nThe number of fruit baskets that the vendor makes = Total number of apples \u00f7 Number of apples the vendor puts in each basket<br \/>\n= 776 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n776 \u00f7 8 = ( 720 + 56 ) \u00f7 8<br \/>\n= ( 720 \u00f7 8 ) + ( 56 \u00f7 8 )<br \/>\n= 90 + 7<br \/>\n= 97 baskets<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 97 fruit baskets that the vendor made.<\/p>\n<p><strong>Make Sense of Problems<\/strong><br \/>\nThe vendor decides that each basket should have 8 of the same colored apples. Does this change your plan to solve the problem? Will this change the answer? Explain.<br \/>\nAnswer: Yes, you have to change your plan to solve the problem but this way will not change the answer as we will get the same answer as above.<\/p>\n<p>Explanation:<br \/>\nGiven that the vendor decides that each basket should have 8 of the same colored apples.<br \/>\nSo,<br \/>\nThe number of fruit baskets that have red apples = 424 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n424 \u00f7 8 = ( 400 + 24 ) \u00f7 8<br \/>\n= ( 400 \u00f7 8 ) + ( 24 \u00f7 8 )<br \/>\n= 50 + 3<br \/>\n= 53 fruit baskets ( for every 8 red apples)<br \/>\nNow,<br \/>\nThe number of fruit baskets that have green apples = 352 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n352 \u00f7 8 = ( 320 + 32 ) \u00f7 8<br \/>\n= ( 320 \u00f7 8 ) + ( 32 \u00f7 8 )<br \/>\n= 40 + 4<br \/>\n= 44 fruit baskets ( for every 8 green apples)<br \/>\nSo,<br \/>\nTotal number of fruit baskets that a vendor make = Number of fruit baskets that have red apples + Number of fruit baskets that have green apples<br \/>\n= 44 + 53 = 97 fruit baskets<br \/>\nHence, from the above,<br \/>\nWe can conclude that we change the plan of solving the problem but the answer remains the same.<\/p>\n<p><strong>Think and Grow: Problem Solving: Division<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe speed of sound in water is 1,484 meters per second. Sound travels 112 more than 4 times as many meters per second in water as it does in air. What is the speed of sound in air?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-2.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 2\" width=\"319\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-2.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-2-300x116.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\n<strong>Understand the Problem<\/strong><br \/>\nWhat do you know?<br \/>\n\u2022 The speed of sound in water is sound 1,484 meters per second.<br \/>\n\u2022 Sound travels 112 more than 4 times as many meters per second in water as it does in air.<\/p>\n<p>What do you need to find?<br \/>\n\u2022 You need to find the speed in the air.<\/p>\n<p><strong>Make a Plan<br \/>\n<\/strong>How will you solve it?<br \/>\n\u2022 Subtract 112 from 1,484 to find 4 times the speed of sound in the air.<br \/>\n\u2022 Then divide the difference by 4 to find the speed of sound in the air.<\/p>\n<p><strong>Solve<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-66.jpg\" alt=\"\" width=\"562\" height=\"326\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-66.jpg 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-66-300x174.jpg 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><br \/>\nSo,<br \/>\nThe speed of sound in air is 343 meters per second.<\/p>\n<p><strong>Show and Grow<br \/>\n<\/strong>Question 1.<br \/>\nExplain how you can check whether your answer above is reasonable.<br \/>\nAnswer:<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Understand the problem. What do you know? What do you need to find? Explain.<\/strong><br \/>\nQuestion 2.<br \/>\nA surf shop owner divides 635 stickers evenly among all of her surfboards. Each surfboard has 3 tiki stickers and 2 turtle stickers. How many surfboards does she have?<br \/>\nAnswer: She has 127 surfboards<\/p>\n<p>Explanation:<br \/>\nGiven that a surf shop owner divides 635 stickers evenly among all of her surfboards and each surfboard has 3 tiki stickers and 2 turtle stickers.<br \/>\nSo,<br \/>\nThe total number of stickers on each surfboard = Number of tiki stickers + Number of turtle stickers<br \/>\n= 3 + 2<br \/>\n= 5 stickers<br \/>\nSo,<br \/>\nTotal number of surfboards = Total number of stickers \u00f7 The number of stickers on each surfboard<br \/>\n= 635 \u00f7 5<br \/>\nBy using the partial quotients method,<br \/>\n635 \u00f7 5 = ( 600 + 35 ) \u00f7 5<br \/>\n= ( 600 \u00f7 5 ) + ( 35 \u00f7 5 )<br \/>\n= 120 + 7<br \/>\n= 127 surfboards<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 127 surfboards.<\/p>\n<p>Question 3.<br \/>\nThere are 1,008 projects in a science fair. The projects are divided into equally 9 rooms. Each room has 8 equal rows of projects. How many projects are in each row?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-4.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 4\" width=\"171\" height=\"128\" \/><br \/>\nAnswer: There are 14 projects in each row.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 1,008 projects in a science fair and the projects are divided into equally 9 rooms. It is also given that each room has 8 equal rows of projects.<br \/>\nSo,<br \/>\nTotal number of rooms = 9 \u00d7 8 =72 rooms<br \/>\nNow,<br \/>\nNumber of projects in each row = Total number of projects \u00f7 Total number of rooms<br \/>\n= 1,008 \u00f7 72<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n1,008 \u00f7 72 = ( 720 + 288 )\u00f7 72<br \/>\n= ( 720 \u00f7 72 ) + ( 288 \u00f7 72 )<br \/>\n= 10 + 4<br \/>\n= 14 projects in each row<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 14 projects in each row.<\/p>\n<p><strong>Understand the problem. Then make a plan. How will you solve it? Explain.<\/strong><br \/>\nQuestion 4.<br \/>\nOf 78 students who work on a mural, 22 students design it, and the rest of the students paint it. The painters are divided equally among 4 areas of the mural. How many painters are assigned to each area?<br \/>\nAnswer: 14 painters are assigned to each area.<\/p>\n<p>Explanation:<br \/>\nGiven that there are 78 students who work on a mural and 22 students designed the mural and the remaining students painted it.<br \/>\nSo,<br \/>\nThe students who painted the mural = Total number of students &#8211; The students who designed the mural<br \/>\n= 78 &#8211; 22<br \/>\n= 56 students<br \/>\nIt is also given that the painters are divided equally among 4 areas of the mural.<br \/>\nSo,<br \/>\nThe number of painters divided = The number of students who painted the mural \u00f7 4<br \/>\n= 56 \u00f7 4<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n56 \u00f7 4 = ( 40 + 16 ) \u00f7 4<br \/>\n= ( 40 \u00f7 4 ) + ( 16 \u00f7 4 )<br \/>\n= 10 + 4<br \/>\n= 14 students<br \/>\nHence, from the above,<br \/>\nwe can conclude that there are 14 students are assigned to each area.<\/p>\n<p>Question 5.<br \/>\nThe Winter Olympics occur twice every 8 years. How many times will the Winter Olympics occur in 200 years?<br \/>\nAnswer:\u00a0 50 times<\/p>\n<p>Explanation:<br \/>\nGiven that the Winter Olympics occur twice every 8 years.<br \/>\nSo, the Winter Olympics occur every 4 years. ( 8 \u00f7 2 = 4 )<br \/>\nSo,<br \/>\nThe number of times Winter Olympics occur in 200 years = 200 \u00f7 4<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n200 \u00f7 4 = ( 160 + 40 ) \u00f7 4<br \/>\n= ( 160 \u00f7 4 ) + ( 40 \u00f7 4 )<br \/>\n= 40 + 10<br \/>\n= 50 times<br \/>\nHence, from the above,<br \/>\nWe can conclude that the Winter Olympics occur 50 times in 200 years.<\/p>\n<p>Question 6.<br \/>\nA party planner wants to put 12 balloons at each of 15 tables. The balloons come in packages of 8. How many packages of balloons must the party planner buy?<br \/>\nAnswer: The party planner buy 176 packages of balloons with 4 leftover balloons<\/p>\n<p>Explanation:<br \/>\nGiven that a part planner wants to put 12 balloons at each of 15 tables.<br \/>\nSo,<br \/>\nTotal number of balloons = 15 \u00d7 12<br \/>\nNow,<br \/>\nBy using the partial products method,<br \/>\n12 \u00d7 15 = ( 10 + 2 ) \u00d7 ( 10 + 5 )<br \/>\n= ( 10 \u00d7 10 ) + ( 10 \u00d7 5 ) + ( 2 \u00d7 10 ) + ( 2 \u00d7 5 )<br \/>\n= 100 + 50 + 20 +10<br \/>\n= 180 balloons<br \/>\nIt is also given that the balloons come in packages of 8.<br \/>\nSo,<br \/>\nThe number of balloons that each package contain = Total number of balloons \u00f7 8<br \/>\n= 180 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n180 \u00f7 8 = ( 160 + 16 ) \u00f7 8<br \/>\n= ( 160 \u00f7 8 ) + ( 16 \u00f7 8 )<br \/>\n= 20 + 2<br \/>\n= 22 R 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of balloons that each package contain is: 22 with 4 leftovers<\/p>\n<p>Question 7.<br \/>\nAn art teacher has 8 boxes of craft sticks. Each box has 235 sticks. The students use the sticks to make as many hexagons as possible. How many sticks are used?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 5\" width=\"153\" height=\"157\" \/><\/p>\n<p>Answer: The number of sticks used is: 313 with 2 leftover<\/p>\n<p>Explanation:<br \/>\nGiven that an art teacher has 8 boxes of craft sticks and each box has 235 sticks.<br \/>\nSo,<br \/>\nTotal number of sticks = 235 \u00d7 8<br \/>\nNow,<br \/>\nBy using the partial products method,<br \/>\n235 \u00d7 8 = ( 200 + 35 ) \u00d7 8<br \/>\n= ( 200 \u00d7 8 ) + ( 35 \u00d7 8 )<br \/>\n= 1,600 + 280<br \/>\n= 1,880 sticks<br \/>\nIt is also given the sticks are used to make hexagons.<br \/>\nWe know that,<br \/>\nThe number of sides of Hexagon = 6<br \/>\nSo,<br \/>\nThe number of sticks used to make hexagons = 1,880 \u00f7 6<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n1,880 \u00f7 6 = ( 1,800 + 60 + 18 ) \u00f7 6<br \/>\n= ( 1,800 \u00f7 6 ) + ( 60 \u00f7 6 ) + ( 18 \u00f7 6 )<br \/>\n= 300 + 10 + 3<br \/>\n= 313 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of sticks used for making hexagons is: 313 with 2 leftover<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA book enthusiast has $200 to buy an e-reader and e-books. He uses a $20 off coupon and buys the e-reader shown. Each e-book costs $6. How many e-books can the book enthusiast buy?<br \/>\nThink: What do you know? What do you need to find? How will you solve it?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 6\" width=\"235\" height=\"194\" \/><br \/>\nStep 1: How much money does the book enthusiast pay for the e-reader?<br \/>\nSubtract $20 from $119.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-19662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-67.jpg\" alt=\"\" width=\"63\" height=\"67\" \/><\/p>\n<p>Step 2: Subtract to find how much money he has left to spend on e-books.<br \/>\n$200 &#8211; _____ = d<br \/>\nd is the unknown difference.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-19663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-68.jpg\" alt=\"\" width=\"234\" height=\"85\" \/><\/p>\n<p>Step 3: Use to find the number of e-books the book enthusiast can buy.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-69.jpg\" alt=\"\" width=\"521\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-69.jpg 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5-69-300x104.jpg 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><br \/>\nSo, the book enthusiast can buy 16 e-books.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 8.<br \/>\nYou run 17 laps around a track. Newton runs 5 times as many laps as you. Descartes runs 35 more laps than Newton. Eight laps around the track are equal to 1 mile. How many miles does Descartes run?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 10\" width=\"160\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-10.png 160w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-10-150x150.png 150w\" sizes=\"(max-width: 160px) 100vw, 160px\" \/><br \/>\nAnswer: Descartes runs 15 miles<\/p>\n<p>Explanation:<br \/>\nGiven that you run 17 laps around a track and Newton runs 5 times as many laps as you.<br \/>\nSo,<br \/>\nThe number of laps covered by Newton = 17 \u00d7 5 = 85 laps<br \/>\nIt is also given that Descartes runs 35 more laps than Newton.<br \/>\nSo,<br \/>\nThe number of laps covered by Descartes = 35 + Number of laps covered by Newton<br \/>\n= 35 + 85<br \/>\n= 120 laps<br \/>\nGiven that,<br \/>\n8 laps = 1 mile<br \/>\nSo,<br \/>\nThe number of miles covered by Descartes = The number of laps covered by Descartes \u00f7 8<br \/>\n= 120 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n120 \u00f7 8 = ( 80 + 40 ) \u00f7 8<br \/>\n= ( 80 \u00f7 8 ) + ( 40 \u00f7 8 )<br \/>\n= 10 + 5<br \/>\n= 15 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that Descartes covers 15 miles.<\/p>\n<h3><a id=\"Problem_Solving:_Division_Practice_5.9\"><\/a>Problem Solving: Division Homework &amp; Practice 5.9<\/h3>\n<p><strong>Understand the problem. Then make a plan. How will you solve it? Explain.<\/strong><br \/>\nQuestion 1.<br \/>\nYou borrow a 235-page book from the library. You read 190 pages. You have 3 days left until you have to return the book. You want to read the same number of pages each day to finish the book. How many pages should you read each day?<\/p>\n<p>Answer:\u00a0 The number of pages you should read each day is: 15 pages<\/p>\n<p>Explanation:<br \/>\nGiven that you borrow a 235-page book and you read 190 pages. It is also given that you have only 3 days left until you have to return the book.<br \/>\nSo,<br \/>\nThe number of remaining pages = 235 &#8211; 190 = 45 pages<br \/>\nSo,<br \/>\nThe number of pages you should read each day = 45 \u00f7 3<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n45 \u00f7 3 = ( 30 + 15 ) \u00f7 3<br \/>\n= ( 30 \u00f7 3 ) + ( 15 \u00f7 3 )<br \/>\n= 10 + 5<br \/>\n= 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of pages you should read each day is: 15 pages<\/p>\n<p>Question 2.<br \/>\nThere are 24 fourth-graders and 38 fifth graders traveling to a math competition. If 8 students can fit into each van, how many vans are needed?<br \/>\nAnswer: The number of vans needed is: 7 R 6<\/p>\n<p>Explanation:<br \/>\nGiven that there are 24 fourth-graders and 38 fifth-graders traveling to a math competition.<br \/>\nSo,<br \/>\nThe total number of students who are traveling to a math competition = Number of fourth-graders + Number of fifth-graders<br \/>\n= 24 + 38<br \/>\n=\u00a0 62 students<br \/>\nIt is also given that 8 students can fit into each van.<br \/>\nSo,<br \/>\nThe number of vans needed = Total number of students \u00f7 Number of students fit into each van<br \/>\n= 62 \u00f7 8<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n62 \u00f7 8 = ( 40 + 16 ) \u00f7 8<br \/>\n= ( 40 \u00f7 8 ) + ( 16 \u00f7 8 )<br \/>\n= 5 + 2<br \/>\n= 7 vans with 6 students leftover<br \/>\n= 7 R 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of vans needed is: 7 vans with 6 students leftover<\/p>\n<p>Question 3.<br \/>\nYour class has 3 bags of buttons to make riding horses for a relay race. Each bag has 54 buttons. What is the greatest number of horses your class can make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 11\" width=\"144\" height=\"176\" \/><br \/>\nAnswer: The greatest number of horses your class can make = 40 horses<\/p>\n<p>Explanation:<br \/>\nGiven that your class has 3 bags of buttons to make riding horses for a relay race and each bag contains 54 buttons<br \/>\nSo,<br \/>\nThe total number of buttons present = 54 \u00d7 3<br \/>\nNow,<br \/>\nBy using the Distributive Property of multiplication,<br \/>\n54 \u00d7 3 = ( 50 + 4 ) \u00d7 3<br \/>\n( 50 \u00d7 3 ) + ( 4 \u00d7 3 )<br \/>\n= 150 + 12<br \/>\n= 162 buttons<br \/>\nIt is also given that each horse needs 4 buttons.<br \/>\nSo,<br \/>\nThe greatest number of horses you can make = Total number of buttons \u00f7 4<br \/>\n= 162 \u00f7 4<br \/>\nNOw,<br \/>\nBy using the partial quotients method,<br \/>\n162 \u00f7 4 = ( 120 + 40 ) \u00f7 4<br \/>\n= ( 120 \u00f7 4 ) + ( 40 \u00f7 4 )<br \/>\n= 30 + 10<br \/>\n= 40 horses with 2 buttons leftover<br \/>\n= 40 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the greatest number of horses you can make = 40 horses<\/p>\n<p>Question 4.<br \/>\nFactory workers make 2,597 small, 2,597 medium, and 2,597 large plush toys. The workers pack the toys into boxes with 4 toys in each box. How many toys are left over?<br \/>\nAnswer: The number of toys leftover are: 3 toys<\/p>\n<p>Explanation:<br \/>\nGiven that factory workers make 2,597 small, 2,597 medium, and 2,597 large plush toys.<br \/>\nSo,<br \/>\nTotal number of toys that factory workers can made = 2,597 + 2,597 + 2,597<br \/>\n= 7,791 toys<br \/>\nIt is also given that the workers pack the toys into boxes with 4 toys in each box.<br \/>\nSo,<br \/>\nThe number of toys in each box = Total number of toys that the factory workers can make \u00f7 4<br \/>\n= 7,791 \u00f7 4<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n7,791 \u00f7 4 = ( 7,200 + 520 + 68 ) \u00f7 4<br \/>\n= ( 7,200 \u00f7 4 ) + ( 520 \u00f7 4 ) + ( 68 \u00f7 4 )<br \/>\n= 1,200 + 130 + 17<br \/>\n=1,347 R 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 3 leftovers after all the toys packed into\u00a0 group of 4.<\/p>\n<p>Question 5.<br \/>\n<strong>Writing<\/strong><br \/>\nWrite and solve a two-step word problem that can be solved using division.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou exercise for 300 minutes this week. Outside of jogging, you divide your exercising time equally among 3 other activities. How many minutes do you spend on each of your other 3 activities?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 12\" width=\"133\" height=\"126\" \/><br \/>\nAnswer: You spend 100 minutes on each of your other 3 activities.<\/p>\n<p>Explanation:<br \/>\nGiven that you exercise for 300 minutes this week.<br \/>\nIt is also given that outside of jogging, you divide your exercising time equally among 3 other activities.<br \/>\nSo,<br \/>\nThe number of minutes you spend on each of your 3 other activities = Total minutes of exercising \u00f7 Total number of activities outside jogging<br \/>\n= 300 \u00f7 3<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n300 \u00f7 3 = ( 270 + 30 ) \u00f7 3<br \/>\n= ( 270 \u00f7 3 ) + ( 30 \u00f7 3 )<br \/>\n= 90 + 10<br \/>\n= 100 minutes.<br \/>\nHence, from the above,<br \/>\nwe can conclude that you spent 100 minutes on each of the 3 other activities outside of jogging.<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nDrones are used to help protect orangutans and their habitats. A drone takes a picture every 2 seconds. How many pictures does the drone take in 30 minutes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-5.9-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 5.9 13\" width=\"261\" height=\"167\" \/><\/p>\n<p>Answer: The drone makes 900 pictures in 30 minutes.<\/p>\n<p>Explanation:<br \/>\nGiven that the drones are used to help protect orangutans and their habitats<br \/>\nIt is also given that a drone takes a picture every 2 seconds.<br \/>\nWe know that,<br \/>\n1 minute = 60 seconds<br \/>\nSo,<br \/>\n30 minutes = 30 \u00d7 60 seconds<br \/>\nNow,<br \/>\nBy using the place-value method,<br \/>\n30 \u00d7 60 = 3 tens \u00d7 60<br \/>\n= 3 tens \u00d7 6 tens<br \/>\n= 18 \u00d7 10 \u00d7 10<br \/>\n= 1,800 seconds<br \/>\nSo,<br \/>\nThe number of pictures does the drone takes in 30 minutes = 1,800 \u00f7 2<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n1,800 \u00f7 2 = ( 1,000 +800 ) \u00f7 2<br \/>\n= ( 1,000 \u00f7 2 ) + ( 800 \u00f7 2 )<br \/>\n= 500 + 400<br \/>\n= 900 pictures<br \/>\nHence, from the above,<br \/>\nwe can conclude that the drone takes 900 pictures in 30 minutes.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product. Check whether your answer is reasonable.<\/strong><br \/>\nQuestion 8.<br \/>\nEstimate: _____<br \/>\n41 \u00d7 22 = _____<br \/>\nAnswer: 41 \u00d7 22 = 902<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n41 \u00d7 22 = ( 40 + 1 ) \u00d7 ( 20 + 2 )<br \/>\n=( 40 \u00d7 20 ) + ( 1 \u00d7 20 ) + ( 40 \u00d7 2 ) + ( 1 \u00d7 2 )<br \/>\n= 800 + 20 + 80 + 2<br \/>\n= 902<br \/>\nSo, 41 \u00d7 22 = 902<br \/>\nEstimate:<br \/>\nLet 41 be rounded to 40.<br \/>\nLet 22 be rounded to 20.<br \/>\nSo, by using the place-value method,<br \/>\n40 \u00d7 20 = 4 tens \u00d7 20<br \/>\n= 80 tens<br \/>\n= 80 \u00d7 10<br \/>\n= 800<br \/>\nSo, 40 \u00d7 20 = 400<br \/>\nHence, from the above,<br \/>\nWe can conclude that the actual answer is not near to the Estimate. So, the answer is not reasonable.<\/p>\n<p>Question 9.<br \/>\nEstimate: ______<br \/>\n87 \u00d7 19 = ______<\/p>\n<p>Answer: 87 \u00d7 19 = 1,653<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n87 \u00d7 19 = ( 80 + 17 ) \u00d7 ( 10 + 9 )<br \/>\n=( 80 \u00d7 10 ) + ( 80 \u00d7 9 ) + ( 17 \u00d7 10 ) + ( 17 \u00d7 9 )<br \/>\n= 800 + 720 + 170 + 153<br \/>\n= 1,653<br \/>\nSo, 87 \u00d7 19 = 1,653<br \/>\nEstimate:<br \/>\nLet 87 be rounded to 85.<br \/>\nLet 19 be rounded to 20.<br \/>\nSo, by using the place-value method,<br \/>\n85 \u00d7 20 = 2 tens \u00d7 85<br \/>\n= 170 tens<br \/>\n= 170 \u00d7 10<br \/>\n= 1,700<br \/>\nSo, 85 \u00d7 20 = 1,700<br \/>\nHence, from the above,<br \/>\nWe can conclude that the actual answer is near to the Estimate. So, the answer is reasonable.<\/p>\n<p>Question 10.<br \/>\nEstimate: _____<br \/>\n36 \u00d7 59 = ______<br \/>\nAnswer: 36 \u00d7 59 = 2,124<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n36 \u00d7 59 = ( 30 + 6 ) \u00d7 ( 50 + 9 )<br \/>\n=( 30 \u00d7 50 ) + ( 30 \u00d7 9 ) + ( 6 \u00d7 50 ) + ( 6 \u00d7 9 )<br \/>\n= 1,500 + 270 + 300 + 54<br \/>\n= 2,124<br \/>\nSo, 36 \u00d7 59 = 2,124<br \/>\nEstimate:<br \/>\nLet 36 be rounded to 35.<br \/>\nLet 59 be rounded to 60.<br \/>\nSo, by using the place-value method,<br \/>\n35 \u00d7 60 = 6 tens \u00d7 35<br \/>\n= 210 tens<br \/>\n= 210 \u00d7 10<br \/>\n= 2,100<br \/>\nSo, 35 \u00d7 60 = 2,100<br \/>\nHence, from the above,<br \/>\nWe can conclude that the actual answer is near to the Estimate. So, the answer is reasonable.<\/p>\n<h3><a id=\"Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Performance_Task\"><\/a>Divide Multi-Digit Numbers by One-Digit Numbers Performance Task<\/h3>\n<p>The students in fourth grade go on a field trip to a planetarium.<br \/>\nQuestion 1.<br \/>\nThe teachers have $760 to buy all of the tickets for the teachers and students. They receive less than $6 in change.<\/p>\n<p>a. Each ticket costs $6. How many tickets do the teachers buy?<br \/>\nb. Exactly how much money is left over?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 1\" width=\"196\" height=\"247\" \/><br \/>\nc. There are 6 groups on the field trip. Each group has 1 teacher. There is an equal number of students in each group. How many students are in each group?<br \/>\nd. Two groups can be in the planetarium for each show. The planetarium has 7 rows of seats with 8 seats in each row. How many seats are empty during each show?<\/p>\n<p>Answer:<br \/>\na) The teachers buy 126 tickets.<br \/>\nb) The money that is leftover: $4<br \/>\nc) The number of students in each group: 20<br \/>\nd) The number of seats empty during each show is: 0<\/p>\n<p>Explanation:<br \/>\nGiven that the teachers have $760 to buy all of the tickets for the teachers and students and they received less than $6 change.<br \/>\na) Given that each ticket cost $6<br \/>\nSo,<br \/>\nThe number of tickets that the teachers can buy = 760 \u00f7 6<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n760 \u00f7 6 = ( 600 + 120 + 36 ) \u00f7 6<br \/>\n= ( 600 \u00f7 6 ) + ( 120 \u00f7 6 ) + ( 36 \u00f7 6 )<br \/>\n= 100 + 20 + 6<br \/>\n= 126 tickets with 4 leftover as change=<br \/>\n= 126 R 4<br \/>\nb) From the above,<br \/>\nThe money that is leftover = $4<br \/>\nc) Given that there are 6 groups on the field trip and each group has 1 teacher.<br \/>\nIt is also given that there is an equal number of students in each group.<br \/>\nFrom the number of tickets, we can conclude that there are 126 students.<br \/>\nSo,<br \/>\nThe number of groups of students = 126 \u00f7 6<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n126 \u00f7 6 = ( 60 + 60 ) \u00f7 6<br \/>\n= ( 60 \u00f7 6 ) + ( 60 \u00f7 6 )<br \/>\n= 10 + 10<br \/>\n= 20 R 6<br \/>\nHence, from the above,<br \/>\nwe can conclude that there are 20 student groups.<br \/>\nd) Given that there are two groups in the planetarium for each show and the planetarium has 7 rows of seats with 8 seats in each row.<br \/>\nSo,<br \/>\nThe total number of seats = 7 \u00d7 8 = 56 seats<br \/>\nSo,<br \/>\nThe number of seats that are empty during each show = 56 \u00f7 2 = 28<br \/>\nHence, there are no empty seats left in each show.<\/p>\n<p>Question 2.<br \/>\nThe groups will be at the planetarium from 11:00 A.M. until 2:30 P.M. During that time they will rotate through 7 events: the planetarium show, 5 activities, and lunch. The planetarium show lasts 45 minutes. Each activity lasts 22 minutes. Students have 5 minutes between each event. How long does each group have to eat lunch?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 2\" width=\"209\" height=\"194\" \/><\/p>\n<p>Answer: Each group has 10 minutes to eat lunch.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThe groups will be at the planetarium from 11:00 A.M. until 2:30 P.M.<br \/>\nThe number of events = 7<br \/>\nThe number of activities = 5<br \/>\nThe time of planetarium show = 45 minutes<br \/>\nThe time each activity lasts = 22 minutes<br \/>\nSo,<br \/>\nThe time at which 5 activities lasts = 22 \u00d7 5 = 110 minutes<br \/>\nThe time for which students have time between each event = 5 minutes<br \/>\nNow,<br \/>\nThe total time that the groups will be at the planetarium = From 11:00 A.M. until 2:30 P.M.<br \/>\n= 3 hours 30 minutes<br \/>\n= 210 minutes<br \/>\nThe time taken by the groups for the activities and events = 45 + 110 =155 minutes<br \/>\nSo,<br \/>\nThe remaining time = 210 &#8211; 155 = 55 minutes<br \/>\nThe time is taken by all the students between the events = 5 \u00d7 7 = 35 minutes<br \/>\nSo, the remaining time = 55 &#8211; 35 = 20 minutes<br \/>\nGiven that there are 2 groups in the above Exercise.<br \/>\nSo, The time is taken for lunch by each group = 20 \u00f7 2 = 10 minutes.<br \/>\nHence, from the above,<br \/>\nwe can conclude that there are 10 minutes for each group to eat lunch.<\/p>\n<p>Question 3.<br \/>\nYou learn that the distance around Mars is about twice the distance around the moon. The distance around Mars is 13,263 miles. To find the distance around the moon, do you think an estimate or an exact answer is needed? Explain.<\/p>\n<p>Answer: We need an Estimate.<\/p>\n<p>Explanation:<br \/>\nGiven that the distance around Mars is about twice the distance around the moon and the distance around Mars is 13,263 miles.<br \/>\nSo,<br \/>\nThe distance of Moon = The distance around Mars \u00f7 2<br \/>\n= 13,263 \u00f7 2<br \/>\nIf we find the value of 13,263 \u00f7 2, we will get the answer with decimals.<br \/>\nSo, we have to take an Estimate to calculate the distance around the Moon.<br \/>\nEstimate:<br \/>\nlet 13,263 be rounded to 13,262<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n13,262 \u00f7 2 = ( 12,000 + 1,000 + 260 + 2 ) \u00f7 2<br \/>\n= ( 12,000 \u00f7 2 ) + ( 1,000 \u00f7 2 ) + ( 260 \u00f7 2 ) + ( 2 \u00f7 2 )<br \/>\n= 6,000 + 500 + 130 +1<br \/>\n= 6,631 miles.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the estimated distance around the Moon = 6,631 miles<\/p>\n<h3><a id=\"Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Activity\"><\/a>Divide Multi-Digit Numbers by One-Digit Numbers Activity<\/h3>\n<p><strong>Division Dots<\/strong><br \/>\n<strong>Directions:<\/strong><br \/>\n1. Players take turns connecting two dots, each using a different color.<br \/>\n2. On your turn, connect two dots, vertically or horizontally. If you close a square around a division problem, find and write the quotient and the remainder. If you do not close a square, your turn is over.<br \/>\n3. Continue playing until all division problems are solved.<br \/>\n4. The player with the most completed squares wins!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers 3\" width=\"687\" height=\"634\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-3.png 687w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-3-300x277.png 300w\" sizes=\"(max-width: 687px) 100vw, 687px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Divide_Multi_Digit_Numbers_by_One_Digit_Numbers_Chapter_Practice\"><\/a>Divide Multi-Digit Numbers by One-Digit Numbers Chapter Practice<\/h3>\n<p><strong>5.1 Divide Tens, Hundreds, and Thousands<\/strong><\/p>\n<p><strong>Find the quotient.<\/strong><br \/>\nQuestion 1.<br \/>\n90 \u00f7 9 = _____<br \/>\nAnswer: The quotient is: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n90 \u00f7 9 =9 tens \u00f7 9<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 90 \u00f7 9 = 10<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 2.<br \/>\n560 \u00f7 7 = _____<br \/>\nAnswer: The quotient is: 80<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n560 \u00f7 7 = 56 tens \u00f7 7<br \/>\n= 8 tens<br \/>\n=80<br \/>\nSo, 560 \u00f7 7 = 80<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 3.<br \/>\n2,700 \u00f7 9 = _____<br \/>\nAnswer: The quotient is: 300<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n2,700 \u00f7 9 = 27 hundreds \u00f7 9<br \/>\n= 3 hundred<br \/>\n=300<br \/>\nSo, 2,700 \u00f7 9 = 300<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 4.<br \/>\n240 \u00f7 4 = ______<br \/>\nAnswer: The quotient is: 60<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n240 \u00f7 4 = 24 tens \u00f7 4<br \/>\n= 6 tens<br \/>\n=60<br \/>\nSo, 240 \u00f7 4 = 60<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 5.<br \/>\n4,500 \u00f7 5 = _____<br \/>\nAnswer: The quotient is: 900<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n4,500 \u00f7 5 = 45 hundreds \u00f7 5<br \/>\n= 9 hundred<br \/>\n=900<br \/>\nSo, 4,500 \u00f7 5 = 900<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 6.<br \/>\n60 \u00f7 6 = _____<br \/>\nAnswer: The quotient is: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n60 \u00f7 6 = 6 tens \u00f7 6<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 60 \u00f7 6 = 10<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 7.<br \/>\n1,600 \u00f7 8 = _____<br \/>\nAnswer: The quotient is: 200<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n1,600 \u00f7 8 = 16 hundreds \u00f7 8<br \/>\n= 2 hundred<br \/>\n=200<br \/>\nSo, 1,600 \u00f7 8 = 200<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 8.<br \/>\n30 \u00f7 3 = ______<br \/>\nAnswer: The quotient is: 10<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n30 \u00f7 3 = 3 tens \u00f7 3<br \/>\n= 1 ten<br \/>\n=10<br \/>\nSo, 30 \u00f7 3 = 10<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p>Question 9.<br \/>\n540 \u00f7 9 = _____<br \/>\nAnswer: The quotient is: 60<\/p>\n<p>Explanation:<br \/>\nThe given Expression is:<br \/>\n540 \u00f7 9 = 54 tens \u00f7 9<br \/>\n= 6 tens<br \/>\n=60<br \/>\nSo, 540 \u00f7 9 = 60<\/p>\n<p><strong>Note:\u00a0<\/strong>The \u201cQuotient\u201d of an Expression is defined as a number that divides the Dividend and the quotient should be an Integer.<\/p>\n<p><strong>Find the missing number.<\/strong><br \/>\nQuestion 10.<br \/>\n720 \u00f7 _____ = 80<br \/>\nAnswer: The missing number is: 9<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\n720 \u00f7 X = 80<br \/>\nSo, X can be calculated by<br \/>\nX= 720 \u00f7 80 = 9<\/p>\n<p>Question 11.<br \/>\n_____ \u00f7 7 = 10<br \/>\nAnswer: 70<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\nX \u00f7 7 = 10<br \/>\nSo, X can be calculated by<br \/>\nX= 7 \u00d7 10 = 70<\/p>\n<p>Question 12.<br \/>\n1,800 \u00f7 _____ = 600<br \/>\nAnswer: The missing number is: 3<\/p>\n<p>Explanation:<br \/>\nLet the missing number be X.<br \/>\nThe given Expression is:<br \/>\n1,800 \u00f7 X = 600<br \/>\nSo, X can be calculated by<br \/>\nX= 1,800 \u00f7 600 = 3<\/p>\n<p><strong>5.2 Estimate Quotients<\/strong><\/p>\n<p>Question 13.<br \/>\n47 \u00f7 7<br \/>\nAnswer: The estimated quotient is: 7<\/p>\n<p>Explanation;<br \/>\nLet 47 be rounded off to 49.<br \/>\nSo, now we have to find 49 \u00f7 7<br \/>\nNow,<br \/>\n49 \u00f7 7 = ( 42 + 7 ) \u00f7 7<br \/>\n= ( 42 \u00f7 7 ) + ( 7 \u00f7 7 )<br \/>\n= 6 + 1<br \/>\n= 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that 47 \u00f7 7 can be rounded off to 7.<\/p>\n<p>Question 14.<br \/>\n593 \u00f7 6<br \/>\nAnswer: The estimated quotient is: 99<\/p>\n<p>Explanation;<br \/>\nLet 593 be rounded off to 594.<br \/>\nSo, now we have to find 594 \u00f7 6<br \/>\nNow,<br \/>\n594 \u00f7 6 = ( 540 + 54 ) \u00f7 6<br \/>\n= ( 540 \u00f7 6 ) + ( 54 \u00f7 6 )<br \/>\n= 90 + 19<br \/>\n= 99<br \/>\nHence, from the above,<br \/>\nWe can conclude that 593 \u00f7 6 can be rounded off to 99<\/p>\n<p><strong>Find two estimates that the quotient is between.<\/strong><br \/>\nQuestion 15.<br \/>\n261 \u00f7 8<br \/>\nAnswer: The quotient of 261 \u00f7 8 is between 30 and 40.<\/p>\n<p>Explanation:<br \/>\nUse 240. 24 \u00f7 8 = 3, so 240 \u00f7 8 = 30.<br \/>\nUse 320. 32 \u00f7 8 = 4, so 320 \u00f7 8 = 40 .<br \/>\n261 is between 240 and 320.<br \/>\nSo, the quotient of 261 \u00f7 8 is between 30 and 40.<\/p>\n<p>Question 16.<br \/>\n7,012 \u00f7 9<br \/>\nAnswer: The quotient of 7,012 \u00f7 9 is between 700 and 800.<\/p>\n<p>Explanation:<br \/>\nUse 6,300. 63 \u00f7 9 = 7, so 6,300 \u00f7 9 = 700.<br \/>\nUse 7,200. 72 \u00f7 9 = 8, so 7,200 \u00f7 9 = 800 .<br \/>\n7,012 is between 6,300 and 7,200.<br \/>\nSo, the quotient of 7,012 \u00f7 9 is between 700 and 800.<\/p>\n<p>Question 17.<br \/>\n<strong>Reasoning<\/strong><br \/>\nExplain how to find a better estimate for 2,589 \u00f7 6 than the one shown.<br \/>\nRound 2,589 to 3,000. Estimate 3,000 \u00f7 6.<br \/>\n3,000 \u00f7 6 = 500, so 2,589 \u00f7 6 is about 500.<br \/>\nAnswer: The better Estimate to find 2,589 \u00f7 6 is to round off 2,589 to 2,580<\/p>\n<p>Explanation:<br \/>\nGiven Expression is 2,589 \u00f7 6<br \/>\nLet 2,589 be rounded to 3,000<br \/>\nSo,<br \/>\n3,000 \u00f7 6 = 300 tens \u00f7 6<br \/>\n= 50 tens<br \/>\n= 500<br \/>\nNow,<br \/>\nLet 2,589 be rounded to 2,580.<br \/>\nSo,<br \/>\n2,580 \u00f7 6 = 258 tens \u00f7 6<br \/>\n= 43 tens<br \/>\n=430<br \/>\nBut, 2,589 is near to 2,580 when compared to 3,000.<br \/>\nSo,<br \/>\nWe can conclude that<br \/>\n2,580 \u00f7 6 = 43<\/p>\n<p><strong>5.3 Understand Division and Remainder<\/strong><\/p>\n<p><strong>Use a model to find the quotient and the remainder.<\/strong><br \/>\nQuestion 18.<br \/>\n14 \u00f7 4 = _____ R _____<br \/>\nAnswer: 3 R 2<\/p>\n<p>Explanation:<br \/>\nDivide 14 into 4 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 3<br \/>\nNumber of units leftover = 2<br \/>\nHence,<br \/>\n26 \u00f7 3 = 3 R 2<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 19.<br \/>\n28 \u00f7 6 = _____ R ______<br \/>\nAnswer: 4 R 4<\/p>\n<p>Explanation:<br \/>\nDivide 28 into 6 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 4<br \/>\nNumber of units leftover = 4<br \/>\nHence,<br \/>\n28 \u00f7 6 = 4 R 4<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 20.<br \/>\n18 \u00f7 7 = _____ R ______<br \/>\nAnswer: 2 R 4<\/p>\n<p>Explanation:<br \/>\nDivide 18 into 7 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 2<br \/>\nNumber of units leftover = 4<br \/>\nHence,<br \/>\n18 \u00f7 7 = 2 R 4<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 21.<br \/>\n23 \u00f7 3 = _____ R _______<br \/>\nAnswer: 7 R 2<\/p>\n<p>Explanation:<br \/>\nDivide 23 into 3 equal parts.<br \/>\nSo, we will get<br \/>\nNumber of Units in each group = 7<br \/>\nNumber of units leftover = 2<br \/>\nHence,<br \/>\n23 \u00f7 3 = 7 R 2<br \/>\nWhere R is the Remainder (or) the number of units leftover<\/p>\n<p>Question 22.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nTours of a factory can have no more than 9 guests. There are 76 guests in line to tour the factory.<br \/>\n\u2022 How many tours are full?<br \/>\n\u2022 How many tours are needed?<br \/>\n\u2022 How many guests are on the last tour?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-chp-22.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers chp 22\" width=\"227\" height=\"202\" \/><br \/>\nAnswer:<\/p>\n<p>a) The number of tours that are full = 8 tours<br \/>\nb) The number of tours needed = 9 tours<br \/>\nc) The number of guests on the last tour = 4 guests<\/p>\n<p>Explanation:<br \/>\nGiven that there are 76 guests in line to tour a\u00a0 factory It is also given that there are no more than 9 guests on the tours of a\u00a0 factory.<br \/>\nWe have to observe that to make all the guests full on all the trips without leftovers, we will need 9 trips. i.e.., 81 guests.<br \/>\nSo, now we have to find the number of guests in each tour of a crayon factory by finding the quotient and remainder of 76 \u00f7 9.<br \/>\nNow,<br \/>\n76 \u00f7 9<br \/>\nFrom this, we can see<br \/>\nThe number of guests in each tour that are full = 8<br \/>\nThe number of guests leftover on the last trip = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\na) 8 Tours are full.<br \/>\nb) 9 Tours are needed.<br \/>\nc) 4 guests are on the last tour.<\/p>\n<p><strong>5.4 Use Partial Quotients<\/strong><\/p>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 23.<br \/>\n\\(\\sqrt [ 8 ]{ 504 } \\)<br \/>\nAnswer: 504 \u00f7 8 = 63<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n504 \u00f7 8 = ( 480 + 24 ) \u00f7 8<br \/>\n( 480 \u00f7 8 ) + ( 24 \u00f7 8 )<br \/>\n= 60 + 3<br \/>\n= 63<br \/>\nHence, 504 \u00f7 8 = 63<\/p>\n<p>Question 24.<br \/>\n\\(\\sqrt [ 4 ]{ 52 } \\)<br \/>\nAnswer: 52 \u00f7 4 = 13<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n52 \u00f7 4 = ( 40 + 12 ) \u00f7 4<br \/>\n= ( 40 \u00f7 4 ) + ( 12 \u00f7 4 )<br \/>\n= 10 + 3<br \/>\n= 13<br \/>\nHence, 52 \u00f7 4 = 13<\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt [ 7 ]{ 119 } \\)<br \/>\nAnswer: 119 \u00f7 7 = 17<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n119 \u00f7 7 = ( 105 + 14 ) \u00f7 7<br \/>\n= ( 105 \u00f7 7 ) + ( 14 \u00f7 7 )<br \/>\n= 15 + 2<br \/>\n= 17<br \/>\nHence, 119 \u00f7 7 = 17<\/p>\n<p><strong>5.5 Use Partial Quotients with an Remainder<\/strong><\/p>\n<p><strong>Use partial quotients to divide.<\/strong><br \/>\nQuestion 26.<br \/>\n\\(\\sqrt [ 5 ]{ 82 } \\)<br \/>\nAnswer: 82 \u00f7 5 = 16 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n82 \u00f7 5 = ( 75 + 5 ) \u00f7 5<br \/>\n= ( 75 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 15 + 1<br \/>\n= 16 R 2<br \/>\nHence, 82 \u00f7 5 = 16 R 2<\/p>\n<p>Question 27.<br \/>\n\\(\\sqrt [ 8 ]{ 759 } \\)<br \/>\nAnswer: 759 \u00f7 8 = 94 R 7<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n759 \u00f7 8 = ( 720 + 32 ) \u00f7 8<br \/>\n= ( 720 \u00f7 8 ) + ( 32 \u00f7 8 )<br \/>\n= 90 + 4<br \/>\n= 94 R 7<br \/>\nHence, 759 \u00f7 8 = 94 R 7<\/p>\n<p>Question 28.<br \/>\n\\(\\sqrt [ 3]{ 5,468 } \\)<br \/>\nAnswer: 5,468 \u00f7 3 = 1,822 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n5,468 \u00f7 3 = ( 5,400 + 66 ) \u00f7 3<br \/>\n= ( 5,400 \u00f7 3 ) + ( 66 \u00f7 3 )<br \/>\n= 1,800 + 22<br \/>\n= 1,822 R 2<br \/>\nHence, 5,468 \u00f7 3 = 1,822 R 2<\/p>\n<p><strong>5.6 Divide Two-Digit Numbers by One-Digit Numbers<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 29.<br \/>\n\\(\\sqrt [ 3 ]{ 58 } \\)<br \/>\nAnswer: 58 \u00f7 3 = 19 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n58 \u00f7 3 = ( 48 + 9 ) \u00f7 3<br \/>\n= ( 48 \u00f7 3 ) + ( 9 \u00f7 3 )<br \/>\n= 16 + 3<br \/>\n= 19 R 1<br \/>\nHence, 58 \u00f7 3 = 19 R 1<\/p>\n<p>Question 30.<br \/>\n\\(\\sqrt [ 4 ]{ 90 } \\)<br \/>\nAnswer: 90 \u00f7 4 = 22 R 2<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n90 \u00f7 4 = ( 80 + 8 ) \u00f7 4<br \/>\n= ( 80 \u00f7 4 ) + ( 8 \u00f7 4 )<br \/>\n= 20 + 2<br \/>\n= 22 R 2<br \/>\nHence, 90 \u00f7 4 = 22 R 2<\/p>\n<p>Question 31.<br \/>\n\\(\\sqrt [ 2 ]{ 67 } \\)<br \/>\nAnswer: 67 \u00f7 2 = 33 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n67 \u00f7 2 = ( 60 + 6 ) \u00f7 2<br \/>\n= ( 60 \u00f7 2 ) + ( 6 \u00f7 2 )<br \/>\n= 30 + 3<br \/>\n= 33 R 1<br \/>\nHence, 67 \u00f7 2 = 33 R 1<\/p>\n<p><strong>5.7 Divide Multi-Digit Numbers by One-Digit Numbers<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 32.<br \/>\n\\(\\sqrt [ 5 ]{ 865 } \\)<br \/>\nAnswer: 865 \u00f7 5 = 173<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n865 \u00f7 5 = ( 800 + 65 )\u00f7 5<br \/>\n= ( 800 \u00f7 5 ) + ( 65 \u00f7 5 )<br \/>\n=\u00a0 160 + 13<br \/>\n= 173<br \/>\nHnece, 865 \u00f7 5 = 173<\/p>\n<p>Question 33.<br \/>\n\\(\\sqrt [ 2 ]{ 7,532 } \\)<br \/>\nAnswer: 7,532 \u00f7 2 = 3,766<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n7,532 \u00f7 2 = ( 7,000 + 500 + 3 ) \u00f7 2<br \/>\n= ( 7,000 \u00f7 2 ) + ( 500 \u00f7 2 )\u00a0 + ( 32 \u00f7 2 )<br \/>\n= 3,500 + 250 + 16<br \/>\n= 3,766<br \/>\nHence, 7,532 \u00f7 2 = 3,766<\/p>\n<p>Question 34.<br \/>\n\\(\\sqrt [ 4 ]{ 507 } \\)<br \/>\nAnswer: 507 \u00f7 4 = 126 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n507 \u00f7 4 = ( 480 + 24 ) \u00f7 4<br \/>\n= ( 480 \u00f7 4 ) + ( 24 \u00f7 4 )<br \/>\n= 120 + 6<br \/>\n= 126 R 3<br \/>\nHence, 507 \u00f7 4 = 126 R 3<\/p>\n<p>Question 35.<br \/>\n\\(\\sqrt [ 6 ]{ 9,127 } \\)<br \/>\nAnswer: 9,127 \u00f7 6 = 1,521 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n9,127 \u00f7 6 = ( 9,000 + 126 ) \u00f7 6<br \/>\n= ( 9,000 \u00f7 6 ) + ( 126 \u00f7 6 )<br \/>\n= 1,500 + 21<br \/>\n= 1,521 R 1<\/p>\n<p>Question 36.<br \/>\n\\(\\sqrt [ 8 ]{ 253 } \\)<br \/>\nAnswer: 253 \u00f7 8 = 31 R 5<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n253 \u00f7 8 = ( 240 + 8 ) \u00f7 8<br \/>\n= ( 240 \u00f7 8 ) + ( 8 v 8 )<br \/>\n= 30 + 1<br \/>\n= 31 R 5<br \/>\nHence,253 \u00f7 8 = 31 R 5<\/p>\n<p>Question 37.<br \/>\n\\(\\sqrt [ 6 ]{ 429 } \\)<br \/>\nAnswer: 429 \u00f7 6 = 71 R 3<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients,<br \/>\n429 \u00f7 6 = ( 420 + 6 ) \u00f7 6<br \/>\n= ( 420 \u00f7 6 ) + ( 6 \u00f7 6 )<br \/>\n= 70 + 1<br \/>\n= 71 R 3<br \/>\nHence, 429 \u00f7 6 = 71 R 3<\/p>\n<p><strong>5.8 Divide by One-Digit Numbers<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 38.<br \/>\n\\(\\sqrt [ 3 ]{ 91 } \\)<br \/>\nAnswer: 91 \u00f7 3 = 30 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n91 \u00f7 3 = ( 60 + 30 ) \u00f7 3<br \/>\n= ( 60 \u00f7 3 ) + ( 30 \u00f7 3 )<br \/>\n= 20 + 10<br \/>\n= 30 R 1<br \/>\nHence, 91 \u00f7 3 = 30 R 1<\/p>\n<p>Question 39.<br \/>\n\\(\\sqrt [ 7 ]{ 914 } \\)<br \/>\nAnswer: 914 \u00f7 7 = 130 R 4<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n914 \u00f7 7 = ( 840 + 70 ) \u00f7 7<br \/>\n= ( 840 \u00f7 7 ) + ( 70 \u00f7 7 )<br \/>\n= 120 + 10<br \/>\n= 130 R 4<br \/>\nHence, 914 \u00f7 7 = 130 R 4<\/p>\n<p>Question 40.<br \/>\n\\(\\sqrt [ 2 ]{ 6,075 } \\)<br \/>\nAnswer: 6,075 \u00f7 2 = 3,037 R 1<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n6,075 \u00f7 2 = ( 6,000 + 74 ) \u00f7 2<br \/>\n= ( 6,000 \u00f7 2 ) + ( 74 \u00f7 2 )<br \/>\n= 3,000 + 37<br \/>\n= 3,037 R 1<br \/>\nHence, 6,075 \u00f7 2 = 3,037 R 1<\/p>\n<p><strong>5.9 Problem Solving: Division<\/strong><\/p>\n<p>Question 41.<br \/>\nA young snake sheds its skin every 2 weeks. How many times will the snake shed its skin in 3 years?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-chp-41.1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers chp 41.1\" width=\"205\" height=\"214\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-5-Divide-Multi-Digit-Numbers-by-One-Digit-Numbers-chp-41.2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers chp 41.2\" width=\"172\" height=\"146\" \/><br \/>\nAnswer: A young snake sheds its skin 78 times in 3 years.<\/p>\n<p>Explanation:<br \/>\nGiven that a young snake sheds its skin every 2 weeks<br \/>\nWe know that,<br \/>\n1 year = 52 weeks<br \/>\nSo,<br \/>\n3 years = 3 \u00d7 52 = 156 weeks<br \/>\nSo,<br \/>\nThe number of times the young snake sheds its skin in 3 years = 156 \u00f7 2<br \/>\nNow,<br \/>\nBy using the partial quotients method,<br \/>\n156 \u00f7 2 = ( 100 + 56 ) \u00f7 2<br \/>\n= ( 100 \u00f7 2 ) + ( 56 \u00f7 2 )<br \/>\n= 50 + 28<br \/>\n= 78 times<br \/>\nHence, from the above,<br \/>\nWe can conclude that the young snake will shed its skin 78 times in 3 years<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>After your preparation please test your knowledge by solving the problems provided at the end of the chapter. You can also prepare the questions on your own and solve the problems if you learn the concepts in depth. Prepare well and secure highest marks in the exams. All the Best!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers are included here to help the students to improve their preparation level. You must practice every question given on Big Ideas Math Answers Grade 4 to aware of the different questions impose in the exam. Practice all the problems and verify &#8230; <a title=\"Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4-chapter-5\/\" aria-label=\"More on Big Ideas Math Answers Grade 4 Chapter 5 Divide Multi-Digit Numbers by One-Digit Numbers\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":89637,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-5.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/13622"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=13622"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/13622\/revisions"}],"predecessor-version":[{"id":90278,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/13622\/revisions\/90278"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89637"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=13622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=13622"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=13622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}