The different lessons of Multiples and Problem Solving Chapter 9 are Use Number Lines to Multiply by Multiples of 10, Use Place Value to Multiply by Multiples of 10, Use Properties to Multiply by Multiples of 10, and Problem Solving: Multiplication and Division. Solve all the problems from BIM Book Grade 3 Chapter 9 Multiples and Problem Solving to enhance your math skills.<\/p>\n
Lesson – 1: Use Number Lines to Multiply by Multiples of 10<\/strong><\/p>\n Lesson – 2: Use Place Value to Multiply by Multiples of 10<\/strong><\/p>\n Lesson – 3: Use Properties to Multiply by Multiples of 10<\/strong><\/p>\n Lesson – 4: Problem Solving: Multiplication and Division<\/strong><\/p>\n Lesson – 5: Problem Solving: All Operations<\/strong><\/p>\n Performance Task<\/strong><\/p>\n Explore and Grow<\/strong><\/p>\n Show 5 jumps of 3. Write a multiplication equation shown by the number line. Answer: 5 \u00d7 3 = 15<\/p>\n Explanation: Show 5 jumps of 30. Write a multiplication equation shown by the number line. Explanation:<\/p>\n The count starts from 0. Structure<\/strong> Think and Grow: Number Lines and Multiples of 10<\/strong><\/p>\n Example<\/strong> Answer: 3 \u00d7 50 = 150<\/p>\n Explanation: Show and Grow<\/strong><\/p>\n Question 1. Explanation: Question 2. Explanation: Apply and Grow: Practice<\/strong><\/p>\n Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Think and Grow: Modeling Real Life<\/strong><\/p>\n A section of an airplane has 20 rows of seats. Each row has 7 seats. Can the section seat more than 150 people? Explain. Answer: Show and Grow<\/strong><\/p>\n Question 8. Question 9. Question 10. Question 1. Answer: 90<\/p>\n Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Question 6. Question 7. Review & Refresh<\/strong><\/p>\n Question 8. Answer: 5<\/p>\n Explanation: Question 9. Explanation: Explore and Grow<\/strong><\/p>\n Use models to find each product. Draw your models. i. Structure<\/strong> Think and Grow: Place Value and Multiples of 10<\/strong><\/p>\n Example<\/strong> Answer: Step 2: Show and Grow<\/strong><\/p>\n Make a quick sketch to find the product<\/strong> Question 2. Apply and Grow: Practice<\/strong><\/p>\n Use place value to find the product.<\/strong> Question 4. Question 5. Question 6. Find the product<\/strong> Explanation: Question 8. Explanation: Question 9. Explanation: Question 10. Explanation: Question 11. Explanation: Question 12. Explanation: Question 13. Question 14. Think and Grow: Modeling Real Life<\/strong><\/p>\n Newton saves $30 each month for 6 months. Does he have enough money to buy the drone? Explain. Show and Grow<\/strong><\/p>\n Question 15. Question 16. Question 17. Make a quick sketch to find the product.<\/strong> Question 2. Use place value to find the product<\/strong> Question 4. Find the product.<\/strong> Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Question 10. Question 11. Review & Refresh<\/strong><\/p>\n Question 12. Explore and Grow<\/strong><\/p>\n Use the colored rectangles to find 5 \u00d7 30. Explanation: Reasoning<\/strong> Think and Grow: Properties and Multiples of 10<\/strong><\/p>\n Example:<\/strong> Answer: Another Way:<\/strong> Answer: Show and Grow<\/strong><\/p>\n Question 1. Question 2. Apply and Grow: Practice<\/strong><\/p>\n Use properties to find the product<\/strong> Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Find the missing factor.<\/strong> Explanation: Question 8. Explanation: Question 9. Explanation: Question 10. Question 11. Question 12. Think and Grow: Modeling Real Life<\/strong><\/p>\n There are 8 tables in the classroom. There are 5 students at each table. Each student has 10 markers. How many markers do the students have in all? Answer: Show and Grow<\/strong><\/p>\n Question 13. Question 14. Question 1. Question 2. Use properties to find the product.<\/strong> Explanation: Question 4. Explanation: Find the missing factor<\/strong> Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Question 9. Question 10. Question 11. Review & Refresh<\/strong><\/p>\n Find the quotient<\/strong> Explanation: Question 13. Explanation: Question 14. Explanation: Question 15. Explanation: Explore and Grow<\/strong><\/p>\n Use any strategy to solve the problem. Structure<\/strong> Think and Grow: Using the Problem-Solving Plan<\/strong><\/p>\n Example<\/strong> What do you need to find?<\/strong> Answer:<\/p>\n \u2022 A box has 8 burritos. What do you know?<\/strong> Answer: Make a Plan<\/strong> Answer:<\/p>\n \u2022 Divide 40 by 8 to find how many burritos the group needs to buy. Solve<\/strong> Step 2: Answer: Show and Grow<\/strong><\/p>\n Question 1. Apply and Grow: Practice<\/strong><\/p>\n Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.<\/strong> Question 3. Question 4. Question 5. Think and Grow: Modeling Real Life<\/strong><\/p>\n There are 4 crates of milk bottles. Each crate holds 20 bottles. You hand out an equal number of bottles to 10 tables of students. How many bottles of milk does each table of students get? Answer: Show and Grow<\/strong><\/p>\n Question 6. Question 7. Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.<\/strong> Question 2. Question 3. Question 4. Question 5. Question 6. Review & Refresh<\/strong><\/p>\n Round to the nearest ten to estimate the difference<\/strong> Question 8. Question 9. Explore and Grow<\/strong><\/p>\n Use any strategy to solve the problem. Structure<\/strong> Think and Grow: One Equation with Two Operations<\/strong><\/p>\n Example<\/strong> Step 2: Subtract from left to right. Answer: Show and Grow<\/strong><\/p>\n Question 1. Question 2. Apply and Grow: Practice<\/strong><\/p>\n Write an equation to solve. Use a letter to represent the unknown number. Check whether your answer is reasonable.<\/strong> Question 4. Question 5. Question 6. Question 7. Think and Grow: Modeling Real Life<\/strong><\/p>\n Newton has $135. He saves $20 each week for 8 weeks. How much money does he have now? Answer: Show and Grow<\/strong><\/p>\n Question 8. Question 9. Question 10. Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Review & Refresh<\/strong><\/p>\n\n
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<\/a>Lesson 9.1 Use Number Lines to Multiply by Multiples of 10<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-1.png\")
\n____ \u00d7 _____ = _____<\/p>\n
\nThe count starts from 0.
\nYou have put 5 jumps of 3 on the number line.
\nSkip by 3 five times.
\nThat means from 0 to 3, 3 to 6, 6 to 9, 9 to 12, 12 to 15.
\n5 \u00d7 3 = 15<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-2.png\")
\n____ \u00d7 ____ = _____
\nAnswer: 5 \u00d7 30 = 150<\/p>\n
\nYou have put 5 jumps of 30 on the number line.
\nSkip by 30 five times.
\nThat means from 0 to 30, 30 to 60, 60 to 90, 90 to 120, 120 to 150.
\n5 \u00d7 30 = 150<\/p>\n
\nCompare the models. How are they the same? How are they different?
\nAnswer: The Multiplication equation for both the models are the same but counts are different.<\/p>\n
\nFind 3 \u00d7 50.
\n3 \u00d7 50 means 3 groups of 50.
\nNumber of jumps: ______
\nSize of each jump: ______
\nStart at 0. Skip count by 50 three times.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-3.png\")
<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 3 jumps of 50.
\nThe count starts at 0. Skip 50 three times.
\nNumber of jumps = 3
\nSize of each jump = 50
\n3 \u00d7 50 = 150<\/p>\n
\nFind 8 \u00d7 20.
\nNumber of jumps: ______
\nSize of each jump: ______
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-4.png\")
\n8 \u00d7 20 = _____
\nAnswer: 160<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 8 jumps of 20.
\nThe count starts at 0. Skip 20 eight times.
\nNumber of jumps = 8
\nSize of each jump = 20
\n8 \u00d7 20 = 160<\/p>\n
\nFind 4 \u00d7 30
\nNumber of jumps: _______
\nSize of each jump: _______
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-5.png\")
\n4 \u00d7 30 = _____
\nAnswer: 120<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 4 jumps of 30.
\nThe count starts at 0. Skip 30 four times.
\nNumber of jumps = 4
\nSize of each jump = 30
\n4 \u00d7 30 = 120<\/p>\n
\nFind 2 \u00d7 60.
\nNumber of jumps: _______
\nSize of each jump: _______
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-6.png\")
\n2 \u00d7 60 = _____
\nAnswer: 120<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 2 jumps of 60.
\nThe count starts at 0. Skip 60 two times.
\nNumber of jumps = 2
\nSize of each jump = 60
\n2 \u00d7 60 = 120<\/p>\n
\nFind 5 \u00d7 50
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-7.png\")
\n5 \u00d7 50 = _____
\nAnswer: 250<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 5 jumps of 50.
\nThe count starts at 0. Skip 50 five times.
\nNumber of jumps = 5
\nSize of each jump = 50
\n5 \u00d7 50 = 250<\/p>\n
\nFind 3 \u00d7 70.
\n3 \u00d7 70 = _____
\nAnswer: 210<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 3 jumps of 70.
\nThe count starts at 0. Skip 70 three times.
\nNumber of jumps = 3
\nSize of each jump = 70
\n3 \u00d7 70 = 210<\/p>\n
\nFind 30 \u00d7 6.
\n30 \u00d7 6 = _____
\nAnswer: 180<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 6 jumps of 30.
\nThe count starts at 0. Skip 30 six times.
\nNumber of jumps = 6
\nSize of each jump = 30
\n30 \u00d7 6 = 180<\/p>\n
\nStructure
\nShow 2 \u00d7 40 on one number line and 4 \u00d7 20 on the other. What is the same about the number lines? What is different?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-10.png\")
\nAnswer: The model is the same on the number line. The counts are different and the number of jumps on the number line is different.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-11.png\")
\nModel:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-12.png\")
\nThe section ______ seat more than 150 people.
\nExplain:<\/p>\n
\nGiven that,
\nA section of an airplane has 20 rows of seats. Each row has 7 seats.
\n20 \u00d7 7 = 140 seats
\nThus the section cannot seat more than 150 people.<\/p>\n
\nThere are 9 rows of seats in an auditorium. Each row has 30 seats. Can the auditorium seat more than 250 people? Explain.
\nAnswer:
\nGiven that,
\nThere are 9 rows of seats in an auditorium. Each row has 30 seats.
\n9 \u00d7 30 = 270 seats
\n270 – 250 = 20
\nThus the auditorium seat more than 250 people.<\/p>\n
\nA mechanic installs new tires on 20 cars and 20 pickup trucks. How many new tires does the mechanic install in all?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-13.png\")
\nAnswer:
\nGiven that,
\nA mechanic installs new tires on 20 cars and 20 pickup trucks.
\n20 \u00d7 4 = 80 cars
\n20 \u00d7 4 = 80 trucks
\n80 + 80 = 160 new tires
\nThus the mechanic install 160 new tires.<\/p>\n
\nDIG DEEPER!<\/strong>
\nNewton saves $5 each week for 20 weeks. How much more money does he need to buy a new bike that costs $130? If he continues to save the same amount each week, how many more weeks does he need to save to buy the bike? Explain.
\nAnswer:
\nGiven that,
\nNewton saves $5 each week for 20 weeks.
\n5 \u00d7 20 = $100
\n$130 – $100 = $30
\nThus Newton need to save $30 to buy the bike.<\/p>\n<\/a>Use Number Lines to Multiply by Multiples of 10 Homework & Practice 9.1<\/h3>\n
\nFind 3 \u00d730.
\nNumber of jumps: _______
\nSize of each jump: _______
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-14.png\")
\n3 \u00d7 30 =<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 3 jumps of 30.
\nThe count starts at 0. Skip 30 three times.
\nNumber of jumps = 3
\nSize of each jump = 30
\n3 \u00d7 30 = 90<\/p>\n
\nFind 7 \u00d7 60.
\nNumber of jumps: _______
\nSize of each jump: _______
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-15.png\")
\n7 \u00d7 60 = _____
\nAnswer: 420<\/p>\n
\nFrom the figure, we can observe that the count starts from 0.
\nIt means that there are 7 jumps of 60.
\nThe count starts at 0. Skip 60 seven times.
\nNumber of jumps = 7
\nSize of each jump = 60
\n7 \u00d7 60 = 420<\/p>\n
\nFind 4 \u00d7 40.
\n4 \u00d7 40 = ____
\nAnswer: 160<\/p>\n
\nWe can find the product by using the distributive property.
\n4 \u00d7 40 = 4 \u00d7 (20 + 20)
\n4 \u00d7 40 = (4 \u00d7 20) + (4 \u00d7 20)
\n4 \u00d7 40 = 80 + 80
\n4 \u00d7 40 = 160<\/p>\n
\nFind 80 \u00d7 3.
\n80 \u00d7 3 = _____
\nAnswer: 240<\/p>\n
\nWe can find the product by using the associative property.
\n80 \u00d7 3 = (8 \u00d7 10) \u00d7 3
\n80 \u00d7 3 = 8 \u00d7 3 \u00d7 10
\n80 \u00d7 3 = 24 \u00d7 10
\n80 \u00d7 3 = 240<\/p>\n
\nStructure
\nComplete the number line. Then write the multiplication equation shown on the number line.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-18.png\")
\n____ \u00d7 ____ = _____
\nAnswer: 5 \u00d7 30 = 150
\nBy using the number line you can write the multiplication equation.
\n30 + 30 + 30 + 30 + 30 = 150<\/p>\n
\nModeling Real Life<\/strong>
\nA gymnasium has 9 rows of seats. Each row has 50 seats. Can the gymnasium seat more than 500 people? Explain.
\nAnswer:
\nGiven,
\nA gymnasium has 9 rows of seats. Each row has 50 seats.
\n9 \u00d7 50 = 450 seats
\n450 – 500 = -50 people
\nNo the gymnasium cannot seat more than 500 people.<\/p>\n
\nModeling Real Life<\/strong>
\nTen adults and 20 children fill their bike tires at a public pump. How many tires are filled in all?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.1-19.png\")
\nAnswer:
\nGiven that,
\nTen adults and 20 children fill their bike tires at a public pump.
\n10 \u00d7 2 = 20
\n20 \u00d7 2 = 40
\n20 + 40 = 60
\nThus 60 tires are filled in all.<\/p>\n
\nThere are 35 counters. The counters are in 7 equal rows. How many counters are in each row?
\n7 rows of _____
\n35 \u00f7 7 = _____<\/p>\n
\nThere are 35 counters.
\nThe counters are in 7 equal rows.
\n35\/7 = 5
\n7 rows of 5
\n35 \u00f7 7 = 5
\nThus there are 5 counters in each row.<\/p>\n
\nYou have 32 counters. You arrange them with 8 counters in each row. How many rows of counters do you make?
\n_____ rows of 8
\n32 \u00f7 8 = ____
\nAnswer: 4<\/p>\n
\nGiven that,
\nYou have 32 counters. You arrange them with 8 counters in each row.
\n32\/8 = 4
\nThus you can make 4 rows of 8.<\/p>\n<\/a>Lesson 9.2 Use Place Value to Multiply by Multiples of 10<\/h3>\n
\n4 \u00d7 6 = _____
\n4 \u00d7 60 = _____
\nAnswer: 24, 240<\/p>\n![\"Bigideas](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Bigideas-Math-Answers-3rd-Grade-Chapter-9-img_1-300x102.png\")
\nMultiply the rows and columns
\n4 \u00d7 6 = 24
\nii. Multiply the two numbers 4 and 60
\n4 \u00d7 60 = 240<\/p>\n
\nCompare the models. How are they the same? How are they different?
\nAnswer: The models for both the problem are the same but the columns are different.<\/p>\n
\nFind 4 \u00d7 70.
\nStep 1:
\nMake a quick sketch to model the product.
\nThink: 4 groups of 70, or 7 tens.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-1.png\")
\n4 \u00d7 70 = 4 \u00d7 ____ tens
\n4 \u00d7 70 = ____ tens<\/p>\n
\n4 \u00d7 70 = 4 \u00d7 7 tens
\n4 \u00d7 70 = 28 tens<\/p>\n
\nRegroup ____ tens
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-3.png\")
\nThere are _____ hundreds and _____ tens.
\nSo, 4 \u00d7 70 = _____.
\nAnswer:
\nThere are 2<\/span> hundred and 8<\/span> tens.
\nNow regroup tens.
\nThere are 2 tens
\nSo, group the tens.
\n2 tens are grouped and the remaining is 8.
\n4 \u00d7 70 = 280<\/p>\n
\nQuestion 1.
\n3 \u00d7 80 = ______
\nAnswer: 240
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-grade-3-chapter-9-img_2.jpg\")
\nThere are 2 hundred and 4 tens.<\/p>\n
\n5 \u00d7 40 = _____
\nAnswer: 200
\n![\"BIM](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-Answer-Key-Grade-3-Chapter-9-img_3.jpg\")
\n5 \u00d7 40 = 20 tens
\nThere are 2 hundred and 0 tens.<\/p>\n
\nQuestion 3.
\n3 \u00d7 90 = 3 \u00d7 ____ tens
\n3 \u00d7 90 = ____ tens
\n3 \u00d7 90 = _____
\nAnswer:
\n3 \u00d7 90 = 3 \u00d7 9 tens
\n3 \u00d7 90 = 27 tens
\n3 \u00d7 90 = 270<\/p>\n
\n6 \u00d7 60 = 6 \u00d7 ____ tens
\n6 \u00d7 60 = ____ tens
\n6 \u00d7 60 = _____
\nAnswer:
\n6 \u00d7 60 = 6 \u00d7 6 tens
\n6 \u00d7 60 = 36 tens
\n6 \u00d7 60 = 360<\/p>\n
\n2 \u00d7 70 = 2 \u00d7 ____ tens
\n2 \u00d7 70 = ____ tens
\n2 \u00d7 70 = _____
\nAnswer:
\n2 \u00d7 70 = 2 \u00d7 7 tens
\n2 \u00d7 70 = 14 tens
\n2 \u00d7 70 = 140<\/p>\n
\n9 \u00d7 20 = 9 \u00d7 ____ tens
\n9 \u00d7 20 = ____ tens
\n9 \u00d7 20 = _____
\nAnswer:
\n9 \u00d7 20 = 9 \u00d7 2 tens
\n9 \u00d7 20 = 18 tens
\n9 \u00d7 20 = 180<\/p>\n
\nQuestion 7.
\n3 \u00d7 30 = ____
\nAnswer: 90<\/p>\n
\n3 \u00d7 30 = 3 \u00d7 3 tens
\n3 \u00d7 30 = 9 tens
\n3 \u00d7 30 = 90<\/p>\n
\n6 \u00d7 80 = ____
\nAnswer: 480<\/p>\n
\n6 \u00d7 80 = 6 \u00d7 8 tens
\n6 \u00d7 80 = 48 tens
\n6 \u00d7 80 = 480<\/p>\n
\n4 \u00d7 40 = _____
\nAnswer: 160<\/p>\n
\n4 \u00d7 40 = 4 \u00d7 4 tens
\n4 \u00d7 40 =\u00a0 16 tens
\n4 \u00d7 40 = 160<\/p>\n
\n7 \u00d7 50 = _____
\nAnswer: 350<\/p>\n
\n7 \u00d7 50 = 7 \u00d7 5 tens
\n7 \u00d7 50 = 35 tens
\n7 \u00d7 50 = 350<\/p>\n
\n8 \u00d7 70 = _____
\nAnswer: 560<\/p>\n
\n8 \u00d7 70 = 8 \u00d7 7 tens
\n8 \u00d7 70 = 56 tens
\n8 \u00d7 70 = 560<\/p>\n
\n5 \u00d7 90 = _____
\nAnswer: 450<\/p>\n
\n5 \u00d7 90 = 5 \u00d7 9 tens
\n5 \u00d7 90 = 45 tens
\n5 \u00d7 90 = 450<\/p>\n
\nReasoning<\/strong>
\nExplain why the product of 6 and 30 has 1 zero and the product of 4 and 50 has 2 zeros.
\nAnswer:
\n6 \u00d7 30 = 180
\n4 \u00d7 50 = 200
\n4 and 50 has two zeros because it is multiplied by 50 If the number is multiplied by 5 or 10 you will get two zeros.<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nIs Descartes correct? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-4.png\")
\nAnswer: Yes, Descartes is correct.
\n3 \u00d7 7 = 21
\n3 \u00d7 70 = 210
\nSo the product of 3 and 70 is equal to the product of 3 and 7 with a 0 written after it.<\/p>\n
\nNewton _______ have enough money to buy the drone.$189
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-5.png\")
\nAnswer:
\nGiven that,
\nNewton saves $30 each month for 6 months.
\n6 \u00d7 $30 = $180
\nThe cost of the drone is $189.
\n180 – 189 = -9
\nTherefore Newton does not have enough money to buy the drone.<\/p>\n
\nDescartes saves $20 each month for 8 months. Does he have enough money to buy the remote control jeep? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-6.png\")
\nAnswer:
\nGiven that,
\nDescartes saves $20 each month for 8 months.
\n8 \u00d7 $20 = $160
\nThe cost of remote control jeep is $129
\n160 – 129 = $31
\nThus Descartes has enough money to buy the remote control jeep.<\/p>\n
\nYou practice playing the guitar for 40 minutes every day. How many minutes do you practice in one week?
\nAnswer:
\nGiven that,
\nYou practice playing the guitar for 40 minutes every day.
\n1 week = 7 days
\n7 \u00d7 40 = 280
\nThus you practice 280 minutes in one week.<\/p>\n
\nA box of snacks has 25 bags of pretzels and 25 bags of peanuts. How many bags are in 9 boxes?
\nAnswer:
\nGiven that,
\nA box of snacks has 25 bags of pretzels and 25 bags of peanuts.
\n25 + 25 = 50
\n50 \u00d7 9 = 450
\nThus there are 450 bags in 9 boxes.<\/p>\n<\/a>Use Place Value to Multiply by Multiples of 10 Homework & Practice 9.2<\/h3>\n
\nQuestion 1.
\n5 \u00d7 70 = _____
\nAnswer: 350
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Grade-3-Chapter-9-Answer-Key-img_4.jpg\")
<\/p>\n
\n3 \u00d7 60 = ____
\nAnswer: 180
\n![\"BIM](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/BIM-Answers-Grade-3-Chapter-9-Multiplies-and-problem-solving-img_5.jpg\")
<\/p>\n
\nQuestion 3.
\n8 \u00d7 50 = 8 \u00d7 ____ tens
\n8 \u00d7 50 = ____ tens
\n8 \u00d7 50 = _____
\nAnswer:
\n8 \u00d7 50 = 8 \u00d7 5 tens
\n8 \u00d7 50 = 40 tens
\n8 \u00d7 50 = 400<\/p>\n
\n7 \u00d7 60 = 7 \u00d7 ____ tens
\n7 \u00d7 60 = ____ tens
\n7 \u00d7 60 = _____
\nAnswer:
\n7 \u00d7 60 = 7 \u00d7 6 tens
\n7 \u00d7 60 = 42 tens
\n7 \u00d7 60 = 420<\/p>\n
\nQuestion 5.
\n6 \u00d7 90 = _____
\nAnswer: 540<\/p>\n
\n6 \u00d7 90 = 6 \u00d7 9 tens
\n6 \u00d7 90 = 54 tens
\n6 \u00d7 90 = 540<\/p>\n
\n8 \u00d7 30 = _____
\nAnswer: 240<\/p>\n
\n8 \u00d7 30 = 8 \u00d7 3 tens
\n8 \u00d7 30 = 24 tens
\n8 \u00d7 30 = 240<\/p>\n
\n5 \u00d7 40 = _____
\nAnswer: 200<\/p>\n
\n5 \u00d7 40 = 5 \u00d7 4 tens
\n5 \u00d7 40 = 20 tens
\n5 \u00d7 40 = 200<\/p>\n
\nIs Newton correct? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-7.png\")
\nAnswer: Newton is incorrect<\/p>\n
\n6 \u00d7 50 = 6 \u00d7 5 tens
\n6 \u00d7 50 = 30 tens
\n6 \u00d7 50 = 300
\nBy this we can say that Newton is incorrect.<\/p>\n
\nStructure<\/strong>
\nWrite an equation for the quick sketch.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-8.png\")
\nAnswer: 2 \u00d7 60 = 120
\nThere are 1 group of tens and 2 are remaining.
\nSo, 2 \u00d7 60 = 120<\/p>\n
\nModeling Real Life<\/strong>
\nDescartes saves $50 each month for 5 months. Does he have enough money to buy the game system? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-9-Multiples-and-Problem-Solving-9.2-9.png\")
\nAnswer:
\nGiven that,
\nDescartes saves $50 each month for 5 months.
\n5 \u00d7 $50 = $250
\nThe cost of the game system is $205.
\n$250 – $205 = $45
\nThus Descartes has enough money to buy the game system.<\/p>\n
\nModeling Real Life<\/strong>
\nA group of staff members packs coolers for a field trip. Each cooler has 15 peanut butter sandwiches and 15 turkey sandwiches. How many sandwiches are in 7 coolers?
\nAnswer:
\nGiven that,
\nA group of staff members packs coolers for a field trip.
\nEach cooler has 15 peanut butter sandwiches and 15 turkey sandwiches.
\n15 + 15 = 30
\n7 \u00d7 30 = 210
\nThus there are 210 sandwiches in 7 coolers.<\/p>\n
\nRound 282 to the nearest ten and to the nearest hundred.
\nNearest ten: ____
\nNearest hundred: _____
\nAnswer:
\nFirst, 282 rounded to the nearest ten is 280.
\nThe number nearest hundred to 282 is 300.<\/p>\n<\/a>Lesson 9.3 Use Properties to Multiply by Multiples of 10<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-1.png\")
\nSo, 5 \u00d7 30 = ______
\nAnswer: 50 + 50 + 50 = 150<\/p>\n
\nThe multiplication equation for the yellow-colored rectangle is 5 \u00d7 10 = 50
\nThe multiplication equation for the blue-colored rectangle is 5 \u00d7 10 = 50
\nThe multiplication equation for the red-colored rectangle is 5 \u00d7 10 = 50
\n50 + 50 + 50 = 150<\/p>\n
\nHow does this model relate to the Distributive Property?
\nAnswer:
\nYes, you can relate the above equation to the distributive property.
\n5 \u00d7 30 = 5 \u00d7 (10 + 20)
\n5 \u00d7 30 = (5 \u00d7 10) + (5 \u00d7 20)
\n5 \u00d7 30 = 50 + 100
\n5 \u00d7 30 = 150<\/p>\n
\nFind 6 \u00d7 20
\nOne Way:<\/strong>
\nUse the Associative Property of Multiplication
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-2.png\")
\n6 \u00d7 20 = 6 \u00d7 (_____ \u00d7 10)
\n6 \u00d7 20 = (6 \u00d7 ____) \u00d7 10
\n6 \u00d7 20 = ____ \u00d7 10
\n6 \u00d7 20 = ____
\nRewrite 20 as _____ \u00d7 10
\nAssociative Property of Multiplication<\/p>\n
\nRewrite 20 as 2\u00d7 10
\n6 \u00d7 20 = 6 \u00d7 (2 \u00d7 10)
\n6 \u00d7 20 = (6 \u00d7 2) \u00d7 10
\n6 \u00d7 20 = 12 \u00d7 10
\n6 \u00d7 20 = 120<\/p>\n
\nUse the Distributive Property
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-3.png\")
\n6 \u00d7 20 = 6 \u00d7 (10 \u00d7 _____)
\n6 \u00d7 20 = (6 \u00d7 10) \u00d7 (6 \u00d7 ____)
\n6 \u00d7 20 = ____ + _____
\n6 \u00d7 20 = ____<\/p>\n
\nRewrite 20 as 10 + 10
\nBy using the Distributive Property we can find the product.
\n6 \u00d7 20 = 6 \u00d7 (10 + 10)
\n6 \u00d7 20 = (6 \u00d7 10) \u00d7 (6 \u00d7 10)
\n6 \u00d7 20 = 60 + 60
\n6 \u00d7 20 = 120<\/p>\n
\nUse the Associative Property of Multiplication to find 4 \u00d7 60.
\n4 \u00d7 60 = 4 \u00d7 (_____ \u00d7 10)
\n4 \u00d7 60 = (4 \u00d7 ____) \u00d7 10
\n4 \u00d7 60 = ____ \u00d7 10
\n4 \u00d7 60 = ____
\nAnswer:
\nYou have to find the product by using the Associative Property of Multiplication.
\n4 \u00d7 60 = 4 \u00d7 (6 \u00d7 10)
\n4 \u00d7 60 = (4 \u00d7 6) \u00d7 10
\n4 \u00d7 60 = 24 \u00d7 10
\n4 \u00d7 60 = 240
\nThus the product of 4 \u00d7 60 = 240.<\/p>\n
\nUse the Distributive Property to find 9 \u00d7 20.
\n9 \u00d7 20 = 9 \u00d7 (10 \u00d7 _____)
\n9 \u00d7 20 = (9 \u00d7 10) \u00d7 (9 \u00d7 ____)
\n9 \u00d7 20 = ____ + _____
\n9 \u00d7 20 = ____
\nAnswer:
\nYou have to find the product by using the Distributive Property of Multiplication.
\n9 \u00d7 20 = 9 \u00d7 (10 + 10)
\n9 \u00d7 20 = (9 \u00d7 10) + (9 \u00d7 10)
\n9 \u00d7 20 = 90 + 90
\n9 \u00d7 20 = 180<\/p>\n
\nQuestion 3.
\n7 \u00d7 30 = _____
\nAnswer: 210<\/p>\n
\nYou have to find the product by using the Associative Property of Multiplication.
\n7 \u00d7 30 = 7 \u00d7 (3 \u00d7 10)
\n7 \u00d7 30 = (7 \u00d7 3) \u00d7 10
\n7 \u00d7 30 = 21 \u00d7 10
\n7 \u00d7 30 = 210<\/p>\n
\n5 \u00d7 80 = _____
\nAnswer: 400<\/p>\n
\nYou have to find the product by using the Associative Property of Multiplication.
\n5 \u00d7 80 = 5 \u00d7 (8 \u00d7 10)
\n5 \u00d7 80 = (5 \u00d7 8) \u00d7 10
\n5 \u00d7 80 = 40 \u00d7 10
\n5 \u00d7 80 = 400<\/p>\n
\n5 \u00d7 20 = _____
\nAnswer: 100<\/p>\n
\nYou have to find the product by using the Associative Property of Multiplication.
\n5 \u00d7 20 = 5 \u00d7 (10 \u00d7 2)
\n5 \u00d7 20 = (5 \u00d7 2) \u00d7 10
\n5 \u00d7 20 = 10 \u00d7 10
\n5 \u00d7 20 = 100<\/p>\n
\n3 \u00d7 90 = _____
\nAnswer: 270<\/p>\n
\nYou have to find the product by using the Associative Property of Multiplication.
\n3 \u00d7 90 = 3 \u00d7 (9 \u00d7 10)
\n3 \u00d7 90 = (3 \u00d7 9) \u00d7 10
\n3 \u00d7 90 = 27 \u00d7 10
\n3 \u00d7 90 = 270<\/p>\n
\nQuestion 7.
\n8 \u00d7 ____ = 320
\nAnswer: 40<\/p>\n
\nLet the missing factor be x.
\n8 \u00d7 x = 320
\nx = 320\/8
\nx = 40
\nThus the missing factor is 40.<\/p>\n
\n____ \u00d7 50 = 300
\nAnswer: 6<\/p>\n
\nLet the missing factor be y.
\ny \u00d7 50 = 300
\ny = 300\/50
\ny = 6
\nThus the missing factor is 6.<\/p>\n
\n_____ \u00d7 30 = 270
\nAnswer: 9<\/p>\n
\nLet the missing factor be z.
\nz \u00d7 30 = 270
\nz = 270\/30
\nz = 9
\nThus the missing factor is 9.<\/p>\n
\nNumber Sense<\/strong>
\nUse the Associative Property of Multiplication to show why
\n4 \u00d7 20 = 8 \u00d7 10.
\nAnswer:
\nYou have to find the product by using the Associative Property of Multiplication.
\n4 \u00d7 20 = 8 \u00d7 10
\n4 \u00d7 (2 \u00d7 10) = 8 \u00d7 10
\n8 \u00d7 10 = 8 \u00d7 10
\nBy this we can say that 4 \u00d7 20 = 8 \u00d7 10.<\/p>\n
\nOpen-Ended<\/strong>
\nWrite three expressions equal to 240.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-4.png\")
\nAnswer:
\nThe three expressions equal to 240 is
\n240\/3 = 80
\n2 \u00d7 40 | 2 \u00d7 40 | 2 \u00d7 40
\n80 + 80 + 80 = 240<\/p>\n
\nNumber Sense<\/strong>
\nWhich equations show the Distributive Property?
\n2 \u00d7 20 = (2 \u00d7 10) + (2 \u00d7 10)
\n4 \u00d7 (3 \u00d7 10) = (4 \u00d7 3) \u00d7 10
\n(7 \u00d7 10) + (7 \u00d7 10) = 7 \u00d7 20
\nAnswer:
\n2 \u00d7 20 = (2 \u00d7 10) + (2 \u00d7 10) is the distributive property.
\n4 \u00d7 (3 \u00d7 10) = (4 \u00d7 3) \u00d7 10 shows the associative property.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-5.png\")
\nThere are ______ markers at each table.
\nThe students have ______ markers in all.<\/p>\n
\nGiven that,
\nThere are 8 tables in the classroom.
\nThere are 5 students at each table.
\n8 \u00d7 5 = 40
\nEach student has 10 markers.
\n40 \u00d7 10 = 400<\/p>\n
\nYour teacher buys 5 boxes of pens. Each box has 6 bundles of 10 pens. How many pens does your teacher buy in all?
\nAnswer:
\nGiven that,
\nYour teacher buys 5 boxes of pens. Each box has 6 bundles of 10 pens.
\n6 \u00d7 10 = 60
\n60 \u00d7 5 = 300 pens
\nThus the teacher buy 300 pens.<\/p>\n
\nDIG DEEPER!<\/strong>
\nNewton earns $30 each work shift. He wants to buy Descartes a cat tree. The tree costs $150. After how many work shifts can Newton buy the tree?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-6.png\")
\nAnswer:
\nGiven,
\nNewton earns $30 each work shift. He wants to buy Descartes a cat tree. The tree costs $150.
\nTo find how many work shifts can Newton buy the tree, you need to divide the cost of the tree by newton’s earned amount.
\n150\/30 = 5
\nAfter 5 work shifts, Newton can buy the tree.<\/p>\n<\/a>Use Properties to Multiply by Multiples of 10 Homework & Practice 9.3<\/h3>\n
\nUse the Associative Property of Multiplication to find 6 \u00d7 70.
\n6 \u00d7 70 = 6 \u00d7 (_____ \u00d7 10)
\n6 \u00d7 70 = (6 \u00d7 ____) \u00d7 10
\n6 \u00d7 70 = ____ \u00d7 10
\n6 \u00d7 70 = ____
\nAnswer:
\n6 \u00d7 70 = 6 \u00d7 (7 \u00d7 10)
\n6 \u00d7 70 = (6 \u00d7 7) \u00d7 10
\n6 \u00d7 70 = 42 \u00d7 10
\n6 \u00d7 70 = 420<\/p>\n
\nUse the Distributive Property to find 3 \u00d7 20.
\n3 \u00d7 20 = 3 \u00d7 (10 \u00d7 _____)
\n3 \u00d7 20 = (3 \u00d7 10) \u00d7 (3 \u00d7 ____)
\n3 \u00d7 20 = ____ + _____
\n3 \u00d7 20 = ____
\nAnswer:
\n3 \u00d7 20 = 3 \u00d7 (10 \u00d7 2)
\n3 \u00d7 20 = (3 \u00d7 10) \u00d7 (1 \u00d7 2)
\n3 \u00d7 20 = 30 \u00d7 2
\n3 \u00d7 20 = 60<\/p>\n
\nQuestion 3.
\n9 \u00d7 20 = _____
\nAnswer: 180<\/p>\n
\nWe can find the product by using the distributive property.
\n9 \u00d7 20 = 9 \u00d7 (10 + 10)
\n9 \u00d7 20 = (9 \u00d7 10) + (9 \u00d7 10)
\n9 \u00d7 20 = 90 + 90
\n9 \u00d7 20 = 180<\/p>\n
\n5 \u00d7 30 = ____
\nAnswer: 150<\/p>\n
\nWe can find the product by using the associative property.
\n5 \u00d7 30 = (5 \u00d7 3) \u00d7 10
\n5 \u00d7 30 = 15 \u00d7 10
\n5 \u00d7 30 = 150<\/p>\n
\nQuestion 5.
\n____ \u00d7 60 = 180
\nAnswer: 3<\/p>\n
\nLet the missing factor be x.
\nx \u00d7 60 = 180
\nx = 180\/60
\nx = 3
\nThus the missing factor is 3.<\/p>\n
\n6 \u00d7 ____ = 240
\nAnswer: 40<\/p>\n
\nLet the missing factor be y.
\n6 \u00d7 y = 240
\ny = 240\/6
\ny = 40
\nThus the missing factor is 40.<\/p>\n
\n____ \u00d7 80 = 720
\nAnswer: 9<\/p>\n
\nLet the missing factor be z.
\nz \u00d7 80 = 720
\nz = 720\/80
\nz = 9
\nThus the missing factor is 9.<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nYour friend draws a model to find 4 \u00d7 20. Is your friend correct? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-7.png\")
\n4 \u00d7 10 = 40 4 \u00d7 10 = 40
\n40 + 40 = 80
\nSo, 4 \u00d7 20 = 80
\nAnswer: Yes your friend is correct.
\nThere are 4 rows and 20 shaded blocks
\n4 \u00d7 20 = 80<\/p>\n
\nNumber Sense<\/strong>
\nHow can you tell whether 7 \u00d7 40 or 8 \u00d7 70 is greater without finding the products?
\nAnswer: We can find a greater number by seeing the numbers.
\n7 < 8
\n40 < 70
\n7 \u00d7 40 = 280
\n8 \u00d7 70 = 560
\nSo, 7 \u00d7 40 < 8 \u00d7 70<\/p>\n
\nModeling Real Life<\/strong>
\nThere are 9 teams in a math competition. Each team has 6 students. Each student answers 10 questions. How many questions are answered in all?
\nAnswer:
\nGiven that,
\nThere are 9 teams in a math competition. Each team has 6 students.
\n9 \u00d7 6 = 54 students
\nEach student answers 10 questions.
\n54 \u00d7 10 = 540
\nThus the students answered 540 questions in all.<\/p>\n
\nDIG DEEPER!<\/strong>
\nA soccer team earns $40 each week washing cars. The team wants to buy an inflatable field for $240. After how many weeks can the team buy the field?
\nAnswer:
\nGiven that,
\nA soccer team earns $40 each week washing cars.
\nThe team wants to buy an inflatable field for $240.
\n240\/40 = 6
\nIt takes 6 weeks to buy the field.<\/p>\n
\nQuestion 12.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-8.png\")
\nAnswer: 6<\/p>\n
\nDivide the two numbers 3 and 18.
\n18\/3 = 6
\nThus the quotient is 6.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-9.png\")
\nAnswer: 8<\/p>\n
\nDivide the two numbers 4 and 32
\n32\/4 = 8
\nThus the quotient is 8.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-10.png\")
\nAnswer: 9<\/p>\n
\nDivide the two numbers 27 and 3
\n27\/3 = 9
\nThus the quotient is 9.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.3-11.png\")
\nAnswer: 4<\/p>\n
\nDivide the two numbers 4 and 16.
\n16\/4 = 4
\nThus the quotient is 4.<\/p>\n<\/a>Lesson 9.4 Problem Solving: Multiplication and Division<\/h3>\n
\nDescartes uses 72 blocks to build ships. He uses 9 blocks for each ship. Each ship has 2 fabric sails. How many sails does Descartes use?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-1.png\")
\nDescartes uses _____ fabric sails.
\nAnswer:
\nGiven that,
\nDescartes uses 72 blocks to build ships. He uses 9 blocks for each ship.
\n72\/9 = 8
\nEach ship has 2 fabric sails.
\n8 \u00d7 2 = 16 sails
\nTherefore Descartes uses 16 fabric sails.<\/p>\n
\nWhat equations did you use to solve? How can you write the equations using a letter to represent the number of fabric sails?
\nAnswer:
\nI used the division and multiplication equation to solve the problem.
\nFirst, you have to divide the number of blocks by the number of blocks for each ship.
\n72\/9 = 8
\nAfter that multiply the blocks by the number of fabric sails.
\n8 \u00d7 2 = 16<\/p>\n
\nA box of 8 burritos costs $9. How much does it cost a group of friends to buy 40 burritos?
\nUnderstand the Problem<\/strong><\/p>\n
\n\u2022 A box has ______ burritos.
\n\u2022 The box costs _____.
\n\u2022 A group of friends wants to buy ______ burritos.<\/p>\n
\n\u2022 The box costs $9.
\n\u2022 A group of friends wants to buy 40 burritos.<\/p>\n
\n\u2022 You need to find how much it _____ costs to buy.<\/p>\n
\nYou can find the answer by using the above question.
\n\u2022 You need to find how much burritos cost to buy.<\/p>\n
\nHow will you solve?
\n\u2022 Divide _____ by _____ to find how many _____ the group needs to buy.
\n\u2022 Then multiply the quotient by _____ to find the total cost.<\/p>\n
\n\u2022 Then multiply the quotient by 9 to find the total cost.<\/p>\n
\nStep 1:
\nHow many boxes does the group need to buy?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-2.png\")
<\/p>\n
\nUse to find the total cost.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-3.png\")
\nIt costs $ _____ for 40 burritos.<\/p>\n
\n
\nFirst divide 40\/8 = 5
\nb = 5
\n
\nc = 5 \u00d7 9 = 45
\nThus the total cost is $45.<\/p>\n
\nYou make 9 shots in a basketball game. Each shot is worth 2 points. Your friend has the same number of points. All of her shots are worth 3 points. How many shots does your friend make?
\nAnswer:
\nGiven that,
\nYou make 9 shots in a basketball game. Each shot is worth 2 points.
\n9 \u00d7 2 = 18 points
\nYour friend has the same number of points. All of her shots are worth 3 points.
\n18\/3 = 6
\nThus your friend needs to make 6 shots.<\/p>\n
\nQuestion 2.
\nYou read 3 chapters. Each chapter has 8 pages. Your friend reads the same number of pages. All of her chapters have 6 pages. How many chapters does your friend read?
\nAnswer:
\nGiven that,
\nYou read 3 chapters. Each chapter has 8 pages.
\n3 \u00d7 8 pages = 24 pages
\nYour friend reads the same number of pages. All of her chapters have 6 pages.
\n24\/6 = 4
\nThus your friend reads 4 pages.<\/p>\n
\nThere are 42 players in a basketball tournament. The players are divided into teams of 7 players. The teams are divided equally among 3 basketball courts. How many teams are at each basketball court?
\nAnswer:
\nGiven that,
\nThere are 42 players in a basketball tournament. The players are divided into teams of 7 players.
\n42\/7 = 6 teams
\nThe teams are divided equally among 3 basketball courts.
\n6\/3 = 3
\nThus there are 3 teams at each basketball court.<\/p>\n
\nYou have 2 dream catcher kits. Each kit makes 4 dream catchers. You make all of the dream catchers and sell them for $9 each. How much money do you earn?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-4.png\")
\nAnswer:
\nGiven that,
\nYou have 2 dream catcher kits. Each kit makes 4 dream catchers.
\n2 \u00d7 4 = 8 dream catchers
\nYou make all of the dream catchers and sell them for $9 each.
\n8 \u00d7 9 = $72
\nThus you earn $72.<\/p>\n
\nA box of 4 test tubes costs $6. How much does it cost to buy 20 test tubes?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-5.png\")
\nAnswer:
\nGiven that,
\nA box of 4 test tubes costs $6.
\n20\/4 = 5
\n5 \u00d7 $6 = $30
\nThus it costs $30 to buy 20 test tubes.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-6.png\")
\nUnderstand the problem:
\nMake a plan:
\nSolve:
\nEach table of students gets _____ bottles of milk.<\/p>\n
\nGiven that,
\nThere are 4 crates of milk bottles. Each crate holds 20 bottles.
\n4 \u00d7 20 = 80 bottles
\nYou hand out an equal number of bottles to 10 tables of students.
\n80\/10 = 8
\nTherefore each table of students gets 8 bottles of milk.<\/p>\n
\nSix groups of hikers have 2 cases of water to share equally. Each case has 30 bottles of water. How many bottles of water does each group get?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-7.png\")
\nAnswer:
\nGiven,
\nSix groups of hikers have 2 cases of water to share equally. Each case has 30 bottles of water.
\n2 \u00d7 30 = 60 bottles of water
\nThere are 6 groups so divide 60 by 6.
\n60\/6 = 10
\nThus each group gets 10 bottles of water.<\/p>\n
\nDIG DEEPER!<\/strong>
\nNewton and Descartes decide to buy 2 pet toys that cost $20 each. Newton saves $5 each week. Descartes saves $3 each week. If they combine their money, how long does it take them to save enough money to buy the toys?
\nAnswer:
\nGiven that,
\nNewton and Descartes decide to buy 2 pet toys that cost $20 each.
\n2 \u00d7 20 = $40
\nNewton saves $5 each week. Descartes saves $3 each week.
\n5 + 3 = 8
\n40\/8 = 5
\nThus it takes 5 weeks to buy the toys.<\/p>\n<\/a>Problem Solving: Multiplication and Division Homework & Practice 9.4<\/h3>\n
\nQuestion 1.
\nYour friend saves $5 each week for 8 weeks. He spends all of the money on 4 toys that each cost the same amount. How much does each toy cost?
\nAnswer:
\nGiven that,
\nYour friend saves $5 each week for 8 weeks.
\nHe spends all of the money on 4 toys that each cost the same amount.
\nTo find the cost of the toy we need to multiply your friend savings and the number of weeks.
\n8 \u00d7 5 = 40
\nThus the cost of the toy is $40.<\/p>\n
\nThere are 3 trees. Each tree has 2 birdhouses. Each birdhouse has 4 birds. How many birds are there in all?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-8.png\")
\nAnswer:
\nGiven that,
\nThere are 3 trees. Each tree has 2 birdhouses.
\n3 \u00d7 2 = 6 birdhouses
\nEach birdhouse has 4 birds.
\n6 \u00d7 4 = 24 birds
\nTherefore there are 24 birds in all.<\/p>\n
\nThere are 54 students at a field day who are divided equally into teams of 6 students. The teams are divided equally among 3 stations. How many teams are at each station?
\nAnswer:
\nGiven that,
\nThere are 54 students at a field day who are divided equally into teams of 6 students.
\n54\/6 = 9 teams
\nThe teams are divided equally among 3 stations.
\nAgain the teams are divided into 3 stations.
\n9\/3 = 3
\nThus there are 3 teams at each station.<\/p>\n
\nNewton runs an equal number of miles 2 days each week. He runs 8 miles each week. One mile is equal to 4 laps around the track. Which equation can you use to find how many laps Newton runs each day?
\nr = 8 \u00f7 4
\nr = 4 \u00f7 4
\nr = 4 \u00d7 4
\nr = 2 \u00d7 4
\nAnswer:
\nGiven that,
\nNewton runs an equal number of miles 2 days each week. He runs 8 miles each week. One mile is equal to 4 laps around the track.
\n8\/2 = 4
\nTo find how many laps Newton runs each day you need to divide 4 by 4
\nr = 4 \u00f7 4
\nThus the correct answer is option b.<\/p>\n
\nModeling Real Life<\/strong>
\nTen classrooms have 3 boxes of white boards to share equally. Each box has 30 white boards. How many white boards does each classroom get?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-9.png\")
\nAnswer:
\nGiven that,
\nTen classrooms have 3 boxes of white boards to share equally.
\nEach box has 30 white boards.
\n1 box = 30 whiteboards
\n3 boxes = 3 \u00d7 30 = 90 white boards
\nNow divide the whiteboards by number of classrooms.
\n90\/10 = 9
\nThus each classroom gets 9 whiteboards.<\/p>\n
\nDIP DEEPER!<\/strong>
\nNewton and Descartes decide to buy 2 amusement park tickets that cost $30 each. Newton saves $2 each week. Descartes saves $4 each week. If they combine their money, how long does it take them to save enough money to buy the tickets?
\nAnswer:
\nGiven that,
\nNewton and Descartes decide to buy 2 amusement park tickets that cost $30 each.
\nNewton saves $2 each week. Descartes saves $4 each week.
\n2 + 4 = 6
\nNow divide the ticket cost by their savings.
\n30\/6 = 5
\nTherefore it takes 5 weeks to save enough money to buy the tickets.<\/p>\n
\nQuestion 7.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-10.png\")
\nAnswer:
\n58 round to the nearest ten is 60.
\n27 round to the nearest ten is 30.
\n60
\n-30<\/span>
\n30
\nThus the estimated difference is 30.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-11.png\")
\nAnswer:
\n763 round to the nearest ten is 760.
\n415 round to the nearest ten is 420.
\n760
\n-420<\/span>
\n340
\nThus the estimated difference is 340.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.4-12.png\")
\nAnswer:
\n686 round to the nearest ten is 690.
\n24 round to the nearest ten is 20.
\n690
\n-20<\/span>
\n670
\nThus the estimated difference is 670.<\/p>\n<\/a>Lesson 9.5 Problem Solving: All Operations<\/h3>\n
\nYou are making 6 fruit baskets. Each basket has 3 pieces of fruit in it to start. You buy 18 bananas and divide them equally among the baskets. How many pieces of fruit are in each fruit basket now?
\nThere are ______ pieces of fruit in each fruit basket now.
\nAnswer:
\nGiven that,
\nYou are making 6 fruit baskets. Each basket has 3 pieces of fruit in it to start.
\n6 \u00d7 3 = 18
\nYou buy 18 bananas and divide them equally among the baskets.
\n18\/18 = 1
\nThus there are 4 pieces of fruit in each fruit basket now.<\/p>\n
\nHow can you solve this problem using one equation?
\nAnswer:
\nWe can solve the above problem by using the multiplication equation.
\nFirst, you need to multiply the number of fruit baskets by the number of pieces of fruit.
\nAfter that divide the number of pieces by the number of bananas.<\/p>\n
\nNewton buys 3 DVDs for $4 each. He pays with a $20 bill. What is his change?
\nYou can write one equation with two operations to solve this problem.
\nThe equation is shown.
\n20 – 3 \u00d7 4 = c \u2190 c is the amount of change.
\nWhen solving a problem with more than one type of operation, use the rules below.
\n\u2022 First, multiply or divide as you read the equation from left to right.
\n\u2022 Then add or subtract as you read the equation from left to right.
\nStep 1:
\nMultiply from left to right.
\n20 – 3 \u00d7 4 = c
\n20 – ____ = c<\/p>\n
\n20 – ____ = c
\n____ = c
\nHis change is ____.<\/p>\n
\nStep 1:
\nMultiply from left to right.
\n20 – 3 \u00d7 4 = c
\n20 – 12 = c
\nStep 2: Subtract from left to right.
\n20 – 12 = c
\n8 = c
\nHis change is 8.<\/p>\n
\nThere are 8 tomato plants. You pick 9 tomatoes from each plant. You give away 35 of them. Use the equation 8 \u00d7 9 – 35 to find how many tomatoes you have left.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-1.png\")
\nAnswer:
\nGiven that,
\nThere are 8 tomato plants. You pick 9 tomatoes from each plant.
\n8 \u00d7 9 = 72
\nYou give away 35 of them.
\nWe can find the number of tomatoes left by using the equation.
\n8 \u00d7 9 – 35
\n72 – 35 = 37
\nThus 37 tomatoes are left.<\/p>\n
\nA family buys 5 tickets for a musical. Each ticket costs $9. They spend $28 at the musical on snacks. Write and solve an equation to find how much they spend in all at the musical. Use to represent the total amount spent.
\nAnswer:
\nGiven that,
\nA family buys 5 tickets for a musical. Each ticket costs $9.
\n5 \u00d7 $9 = $45
\nThey spend $28 at the musical on snacks.
\n45 – 28 = 17
\nThe equation to find how much they spend in all at the musical is 5 \u00d7 9 – 45<\/p>\n
\nQuestion 3.
\nNewton buys 2 movie tickets. Each ticket costs $7. Descartes spends $23 at the movie on snacks. How much money do they spend in all at the movie?
\nAnswer:
\nGiven,
\nNewton buys 2 movie tickets. Each ticket costs $7.
\n2 \u00d7 7 = $14
\nDescartes spends $23 at the movie on snacks.
\n23 + 2 \u00d7 7
\n23 + 14 = $37<\/p>\n
\nNewton has 28 cards. Descartes has 24 cards. Newton divides his cards into 4 equal stacks and gives Descartes one stack. How many cards does Descartes have now?
\nAnswer:
\nGiven,
\nNewton has 28 cards. Descartes has 24 cards. Newton divides his cards into 4 equal stacks and gives Descartes one stack.
\n28\/4 = 7
\nThus there are 7 cards in each stack.
\n24 + 7 = 31 cards
\nTherefore Descartes has 31 cards now.<\/p>\n
\nThere are 12 apps divided into 3 equal rows on a smart phone. One row of apps is removed. How many apps are left?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-2.png\")
\nAnswer:
\nGiven that,
\nThere are 12 apps divided into 3 equal rows on a smart phone.
\n12\/3 = 4
\nThere are 4 apps in each row
\nOne row of apps is removed.
\n12 – 4 = 8
\nThus 8 apps are left.<\/p>\n
\nIt costs $240 each week to rent a car. Newton has a coupon that saves him $10 each day he rents the car. How much will it cost him to rent the car for a week with the coupon?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-3.png\")
\nAnswer:
\nGiven that,
\nIt costs $240 each week to rent a car. Newton has a coupon that saves him $10 each day he rents the car.
\n1 week – 7 days
\n1 day – $10
\n7 \u00d7 10 = $70
\n240 – 70 = $170<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nYour friend says 24 – 6 \u00f7 2 = 9. Is your friend correct? Explain.
\nAnswer:
\nNo, because you need to solve the equation from the left.
\n24 – (6 \u00f7 2) = 24 – 12
\n= 12
\nThus your friend is incorrect.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-4.png\")
\nUnderstand the problem:
\nMake a plan:
\nSolve:
\nNewton now has _____.<\/p>\n
\nGiven,
\nNewton has $135. He saves $20 each week for 8 weeks.
\n20 \u00d7 8 = 160
\n$135 + $160 = $295
\nThus Newton now gas $295.<\/p>\n
\nYour teacher buys 3 packages of napkins for a class party. Each package has 50 napkins. The class uses 79 napkins. How many napkins are left?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-5.png\")
\nAnswer:
\nGiven,
\nYour teacher buys 3 packages of napkins for a class party. Each package has 50 napkins.
\n1 pack – 50 napkins
\n3 packs – 3 \u00d7 50 = 150
\nThe class uses 79 napkins.
\n150 – 79 = 71
\nThus 71 napkins are left.<\/p>\n
\nThere are 60 seconds in one minute. It takes you 2 minutes and 16 seconds to run from your home to your friend\u2019s home. How many seconds does it take you?
\nAnswer:
\nGiven,
\nThere are 60 seconds in one minute. It takes you 2 minutes and 16 seconds to run from your home to your friend\u2019s home.
\n1 min – 60 seconds
\n2 mins – 2 \u00d7 60 = 120 seconds
\n120 + 16 = 136 seconds
\nThus it takes 136 seconds to run from your home to your friend\u2019s home.<\/p>\n
\nA store is selling comic books for $5 each. The store sells 33 superhero comic books and 57 science-\ufb01ction comic books. How much money does the store earn?
\nAnswer:
\nGiven,
\nA store is selling comic books for $5 each.
\nThe store sells 33 superhero comic books and 57 science-\ufb01ction comic books.
\n33 + 57 = 90
\n5 \u00d7 90 = $450
\nThus the store earn $450.<\/p>\n<\/a>Problem Solving: All Operations Homework & Practice 9.5<\/h3>\n
\nThere are 20 math problems divided into 4 equal columns on a worksheet. Your teacher has you cross out one column of problems. Use the equation 20 – 20 \u00f7 4 = p to find how many problems are left.
\nAnswer:
\nGiven that,
\nThere are 20 math problems divided into 4 equal columns on a worksheet. Your teacher has you cross out one column of problems.
\n20 – 20 \u00f7 4 = p
\n20 – 5 = p
\n15 = p
\nThus 15 problems are left.<\/p>\n
\nNewton has 42 blocks. Descartes has 48 blocks. Newton divides his blocks into 6 equal groups and gives Descartes one group. How many blocks does Descartes have now? Use d to represent how many blocks Descartes has now.
\nAnswer:
\nGiven,
\nNewton has 42 blocks. Descartes has 48 blocks. Newton divides his blocks into 6 equal groups and gives Descartes one group.
\n42\/6 = 7 blocks
\n48 + 7 = 55 blocks
\nThus Descartes has 55 blocks now.<\/p>\n
\nThere are 6 palm trees. An islander gathers 8 coconuts from each tree. She gives away 19 of them. How many coconuts does she have now? Write an equation to solve. Use a letter to represent the unknown number. Check whether your answer is reasonable.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-6.png\")
\nAnswer:
\nGiven,
\nThere are 6 palm trees. An islander gathers 8 coconuts from each tree. She gives away 19 of them.
\n6 \u00d7 8 – 19 = p
\n48 – 19 = p
\n29 = p
\nThus the unknown number is 29.<\/p>\n
\nDIG DEEPER!<\/strong>
\nFind the number that makes 5 \u00d7 ____ – 15 = 5 true. Explain.
\nAnswer:
\n5 \u00d7 ____ – 15 = 5
\n5 \u00d7 p – 15 = 5
\np – 15 = 5\/5
\np – 15 = 1
\np = 1 + 15
\np = 16
\nThus the value of the number is 16.<\/p>\n
\nNumber Sense<\/strong>
\nWhich equations are true?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-9-Multiples-and-Problem-Solving-9.5-7.png\")
\nAnswer:
\n3 + 5 \u00d7 2 = 13
\nSolve from left to right.
\n3 + 10 = 13
\n13 = 13 (true)
\n20 – 10 \u00d7 2 = 20
\n20 – 20 = 0 (false)
\n36 \u00f7 6 + 3 = 4
\n36 \u00f7 9 = 4
\n4 = 4 (true)
\n26 – 8 \u00f7 2 = 22
\n26 – 4 = 22
\n22 = 22 (true)<\/p>\n
\nModeling Real Life<\/strong>
\nA school nurse orders 7 packages of bandages. Each package has 20 bandages. The nurse uses 53 bandages. How many bandages are left?
\nAnswer:
\nGiven,
\nA school nurse orders 7 packages of bandages. Each package has 20 bandages.
\n7 \u00d7 20 = 140 bandages
\nThe nurse uses 53 bandages.
\n140 – 53 = 87 bandages
\nThus 87 bandages are left.<\/p>\n
\nModeling Real Life<\/strong>
\nThere are 60 seconds in one minute. You record a video that is 3 minutes and 48 seconds long. How many seconds long is the video?
\nAnswer:
\nGiven,
\nThere are 60 seconds in one minute. You record a video that is 3 minutes and 48 seconds long.
\n3 mins = 3 \u00d7 60 = 180 seconds
\n180 + 48 = 228 seconds
\nThus the video is 228 seconds long.<\/p>\n