Lesson 1: Multiply by Tens<\/strong><\/p>\n Lesson 2: Estimate Products<\/strong><\/p>\n Lesson 3: Use Area Models to Multiply Two-Digit Numbers<\/strong><\/p>\n Lesson 4: Use the Distributive Property to Multiply Two-Digit Numbers<\/strong><\/p>\n Lesson 5: Use Partial Products to Multiply Two-Digit Numbers<\/strong><\/p>\n Lesson 6: Multiply Two-Digit Numbers<\/strong><\/p>\n Lesson 7: Practice Multiplication Strategies<\/strong><\/p>\n Lesson 8: Problem Solving: Multiplication with Two-Digit Numbers<\/strong><\/p>\n Performance Task<\/strong><\/p>\n Explore and Grow<\/strong> Answer: Explanation: Answer: Explanation: Answer: Explanation: Answer: Explanation: Answer: Explanation: Answer: 360<\/p>\n Explanation: Question 1. Answer: Explanation: Question 2. Answer: Explanation: Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Question 7. Answer: 1400<\/p>\n Explanation: Question 8. Answer: 330<\/p>\n Explanation: Question 9. Answer: 480<\/p>\n Explanation: Question 10. Answer: 750<\/p>\n Explanation: Question 11. Answer: 390<\/p>\n Explanation: Question 12. Answer: 760<\/p>\n Explanation: Question 13. Answer: 1,000<\/p>\n Explanation: Question 14. Answer: 30 Question 15. Answer: 90 Question 16. Answer: 70 Question 17. Answer: 80 Question 18. Answer: 40 Question 19. Answer: 50 Question 20. Answer: 60 \u00d7 30 is equal to 1,800<\/p>\n Explanation: Question 21. Answer: 480 is greater than 460<\/p>\n Explanation: Question 22. Answer: 2,250 is less than 2,340<\/p>\n Explanation: Question 23. Answer: 200 days<\/p>\n Explanation: Question 24. Answer:<\/p>\n Question 25. Answer: He is correct<\/p>\n Explanation: Example<\/strong> Question 26 Answer: 724<\/p>\n Explanation: Question 27. Answer: 240 feet<\/p>\n Explanation: Question 28. Answer: Explanation: Find the product.<\/strong><\/p>\n Question 1. Answer: 300<\/p>\n Explanation: Question 2. Answer: 1800<\/p>\n Explanation: Question 3. Answer: 3500<\/p>\n Explanation: Question 4. Answer: 520<\/p>\n Explanation: Question 5. Answer: 1620<\/p>\n Explanation: Question 6. Answer: 4480<\/p>\n Explanation: Question 7. Answer: 30<\/p>\n Explanation: Question 8. Answer: 90 Question 9. Answer: 40 Question 10. Answer: 80 Question 11. Answer: 60 Question 12. Answer: 60 Question 13. Answer: 7,200 is less than 8,100<\/p>\n Explanation: Question 14. Answer: 1,200 is greater\u00a0 than 1,020<\/p>\n Explanation: Question 15. Answer: 2,380 is equal to 2,380<\/p>\n Explanation: Question 16. Answer: 15 kilometers<\/p>\n Explanation: Question 17. Answer:<\/p>\n Question 18. Answer: By using the Associative Property of Multiplication, Question 19. Answer: 20, 40<\/p>\n Explanation: Question 20. Answer: 420<\/p>\n Explanation: Question 21. Answer: 1013 meters<\/p>\n Explanation: Given that an Olympic pool has a length of 50 meters. But, there are 20 Olympic pools. Question 22. Answer: The place-value of 8 in the given number is: 8<\/p>\n Explanation:\n
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<\/a>Lesson 4.1 Multiply by Tens<\/h3>\n
\nModel each product. Draw each model.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-1.png\")
\nWhat pattern do you notice in the products?<\/p>\n
\nThe Place- value method. From the above pattern, we can conclude that the result has different place-values of 6<\/p>\n
\nThe position of 3 is different in the given 4 multiplications.
\nSo,
\n2 \u00d7 3 = 6
\n2 \u00d7 30 = 60
\n2 \u00d7 300 = 600
\n2 \u00d7 3000 = 6,000
\nFrom the above pattern, we can conclude that the result has different place-values of 6
\nRepeated Reasoning<\/strong>
\nHow can the pattern above help you find 20 \u00d7 30?<\/p>\n
\n20 \u00d7 30 = 600<\/p>\n
\nYou can think of 20 as two tens and 30 as Three tens.
\nSo,
\n20 \u00d7 30 = 2 \u00d7 1 ten \u00d7 3 \u00d7 1 ten = 2 tens \u00d7 2 \u00d7 3 = 6 \u00d7 2 tens = 600
\nThink and Grow: Multiply by Multiples of Tens<\/strong>
\nYou can use place value and properties to multiply two-digit numbers by multiples of ten.
\nExample<\/strong>
\nFind 40 \u00d7 20.
\nOne Way: Use place value.
\n40 \u00d7 20 = 40 \u00d7 ____ tens
\n= ____ tens
\n= _____
\nSo, 40 \u00d7 20 = _____.<\/p>\n
\n800<\/p>\n
\nBy using the Place-value method,
\n40 \u00d7 20 = 40 \u00d7 2 tens
\n= 80 tens
\n= 800
\nSo, 40 \u00d7 20 = 800
\nAnother Way: Use the Associative Property of Multiplication.
\n40 \u00d7 20 = 40 \u00d7 (2 \u00d7 10) Rewrite 20 as 2 \u00d7 10.
\n= (40 \u00d7 2) \u00d7 10 Associative Property of Multiplication
\n= ____ \u00d7 10
\n= ____
\nSo, 40 \u00d7 20 = _____.<\/p>\n
\n800<\/p>\n
\nBy using the Associative Property of Multiplication,
\n40 \u00d7 20 = 40 \u00d7 (2 \u00d7 10)
\n= (40 \u00d7 2) \u00d7 10
\n= 80 \u00d7 10
\n= 800
\nNote<\/strong><\/em>: Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c
\nFind 12 \u00d7 30.
\nOne Way: Use place value
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-2.png\")
\n12 \u00d7 30 = 12 \u00d7 _____ tens
\n= ____ tens
\n= _____
\nSo, 12 \u00d7 30 = _____.<\/p>\n
\n360<\/p>\n
\nUsing the Place-value method,
\n12 \u00d7 30 = 12 \u00d7 3 tens
\n= 36 tens
\n= 360
\nSo, 12 \u00d7 30 = 360
\nAnother Way: Use the Associative Property of Multiplication
\n12 \u00d7 30 = 12 \u00d7 (3 \u00d7 10) Rewrite 30 as 3 \u00d7 10.
\n= (12 \u00d7 3) \u00d7 10 Associative Property of Multiplication
\n= ____ \u00d7 10
\n= _____
\nSo, 12 \u00d7 30 = ____.<\/p>\n
\nBy using the Associative Property of Multiplication,
\n12 \u00d7 30 = 12 \u00d7 (3 \u00d7 10)
\n= (12 \u00d7 3) \u00d7 10
\n= 36 \u00d7 10
\n= 360
\nNote<\/strong><\/em>: Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c
\nShow and Grow<\/strong>
\nFind the product.<\/strong><\/p>\n
\n70 \u00d7 40 = _____<\/p>\n
\n2800<\/p>\n
\nBy using the Associative Property of Multiplication,
\n70 \u00d7 40 = 70 \u00d7 (4 \u00d7 10)
\n= (70 \u00d7 4) \u00d7 10
\n= 280 \u00d7 10
\n= 2800
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n50 \u00d7 80 = ____<\/p>\n
\n4,000<\/p>\n
\nBy using the Associative Property of Multiplication,
\n50 \u00d7 80 = 50 \u00d7 (8 \u00d7 10)
\n= (50 \u00d7 8) \u00d7 10
\n= 400 \u00d7 10
\n= 4000
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n24 \u00d7 90 = _____<\/p>\n
\n2160<\/p>\n
\nBy using the Associative Property of Multiplication,
\n24 \u00d7 90 = 24 \u00d7 (9 \u00d7 10)
\n= (24 \u00d7 9) \u00d7 10
\n= (8 \u00d7 3 \u00d7 9) \u00d7 10
\n= 216 \u00d7 10
\n= 2160
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\n<\/span>a \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n45 \u00d7 60 = _____<\/p>\n
\n2700<\/p>\n
\nBy using the Associative Property of Multiplication,
\n45 \u00d7 60 = 45 \u00d7 (6 \u00d7 10)
\n= (45 \u00d7 6) \u00d7 10
\n= (5 \u00d7 9 \u00d7 6) \u00d7 10
\n= 270 \u00d7 10
\n= 2700
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c
\nApply and Grow: Practice<\/strong>
\nFind the product.<\/strong><\/p>\n
\n90 \u00d7 10 = _____<\/p>\n
\n900<\/p>\n
\nBy using the place-value method,
\n90 \u00d7 10 = 10 \u00d7 9 tens
\n= 90 tens
\n= 900
\nSo,
\n90 \u00d7 10 = 900<\/p>\n
\n40 \u00d7 60 = ____<\/p>\n
\n2400
\nExplaination:
\nBy using the place-value method,
\n40 \u00d7 60 = 40 \u00d7 6 tens
\n= 4 tens \u00d7 6 tens
\n= 24 \u00d7 tens \u00d7 tens
\n= 2400
\nSo,
\n40 \u00d7 60 = 2400<\/p>\n
\n20 \u00d7 70 = _____<\/p>\n
\nBy using the place-value method,
\n70 \u00d7 20 = 70 \u00d7 2 tens
\n= 7 tens \u00d7 2 tens
\n= 14 \u00d7 tens \u00d7 tens
\n= 1400
\nSo,
\n70 \u00d7 20 = 1400<\/p>\n
\n11 \u00d7 30 = ____<\/p>\n
\nBy using the place-value method,
\n11 \u00d7 30 = 11 \u00d7 3 tens
\n= 33 tens
\n= 330
\nSo,
\n11 \u00d7 30 = 330<\/p>\n
\n12 \u00d7 40 = ____<\/p>\n
\nBy using the place-value method,
\n12 \u00d7 40 = 12 \u00d7 4 tens
\n= 48 tens
\n= 480
\nSo,
\n12 \u00d7 40 = 480<\/p>\n
\n15 \u00d7 50 = _____<\/p>\n
\nBy using the place-value method,
\n15 \u00d750 = 15 \u00d7 5 tens
\n= 75 tens
\n= 750
\nSo,
\n15 \u00d7 50 = 750<\/p>\n
\n30 \u00d7 13 = _____<\/p>\n
\nBy using the place-value method,
\n13 \u00d7 30 = 13 \u00d7 3 tens
\n= 39 tens
\n= 390
\nSo,
\n13 \u00d7 30 = 390<\/p>\n
\n10 \u00d7 76 = _____<\/p>\n
\nBy using the place-value method,
\n10 \u00d7 76 = 76 \u00d7 1 ten
\n= 76 tens
\n= 760
\nSo,
\n76 \u00d7 10 = 760<\/p>\n
\n40 \u00d7 25 = ____<\/p>\n
\nBy using the place-value method,
\n25 \u00d7 40 = 25 \u00d7 4 tens
\n= 5 \u00d7 5\u00d7 4 tens
\n= 100 tens
\n= 1,000
\nSo,
\n25 \u00d7 40 = 1,000
\nFind the missing factor.<\/strong><\/p>\n
\n50 \u00d7 ____ = 1,500<\/p>\n
\nExplanation;
\nLet the missing number be X
\nSo, 50 \u00d7 X = 1,500
\nX = 1,500 \/ 50 = 30
\nHence, the value of X is: 30<\/p>\n
\n20 \u00d7 ____ = 1,800<\/p>\n
\nExplanation;
\nLet the missing number be X
\nSo, 20 \u00d7 X = 1,800
\nX = 1,800 \/20 = 90
\nHence, the value of X is: 90<\/p>\n
\n60 \u00d7 ___ = 4,200<\/p>\n
\nExplanation;
\nLet the missing number be X
\nSo, 60 \u00d7 X = 4,200
\nX = 4,200 \/ 60 = 70
\nHence, the value of X is: 70<\/p>\n
\n____ \u00d7 80 = 6,400<\/p>\n
\nExplanation;
\nLet the missing number be X
\nSo, X \u00d7 80 = 6,400
\nX = 6,400 \/ 80 = 80
\nHence, the value of X is: 80<\/p>\n
\n____ \u00d7 90 = 3,600<\/p>\n
\nExplanation;
\nLet the missing number be X
\nSo, X \u00d7 90 = 3,600
\nX = 3,600 \/ 90 = 40
\nHence, the value of X is: 40<\/p>\n
\n____ \u00d7 70 = 3,500<\/p>\n
\nExplanation;
\nLet the missing number be X
\nSo, X \u00d7 70 = 3,500
\nX = 3,500 \/ 70 = 50
\nHence, the value of X is: 50
\nCompare.<\/strong><\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-3.png\")
<\/p>\n
\n60 \u00d7 30 = 1,800
\nGiven numbers are: 1,800 and 1,800
\nBy comparing 2 values, we can conclude that 1,800 is equal to 1,800<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-4.png\")
<\/p>\n
\n40 \u00d7 12 = 480
\nGiven numbers are: 480 and 460
\nBy comparing 2 values, we can conclude that480 is greater than 460<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-5.png\")
<\/p>\n
\n25 \u00d7 90 = 2,250
\nGiven numbers are 2,250 and 2,340
\nBy comparing 2 values, we can conclude that 2,250 is less than 2,340<\/p>\n
\nIt takes 10 days to film 1 episode of a television show. How many days will it take to film a 20-episode season?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-6.png\")
<\/p>\n
\nGiven that it takes 10 days to film 1 episode of a Television show.
\nSo,
\nThe number of days it will take to film a 20-episode season is: 20 \u00d7 10 = 200 days<\/p>\n
\nReasoning<\/strong>
\nWhat is Descartes\u2019s number? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-7.png\")
<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nNewton says that the product of two multiples of ten will always have exactly two zeros. Is he correct? Explain.<\/p>\n
\nLet us suppose 2 numbers 10 and 20 which are the two multiples of 10.
\nNow,
\n10 \u00d7 20 = 200
\nAccording to Newton, the product of two multiples of ten will always have exactly two zeroes.
\nSo, from the above multiplication, we can say that Newton is correct.
\nThink and Grow: Modeling Real Life<\/strong><\/p>\n
\nFood drive volunteers collect 1,328 cans of food. The volunteers have50 boxes. Each box holds 20 cans. How many cans will fit in the boxes?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-8.png\")
\nMultiply to find how many cans will fit in the boxes.
\n20 \u00d7 50 = 50 \u00d7 (5 \u00d7 10)
\nRewrite 50 as 5 \u00d7 10.
\n= (20 \u00d7 5) \u00d7 10 Associative Property of Multiplication
\n= 100 \u00d7 10
\n= 1,000
\nSo, 1,000 cans fit in the boxes.
\nSubtract the number of cans that will fit in the boxes from the total number of cans collected.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-9.png\")
\nThe cans that can not fit in the boxes = 1,328 – 1,000 = 328
\nSo,
\n328 cans will not fit in the boxes.
\nShow and Grow<\/strong><\/p>\n
\nA library has 2,124 new books. The library has 40 empty shelves. Each shelf holds 35 books. How many not books
\nwill fit on the empty shelves?<\/p>\n
\nMultiply to find how many books will hold on the shelves.
\n40 \u00d7 35 = 35 \u00d7 (4 \u00d7 10)
\nRewrite 40 as 5 \u00d7 10.
\n= (35 \u00d7 4) \u00d7 10 Associative Property of Multiplication<\/strong><\/em>
\n= 140 \u00d7 10
\n= 1,400
\nSo, 1,400 cans fit in the boxes.
\nSubtract the number of books that will hold on the shelves from the total number of books collected.
\nThe number of books that will not hold on the shelves = 2,124 – 1,400 = 724
\nSo,
\n724 books will not hold on the shelves<\/p>\n
\nAn apartment building has 15 floors. Each floor is 10 feet tall. An office building has 30 floors. Each floor is 13 feet tall. How much taller is the office building than the apartment building?<\/p>\n
\nGiven that an apartment has 15 floors and in that, each floor is 10 feet tall.
\nSo, the height of the apartment = 15 \u00d7 10 = 150 feet
\nGiven that an office building has 30 floors and in that, each floor is 13 feet tall.
\nSo, the height of the office building = 30 \u00d7 13 = 390 feet
\nNow, to calculate how much taller an office building than the apartment, we have to subtract both the heights of the apartment and the office building.
\nSo,
\nThe difference in height between the office building and the apartment = 390 feet – 150 feet = 240 feet.
\nFrom the above, we can conclude that the office building is 240 feet taller than the apartment.<\/p>\n
\nYou burn 35 calories each hour you spend reading and 50 calories each hour you spend playing board games. In 2
\nweeks, you spend14 hours reading and 28 hours playing board games. How many calories do you burn reading
\nand playing board games?<\/p>\n
\nThe calories burned during reading in 2 weeks = 490 calories
\nThe calories burned during playing board games = 1400 calories<\/p>\n
\nGiven that,
\nThe calories burned during reading is: 35 calories each hour
\nThe calories burned during playing board games is: 50 calories each hour
\nIt is also given that In 2 weeks,
\nthe time spend on reading and Playing Board Games are 14 hours and 28 hours
\nSo, to calculate the calorie consumption in these 2 weeks, we have to multiply the number of hours and the number of calories.
\nSo,
\nThe calories burned during reading in 2 weeks = 490 calories
\nThe calories burned during playing board games in 2 weeks = 1400 calories<\/p>\n<\/a>Multiply by Tens Homework & Practice 4.1<\/h3>\n
\n30 \u00d7 10 = _____<\/p>\n
\nThe product of multiply by tens can be done in 2 ways. They are:
\nA) The place-value method\u00a0 B) The Associative Property of Multiplication
\nA) By using the place-value method:
\n30 \u00d7 10 = 10 \u00d7 3 tens
\n= 1 ten \u00d7 3 tens
\n= 3 \u00d7 1 ten \u00d7 1 ten
\n= 3 \u00d7 100
\n= 300
\nB) The Associative Property of Multiplication:
\n30 \u00d7 10 = 3 \u00d7 (10 \u00d7 10)
\n= (3 \u00d7 10) \u00d7 10
\n= 30 \u00d7 10
\n= 300
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n20 \u00d7 90 = _____<\/p>\n
\nThe product of multiply by tens can be done in 2 ways. They are:
\nA) The place-value method\u00a0 B) The Associative Property of Multiplication
\nA) By using the place-value method:
\n20 \u00d7 90 = 20 \u00d7 9 tens
\n= 2 tens \u00d7 9 tens
\n= 18 \u00d7 1 ten \u00d7 1 ten
\n= 18 \u00d7 100
\n= 1800
\nB) The Associative Property of Multiplication:
\n20 \u00d7 90 = 20 \u00d7 (9 \u00d7 10)
\n= (20 \u00d7 9) \u00d7 10
\n=(5 \u00d7 4 \u00d7 9) \u00d7 10
\n= 180 \u00d7 10
\n= 1800
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n50 \u00d7 70 = _____<\/p>\n
\nThe product of multiply by tens can be done in 2 ways. They are:
\nA) The place-value method\u00a0 B) The Associative Property of Multiplication
\nA) By using the place-value method:
\n50 \u00d7 70 = 50 \u00d7 7 tens
\n= 5 tens \u00d7 7 tens
\n= 35 \u00d7 1 ten \u00d7 1 ten
\n= 35 \u00d7 100
\n= 3500
\nB) The Associative Property of Multiplication:
\n50 \u00d7 70 = 50 \u00d7 (7 \u00d7 10)
\n= (50 \u00d7 7) \u00d7 10
\n=(5 \u00d7 10 \u00d7 7) \u00d7 10
\n= 350 \u00d7 10
\n= 3500
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n40 \u00d7 13 = ______<\/p>\n
\nThe product of multiply by tens can be done in 2 ways. They are:
\nA) The place-value method\u00a0 B) The Associative Property of Multiplication
\nA) By using the place-value method:
\n40 \u00d7 13 = 13 \u00d7 4 tens
\n= 13 \u00d7 4 tens
\n= 52 \u00d7 1 ten
\n= 52 \u00d7 10
\n= 520
\nB) The Associative Property of Multiplication:
\n40 \u00d7 13 = 13 \u00d7 (4 \u00d7 10)
\n= (13 \u00d7 4) \u00d7 10
\n=(13 \u00d72\u00d7 2) \u00d7 10
\n= 54 \u00d7 10
\n= 540
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n27 \u00d7 60 = _____<\/p>\n
\nThe product of multiply by tens can be done in 2 ways. They are:
\nA) The place-value method\u00a0 B) The Associative Property of Multiplication
\nA) By using the place-value method:
\n27 \u00d7 60 = 27 \u00d7 6 tens
\n= 3 \u00d7 9 \u00d7 6 tens
\n= 162 \u00d7 1 ten
\n= 162 \u00d7 10
\n= 1620
\nB) The Associative Property of Multiplication:
\n27 \u00d7 60 = 27 \u00d7 (6 \u00d7 10)
\n= (27 \u00d7 6) \u00d7 10
\n=(6 \u00d7 3 \u00d7 9) \u00d7 10
\n= 162 \u00d7 10
\n= 1620
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\n80 \u00d7 56 = _____<\/p>\n
\nThe product of multiply by tens can be done in 2 ways. They are:
\nA) The place-value method\u00a0 B) The Associative Property of Multiplication
\nA) By using the place-value method:
\n80 \u00d7 56 = 56 \u00d7 8 tens
\n= 7 \u00d7 8 \u00d7 8 tens
\n= 448 \u00d7 1 ten
\n= 448 \u00d7 10
\n= 4480
\nB) The Associative Property of Multiplication:
\n56 \u00d7 80 = 56 \u00d7 (8 \u00d7 10)
\n= (56 \u00d7 8) \u00d7 10
\n=(8 \u00d7 7 \u00d7 8) \u00d7 10
\n= 448 \u00d7 10
\n= 4480
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c
\nFind the missing factor.<\/strong><\/p>\n
\n70 \u00d7 ____ = 2,100<\/p>\n
\nLet the missing number be X
\nSo, 70 \u00d7 X = 2,100
\nX = 2,100 \/ 70 = 30
\nHence, the value of X is: 30<\/p>\n
\n____ \u00d7 10 = 900<\/p>\n
\nLet the missing number be X
\nSo, X \u00d7 10 = 900
\nX = 900 \/ 10 =90
\nHence, the value of X is: 90<\/p>\n
\n40 \u00d7 ____ = 1,600<\/p>\n
\nLet the missing number be X
\nSo, 40 \u00d7 X = 1,600
\nX = 1,600 \/ 40 = 40
\nHence, the value of X is: 40<\/p>\n
\n____ \u00d7 20 = 1,600<\/p>\n
\nLet the missing number be X
\nSo, X\u00d7 20 = 1,600
\nX = 1,600 \/ 20 = 80
\nHence, the value of X is: 80<\/p>\n
\n30 \u00d7 ____ = 1,800<\/p>\n
\nLet the missing number be X
\nSo, 30 \u00d7 X = 1,800
\nX = 1,800 \/ 30 = 60
\nHence, the value of X is: 60<\/p>\n
\n____ \u00d7 50 = 3,000<\/p>\n
\nLet the missing number be X
\nSo, X \u00d7 50 = 3,000
\nX = 3,000 \/ 50 = 60
\nHence, the value of X is: 60
\nCompare.<\/strong><\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-10.png\")
<\/p>\n
\n90 \u00d7 80 = 7,200
\nGiven numbers are: 7,200 and 8,100
\nBy comparing 2 values, we can conclude that 7,200 is less than 8,100<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-11.png\")
<\/p>\n
\n60 \u00d717 = 1,020
\nGiven numbers are: 1,200 and 1,020
\nBy comparing 2 values, we can conclude that 1,200 is greater than 1,020<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-12.png\")
<\/p>\n
\n34 \u00d7 70 = 2,380
\nGiven numbers are:2,380 and 2,380
\nBy comparing the 2 values, we can conclude that 2,380 is equal to2,380<\/p>\n
\nA shallow moonquake occurs 20 kilometers below the moon\u2019s surface. A deep moonquake occurs 35 times deeper than a shallow moonquake. How many kilometers below the surface does the deep moonquake occur?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-13.png\")
<\/p>\n
\nGiven that a shallow moonquake occurred 20 kilometers below the moon’s surface and a deep moonquake occurs 35 meters deeper than a shallow moonquake.
\nNow, to calculate how much distance the deep moonquake occurred from the surface, we have to subtract the distance that a shallow moonquake occurred from the deep moonquake occurred.
\nHence,
\nThe distance below the surface the deep moonquake occurred = 30 – 25 = 15 kilometers<\/p>\n
\nStructure<\/strong>
\nWrite the multiplication equation represented by the number line.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-4-Multiply-by-Two-Digit-Numbers-4.1-14.png\")
<\/p>\n
\nWriting<\/strong>
\nExplain how you can use 20 \u00d7 10 = 200 to find 20 \u00d7 12.<\/p>\n
\n20 \u00d7 10 = 10 \u00d7 (2 \u00d7 10)
\n= (10 \u00d7 2) \u00d7 10
\n= 20 \u00d7 10
\n= 200
\nBy using the same method, we can also find the value of 20 \u00d7 12.
\nNow,
\nBy using the Associative Property of Multiplication,
\n20 \u00d7 12 = 12 \u00d7 (2 \u00d7 10)
\n= (12 \u00d7 2) \u00d7 10
\n= 24 \u00d7 10
\n= 240
\nNote<\/strong><\/em>:\u00a0Associative Property of Multiplication<\/strong>
\nTake 3 numbers a, b, c.
\nBy using Associative Property, we can write
\na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c<\/p>\n
\nDIG DEEPER!<\/strong>
\nThe product of a number and twice that number is 800. What are the numbers?<\/p>\n
\nLet the number be X
\nGiven that,
\nX \u00d7 2X = 800
\nTake X as a common multiple.
\nHence,
\nX \u00d7 X ( 1 \u00d7 2) = 800
\nX \u00d7 X \u00d7 2 = 800
\nX \u00d7 X = 800\/2 = 400
\nX \u00d7 X = 20 \u00d7 20
\nFrom the above, we can conclude that the value of X is 20
\nHence, the value of twice the X is\u00a0 20 \u00d7 2 = 40
\nSo,
\nThe numbers that can give the product 800 are 20, 40<\/p>\n
\nModeling Real Life<\/strong>
\nThere are 506 new plants in a greenhouse. A worker programs a robot to arrange the plants into14 rows with 30 plants in each row. How many plants will fit in the rows?<\/p>\n
\nGiven that there are 506 new plants in a greenhouse and a robot can arrange the plants into 14 rows with 30 plants each.
\nSo, to find how many plants will fit in the row, we have to multiply 14 and 30( Since the robot arranges the plants in rows)
\nNow, By using the Associative Property of Multiplication,
\n14 \u00d7 30 =\u00a0 14 \u00d7 (3 \u00d7 10)
\n= (14 \u00d7 3) \u00d7 10
\n= (2 \u00d7 7 \u00d7 3) \u00d7 10
\n= 42 \u00d7 10
\n= 420
\nFrom the above, we can conclude that 420 plants will fit in the row.<\/p>\n
\nModeling Real Life<\/strong>
\nThe world\u2019s largest pool is 13 meters longer than the total length of 20 Olympic pools. An Olympic pool is 50 meters long. How long is the world\u2019s largest pool?<\/p>\n
\nSo, to find the total length of the Olympic Pool, we have to multiply the number of pools and the length of each pool.
\nBy using the Associative Property of Multiplication,
\n50 \u00d7 20 = 50 \u00d7 (2 \u00d7 10)
\n= (50 \u00d7 2) \u00d7 10
\n= ( 5 \u00d7 10 \u00d7 2) \u00d7 10
\n= 100 \u00d7 10
\n= 1,000 meters
\nSo, the total length of the 20 Olympic pools = 1,000 meters
\nThe
\nQuestion also mentions that the world\u2019s largest pool is 13 meters longer than the total length of 20 Olympic pools.
\nHence,
\nThe length of the World’s largest pool = 1,000 + 13 = 1,013 meters.
\nSo, the length of the World’s largest pool is 1,013 meters
\nReview & Refresh<\/strong>
\nFind the value of the underlined digit.<\/strong><\/p>\n
\n52,618<\/span><\/p>\n
\nWe can find the position of any given number by using the place- value method.
\nFrom this, we can conclude that the place-value of 8 is: 8<\/p>\n
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-4-Multiply-by-Two-Digit-Numbers-4.2-1.png\")
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-4-Multiply-by-Two-Digit-Numbers-4.2-2.png\")
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-4-Multiply-by-Two-Digit-Numbers-4.2-3.png\")
<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-4-Multiply-by-Two-Digit-Numbers-4.2-4.png\")
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-4-Multiply-by-Two-Digit-Numbers-4.2-5.png\")