Using Partial Products to Multiply Whole Numbers 5.NBT.B.5

1 8 × 1 3 Using Partial Products to Multiply Whole Numbers Multiplying two numbers that are each greater than 10 requires some new strategies. Let’s begin by looking at a picture that shows 18 x 13. Let’s begin by looking at a picture that shows 18 x 13. Multiplying two numbers that are each greater than 10 requires some new strategies.

Using Partial Products to Multiply Whole Numbers 10 18 8 100 80 10 30 13 + 24 To show 18 x 13, here is a large array of squares. This array measures 18 squares … … by 13 squares. 18 is equal to … 10 + 8 13 is equal to … 10 + 3 What is 10 x 10? 100 What is 8 x 10? 80 What is 10 x 3? 30 What is 8 x 3? 24 What is the sum of 100 + 80 + 30 + 24? 234 To find the total number of squares, we can multiply 18 by 13. We can also decompose 18 and 13 into smaller numbers, and then multiply those numbers. Now, let’s multiply the parts of the picture. Then we can add those parts together. So, 234 is the product of 18 and 13. 3 234 To find the total number of squares, we can multiply 18 by 13. 234 What is the sum of 100 + 80 + 30 + 24? Now, let’s multiply the parts of the picture. Then we can add those parts together. So, 234 is the product of 18 and 13. 24 We can also decompose 18 and 13 into smaller numbers, and then multiply those numbers. What is 8 x 10? 18 is equal to … 10 + 8 … by 13 squares. This array measures 18 squares … To show 18 x 13, here is a large array of squares. 13 is equal to … 10 + 3 What is 10 x 3? 30 80 100 What is 10 x 10? What is 8 x 3?

Using Partial Products to Multiply Whole Numbers 18 × 13 = 234 234 13 × 18 = 234 234 ÷ 18 = 13 18 13 234 ÷ 13 = 18 Since we know that 18 x 13 … … is equal to 234 … … we also know that 13 x 18 … … is equal to 234. We also know that 234 divided by 18 … … is equal to 13. And, 234 divided by 13 … … is equal to 18. And, 234 divided by 13 … … is equal to 13. … is equal to 18. … is equal to 234 … Since we know that 18 x 13 … … we also know that 13 x 18 … … is equal to 234. We also know that 234 divided by 18 …

1 7 × 1 5 Using Partial Products to Multiply Whole Numbers Here is 17 x 15. Let’s look at a picture that shows 17 x 15. Here is 17 x 15. Let’s look at a picture that shows 17 x 15.

Using Partial Products to Multiply Whole Numbers 10 17 7 100 70 10 15 50 + 35 To show 17 x 15, here is a large array of squares. This array measures 17 squares … To find the total number of squares, we can multiply 17 by 15. We can also decompose 17 and 15 into smaller numbers, and then multiply those numbers. … by 15 squares. 17 is equal to … 10 + 7 15 is equal to … 10 + 5 Now, let’s multiply the parts of the picture. Then we can add those parts together. What is 10 x 10? 100 What is 7 x 10? 70 What is 10 x 5? 50 What is 7 x 5? 35 What is the sum of 100 + 70 + 50 + 35? 255 So, 255 is the product of 17 and 15. 255 5 255 So, 255 is the product of 17 and 15. Now, let’s multiply the parts of the picture. Then we can add those parts together. We can also decompose 17 and 15 into smaller numbers, and then multiply those numbers. To find the total number of squares, we can multiply 17 by 15. This array measures 17 squares … What is the sum of 100 + 70 + 50 + 35? 70 10 + 7 15 is equal to … 17 is equal to … … by 15 squares. To show 17 x 15, here is a large array of squares. 10 + 5 What is 10 x 10? 50 What is 7 x 5? What is 10 x 5? What is 7 x 10? 100 35

Using Partial Products to Multiply Whole Numbers 17 × 15 = 255 255 15 × 17 = 255 255 ÷ 17 = 15 17 15 255 ÷ 15 = 17 Since we know that 17 x 15 … … is equal to 255 … … we also know that 15 x 17 … … is equal to 255. 255 divided by 17 … … is equal to 15. And, 255 divided by 15 … … is equal to 17. And, 255 divided by 15 … … is equal to 15. … is equal to 17. … is equal to 255 … Since we know that 17 x 15 … … we also know that 15 x 17 … … is equal to 255. 255 divided by 17 …

1 9 × 1 4 Using Partial Products to Multiply Whole Numbers Here is 19 x 14. Let’s look at a picture that shows 19 x 14. Here is 19 x 14. Let’s look at a picture that shows 19 x 14.

Using Partial Products to Multiply Whole Numbers 10 19 9 100 90 10 40 14 + 36 To show 19 x 14, here is a large array of squares. This array measures 19 squares … … by 14 squares. To find the total number of squares, we can multiply 19 by 14. We can also decompose 19 and 14 into smaller numbers, and then multiply those numbers. 19 is equal to … 10 + 9 14 is equal to … 10 + 4 Now, let’s multiply the parts of the picture. Then we can add those parts together. What is 10 x 10? 100 What is 9 x 10? 90 What is 10 x 4? 40 What is 9 x 4? 36 What is the sum of 100 + 90 + 40 + 36? 266 So, 266 is the product of 19 and 14. 266 4 266 So, 266 is the product of 19 and 14. Now, let’s multiply the parts of the picture. Then we can add those parts together. We can also decompose 19 and 14 into smaller numbers, and then multiply those numbers. To find the total number of squares, we can multiply 19 by 14. This array measures 19 squares … What is the sum of 100 + 90 + 40 + 36? 90 10 + 9 14 is equal to … 19 is equal to … … by 14 squares. To show 19 x 14, here is a large array of squares. 10 + 4 What is 10 x 10? 40 What is 9 x 4? What is 10 x 4? What is 9 x 10? 100 36

Using Partial Products to Multiply Whole Numbers 19 × 14 = 266 266 14 × 19 = 266 266 ÷ 19 = 14 19 14 266 ÷ 14 = 19 Since we know that 19 x 14 … … is equal to 266 … … we also know that 14 x 19 … … is equal to 266. 266 divided by 19 … … is equal to 14. And, 266 divided by 14 … … is equal to 19. And, 266 divided by 14 … … is equal to 14. … is equal to 19. … is equal to 266 … Since we know that 19 x 14 … … we also know that 14 x 19 … … is equal to 266. 266 divided by 19 …

3 8 × 2 3 Using Partial Products to Multiply Whole Numbers Here is 38 x 23. Here is 38 x 23.

Using Partial Products to Multiply Whole Numbers 30 38 8 600 160 20 23 90 To show 38 x 23, here is a sketch. This shows 38 … … by 23. On the sketch, let’s draw two lines … … so that we can decompose each number. 38 is equal to … 30 + 8 23 is equal to … 20 + 3 Now, let’s multiply the parts of the picture. Then we can add those parts together. What is 30 x 20? 600 What is 8 x 20 ? 160 What is 30 x 3? 90 What is 8 x 3? 24 What is the sum of 600 + 160 + 90 + 24? 874 So, 874 is the product of 38 and 23. + 24 3 874 874 What is the sum of 600 + 160 + 90 + 24? So, 874 is the product of 38 and 23. … so that we can decompose each number. On the sketch, let’s draw two lines … This shows 38 … Now, let’s multiply the parts of the picture. Then we can add those parts together. 160 30 + 8 23 is equal to … 38 is equal to … … by 23. To show 38 x 23, here is a sketch. 20 + 3 What is 30 x 20? 90 What is 8 x 3? What is 30 x 3? What is 8 x 20 ? 600 24

Using Partial Products to Multiply Whole Numbers 38 × 23 = 874 874 23 × 38 = 874 874 ÷ 38 = 23 38 23 874 ÷ 23 = 38 Since we know that 38 x 23 … … is equal to 874 … … we also know that 23 x 38 … … is equal to 874. 874 divided by 38 … … is equal to 23. And, 874 divided by 23 … … is equal to 38. And, 874 divided by 23 … … is equal to 23. … is equal to 38. … is equal to 874 … Since we know that 38 x 23 … … we also know that 23 x 38 … … is equal to 874. 874 divided by 38 …

5 6 × 8 2 Using Partial Products to Multiply Whole Numbers Here is 56 x 82. Here is 56 x 82.

Using Partial Products to Multiply Whole Numbers 50 56 6 4,000 480 80 82 100 To show 56 x 82, here is a sketch. This shows 56 … … by 82. On the sketch, let’s draw two lines … … so that we can decompose each number. 56 is equal to … 50 + 6 82 is equal to … 80 + 2 Now, let’s multiply the parts of the picture. Then we can add those parts together. What is 50 x 80? 4,000 What is 6 x 80? 480 What is 50 x 2? 100 What is 6 x 2? 12 What is the sum of 4,000 + 480 + 100 + 12? 4,592 So, 4,592 is the product of 56 and 82. + 12 2 4,592 4,592 What is the sum of 4,000 + 480 + 100 + 12? So, 4,592 is the product of 56 and 82. … so that we can decompose each number. On the sketch, let’s draw two lines … This shows 56 … Now, let’s multiply the parts of the picture. Then we can add those parts together. 480 50 + 6 82 is equal to … 56 is equal to … … by 82. To show 56 x 82, here is a sketch. 80 + 2 What is 50 x 80? 100 What is 6 x 2? What is 50 x 2? What is 6 x 80? 4,000 12

Using Partial Products to Multiply Whole Numbers Closing Question

7 5 × 6 4 Using Partial Products to Multiply Whole Numbers Here is 75 x 64. Here is 75 x 64.

Using Partial Products to Multiply Whole Numbers 70 75 5 4,200 300 60 64 280 To show 75 x 64, here is a sketch. This shows 75 … … by 64. On the sketch, let’s draw two lines … … so that we can decompose each number.75 is equal to … 70 + 5 64 is equal to … 60 + 4 Now, let’s multiply the parts of the picture. Then we can add those parts together. What is 70 x 60? 4,200 What is 5 x 60? 300 What is 70 x 4? 280 What is 5 x 4? 20 What is the sum of 4,200 + 300 + 280 + 20? 4,800 So, 4,800 is the product of 75 and 64. + 20 4 4,800 4,800 What is the sum of 4,200 + 300 + 280 + 20? So, 4,800 is the product of 75 and 64. … so that we can decompose each number. On the sketch, let’s draw two lines … This shows 75 … Now, let’s multiply the parts of the picture. Then we can add those parts together. 300 70 + 5 64 is equal to … 75 is equal to … … by 64. To show 75 x 64, here is a sketch. 60 + 4 What is 70 x 60? 280 What is 5 x 4? What is 70 x 4? What is 5 x 60? 4,200 20