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Using Partial Products to Multiply Whole Numbers

Using Partial Products to Multiply Whole Numbers. 5 .NBT.B.5. Using Partial Products to Multiply Whole Numbers. 1. 8. ×. 1. 3. 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.

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Using Partial Products to Multiply Whole Numbers

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

  2. Using Partial Products to Multiply Whole Numbers 1 8 × 1 3 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.

  3. Using Partial Products to Multiply Whole Numbers 10 18 8 100 80 10 30 13 24 + 3 234 13 is equal to … 10 + 3 What is 10 x 10? … by 13 squares. What is 8 x 10? 80 What is 10 x 3? 30 What is 8 x 3? This array measures 18 squares … 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. 18 is equal to … To show 18 x 13, here is a large array of squares. So, 234 is the product of 18 and 13. 10 + 8 24 100

  4. Using Partial Products to Multiply Whole Numbers 18 × 13 = 234 13 × 18 = 234 234 234 ÷ 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.

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

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

  7. Using Partial Products to Multiply Whole Numbers 17 × 15 = 255 15 × 17 = 255 255 255 ÷ 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.

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

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

  10. Using Partial Products to Multiply Whole Numbers 19 × 14 = 266 14 × 19 = 266 266 266 ÷ 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.

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

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

  13. Using Partial Products to Multiply Whole Numbers 38 × 23 = 874 23 × 38 = 874 874 874 ÷ 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.

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

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

  16. Using Partial Products to Multiply Whole Numbers Closing Question

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

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

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