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Multiplication: Area Model

Think of multiplication of two numbers a x b as a rows of b columns. Multiplication: Area Model. The Distributive Property. a * (b + c) = ab + ac. ac. ab. (b + c). a. a rows of b columns. Multiplication: Area Model. So: if a = 2 and b = 3 , we get

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Multiplication: Area Model

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  1. Think of multiplication of two numbers a x b as a rows of b columns Multiplication: Area Model

  2. The Distributive Property a * (b + c) = ab + ac ac ab (b + c) a

  3. a rows of b columns Multiplication: Area Model So: if a = 2 and b = 3, we get 2 rows of 3 columns This is why 2 x 3 = 6

  4. 4 x 12 Example: Multiplication: Area Model

  5. 4 x 12 Example: 10 2 4 4 x 12 Multiplication: Area Model The Distributive Property of Multiplication over Addition says: + 4 x 2 = 4 x 10 =48 + 8 8 40 4 x 12 = 40

  6. 15 x 12 150 = 15 x 10 Multiplication: Area Model 15 x 12 Example: 15 x 2 15 x 10 + 30 = 15 x 2 180

  7. Multiplication: Area Model Example: x 12=15 x 10 +15x 2 15 15 x 10 = (10 + 5) x 10 = (10 x 10) + (5 x 10) (10 x 10) (10x 2) 15x 2 = (10 + 5) x 2 = (10x 2) + (5x 2) (5x 2) (5 x 10)

  8. Multiplication: Area Model Example: x 12=15 x 10 +15x 2 15 15 x 10 = (10 + 5) x 10 = (10 x 10) + (5 x 10) (10 x 10) (5 x 10) (10 x 10) (10x 2) 100 20 15x 2 = (10 + 5) x 2 = (10x 2) + (5x 2) (10x 2 ) (5 x 2 ) (5x 2) (5 x 10) 10 50 50 10 100 + 50 + 20 + 10 = 180 20 100

  9. Multiplication: Area Model x 12= Example: 15 15 x12 5 2 10 =5 x 2 (10 x 10) (10x 2) 100 20 (5x 2) (5 x 10) 10 50 100 + 50 + 20 + 10 = 180 10

  10. Multiplication: Area Model x 12= Example: 15 15 x12 10 2 10 =5 x 2 (10 x 10) (10x 2) 20 =10 x 2 100 20 (5x 2) (5 x 10) 10 50 100 + 50 + 20 + 10 = 180 20

  11. Multiplication: Area Model x 12= Example: 15 15 x12 5 10 10 =5 x 2 (10 x 10) (10x 2) 20 =10 x 2 100 20 50 =10 x 5 (5x 2) (5 x 10) 10 50 100 + 50 + 20 + 10 = 180 50

  12. Multiplication: Area Model x 12= Example: 15 15 x12 10 10 10 =5 x 2 (10 x 10) (10 x 10) (10x 2) 20 =10 x 2 100 100 100 20 20 20 50 =10 x 5 100 =10 x 10 (5x 2) (5 x 10) 180 180 10 50 100 + 50 + 20 + 10 100 50

  13. Multiplication: Area Model x 12= Example: 15 10 + 2 (10 x 10) 10 (10x 2) 100 20 + 5 (5x 2) (5 x 10) 10 50 100 + 50 + 20 + 10 100 50

  14. Multiplication: Area Model x 18= 23 23 x18 10 + 8 24 (20 x 10) 20 30 (20x 8) 200 160 160 200 + 3 (3x 8) (3 x 10) 414 24 30 200 30 + + 160 + 24 = 414

  15. Multiplication: Partial Products 23 x18 24 = 8 x 3 160 = 8 x 20 30 = 10 x 3 200 = 10 x 20 414

  16. Multiplication: Partial Products 23 x18 23 x18 200 160 24 24 30 24 = 8 x 3 30 160 = 8 x 20 160 30 = 10 x 3 200 200 = 10 x 20 414 414

  17. Multiplication: Partial Products 37 x42 14 = 2 x 7 60 =2 x 30 280 = 40 x 7 1200 = 40 x 30 1554

  18. Multiplication: Partial Products 215 x36 3 0 30 = 6 x 5 9 60 = 6 x 10 1200 = 6 x 200 1 3 14 150 = 30 x 5 300 = 30 x 10 7 6000= 30 x 200 7 1 4

  19. Multiplication: Partial Products 215 x36 30 + 6 150 30 300 60 30 = 6 x 5 60 = 6 x 10 200 + 10 + 5 1200 = 6 x 200 150 = 30 x 5 6000 300 = 30 x 10 1200 6000= 30 x 200 7740

  20. Multiplication: Partial Products Try These: • 73 x 42 = • 87 x 26 = • 127 x 15 = • 907 x 43 = • 6.4 x 4.2 =

  21. Multiplication: Partial Products Try These: • 73 x 42 = • 87 x 26 = • 127 x 15 = • 907 x 43 = • 6.4 x 4.2 = 3066 2262 1905 39001 26.88

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