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Properties of Multiplication

Properties of Multiplication. 6.C.1.a Multiply whole numbers 3.A.1.a.Use technology tools, including software and hardware, from a range of teacher-selected options to learn a new content or reinforce skills. Definitions. Zero Property – The product of any factor and 0 equals 0. 65 x 0 = 0

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Properties of Multiplication

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  1. Properties of Multiplication 6.C.1.a Multiply whole numbers 3.A.1.a.Use technology tools, including software and hardware, from a range of teacher-selected options to learn a new content or reinforce skills

  2. Definitions • Zero Property – The product of any factor and 0 equals 0. • 65 x 0 = 0 • 8 x 0 = 0

  3. Zero Property • 5 x 0 = 0 4 x 0 = 0 • a x 0 = 0 b x 0 = 0 • 6 x 0 = 0 3 x 0 = 0 • y x 0 = 0 z x 0 = 0 • 18 x 0 = 0 19 x 0 = 0

  4. Solve these equations using the zero property n = 0 • 7 x n = 0 • 2 x m = 0 • 3 x z = 0 • 6 x g = 0 • 4 x s = 0 • 8 x c = 0 m = 0 z = 0 g = 0 s = 0 c = 0

  5. Definitions • Commutative Property – The order of the factors does not change the product. • 6 x 8 = 8 x 6 • 14 x 3 = 3 x 14

  6. Commutative Property • 5 x 4 = 20 4 x 5 = 20 • a x b = c b x a = c • 6 x 3 = 18 3 x 6 = 18 • a x y = z y x a = z • 3 x 4 x 1 = 12 1 x 3 x 4 = 12

  7. Solve these equations using the commutative property n = 4 • n + 7 = 7 + 4 • m + 2 = 2 + 5 • z + 3 = 3 + 9 • g + 6 = 6 + 11 • s + 4 = 4 + 20 • c + 8 = 8 + 32 m = 5 z = 9 g = 11 s = 20 c = 32

  8. Definitions • Associative Property – The way factors are grouped does not change a product. • (11 x 3) x 4 = 11 x (3 x 4) • 5 x (5 x 10) = (5 x 5) x 10

  9. Associative Property • 5 x (7 x 4) = (5 x 7) x 4 • a x (b x c) = (a x b) x c • (6 x 3) x 2 = 6 x (3 x 2) • 12 x (8 x 1) = (12 x 8) x 1 • (9 x 10) x 2 = 9 x (10 x 2)

  10. Rewrite these equations using the associative property • 2 x (3 x 3) = • 4 x (9 x 8) = • 3 x (7 x 4) = • 5 x (6 x 3) = • 10 x (5 x 7) = • 11 x (2 x 2) = (2 x 3) x 3 (4 x 9) x 8 (3 x 7) x 4 (5 x 6) x 3 (10 x 5) x 7 (11 x 2) x 2

  11. Definitions • Identity Property –The product of any factor and 1 equals the factor. • 56 x 1 = 56 • 38 x 1 = 38

  12. Identity Property • 5 x 1 = 5 4 x 1 = 4 • a x 1 = a b x 1 = b • 6 x 1 = 6 3 x 1 = 3 • y x 1 = y z x 1 = z • 18 x 1 = 18 19 x 1 = 19

  13. Solve these equations using the identity property • n x 1 = 8 • b x 1 = 7 • 3 x 1 = m • v x 1 = 5 • 4 x 1 = w • r x 1 = 2 n = 8 b = 7 m = 3 v = 5 w = 4 r = 2

  14. Definitions • Distributive Property of Multiplication over Addition – Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. • 6 x (12 + 9) = (6 x 12) + (6 x 9) • 4 x (15 + 6) = (4 x 15) + (4 x 6)

  15. Distributive Property of Multiplication over Addition • 5 x (7 + 4) = (5 x 7) + (5 x 4) • a x (b + c) = (a x b) + (a x c) • 6 x (3 + 2) = (6 x 3) + (6 x 2) • 12 x (8 + 1) = (12 x 8) + (12 x 1) • 9 x (10 + 2) = (9 x 10) + (9 x 2)

  16. Solve these equations using the distributive property of multiplication over addition • 10 x (5 + 2) = • 3 x (3 + 4) = • 8 x (9 + 2) = • 12 x (4 + 8) = • 15 x (10 + 11) = • 13 x (6 + 3) = (10 x 5) + (10 x 2) = 70 (3 x 3) + (3 x 4) = 21 (8 x 9) + (8 x 2) = 88 (12 x 4) + (12 x 8) = 144 (15 x 10) + (15 x 11) = 315 (13 x 6) + (13 x 3) = 117

  17. Definitions • Distributive Property of Multiplication over Subtraction – To multiply a difference of two numbers by a third number, you can multiply the first two numbers by the third, and then find the difference of the products. • 7 x (23 – 9) = (7 x 23) – (7 x 9) • 5 x (9 – 3) = (5 x 9) – (5 x 3)

  18. Distributive Property of Multiplication over Subtraction • 5 x (7 - 4) = (5 x 7) - (5 x 4) • a x (b - c) = (a x b) - (a x c) • 6 x (3 - 2) = (6 x 3) - (6 x 2) • 12 x (8 - 1) = (12 x 8) - (12 x 1) • 9 x (10 - 2) = (9 x 10) - (9 x 2)

  19. Solve these equations using the distributive property of multiplication over subtraction • 10 x (5 - 2) = • 3 x (4 - 3) = • 8 x (9 - 2) = • 12 x (8 - 4) = • 15 x (11 - 10) = • 13 x (6 - 3) = (10 x 5) - (10 x 2) = 30 (3 x 4) - (3 x 3) = 3 (8 x 9) - (8 x 2) = 56 (12 x 8) - (12 x 4) = 48 (15 x 11) - (15 x 10) = 15 (13 x 6) - (13 x 3) = 39

  20. Properties with Beans • Now that you have learned about the different properties we are going to do a hands-on activity.

  21. 9 Name the property…3 X 11 = 11 X 3 • Identity • Commutative • Zero • associative

  22. 10 Name the property…13 X 1 = 13 • Identity • Commutative • Zero • associative

  23. 10 Name the property…20 X 0 • Identity • Commutative • Zero • associative

  24. 10 Name the property…(12 X 4) X 3 = 12 X (4 X 3) • Identity • Commutative • Zero • associative

  25. 10 Name the property…3 X (9 – 1) = (3 X 9) – (3 X 1) • Identity • Commutative • Distributive of multiplication over subtraction • Distributive of multiplication over addition

  26. 10 Name the property…5 X (6 + 2) = (5 X 6) + (5 X 2) • Identity • Commutative • Distributive of multiplication over subtraction • Distributive of multiplication over addition

  27. Now that you can identify the properties… Let’s use those properties to solve some problems.

  28. 10 8 x 56 • 400 • 448 • 500 • 456

  29. 10 4 x (30 + 15) • 120 • 140 • 160 • 180

  30. 10 (2000 x 0) x 16 • 32000 • 320000 • 0 • 16

  31. 10 (210 x 1) x 1 • 212 • 210 • 211 • 220

  32. 10 8 x (60 – 4) • 416 • 420 • 406 • 448

  33. 10 4 x (80 – 5) • 300 • 285 • 320 • 220

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