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Multiplication Properties

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  1. Multiplication Properties

  2. Vocabulary Factor Product Commutative property Associative property Distributive property

  3. Factor The numbers multiplied Example: 23 X 48 = 1,104

  4. Product The answer to a multiplication problem. Example: 23 X 48 = 1,104

  5. Multiplication Properties • Commutative Property • Associative Property • Identity Property • Zero Property • Distributive Property

  6. Why Should you Learn about the Properties of Multiplication? • It helps you solve problems without working them out. • It helps with mental math. • It makes understanding math easier.

  7. Commutative Property • The order of the numbers doesn’t change the result (answer to the problem) • p X q = q X p

  8. Commutative Property • 9 X 3 = 3 X w • 56 X p = 11 X 56 • q X 8 = 8 X 4 • 5 X 9 = r X 5 The answers are on the next slide.

  9. Commutative Property • 9 X 3 = 3 X 9 • 56 X 11 = 11 X 56 • 4 X 8 = 8 X 4 • 5 X 9 = 9 X 5

  10. Associative Property • The grouping of the factors doesn’t change the answer. • (p X q) X r = p X (q X r)

  11. Associative Property • 3 X (4 X 2) = (n X 4) X 2 • 4 X (p X 7) = (4 X 1) X 7 • 5 X (7 X 2) = (5 X 7) X n • (2 X z) X 5 = 2 X (8 X 5) Is this Associative? • 5 X (n X 2) = (2 X 5) X 5 Watch out! Answers are on the next slide.

  12. Associative Property • 3 X (4 X 2) = (3 X 4) X 2 • 4 X (1 X 7) = (4 X 1) X 7 • 5 X (7 X 2) = (5 X 7) X 2 • (2 X 8) X 5 = 2 X (8 X 5) Is this Associative? No, it’s commutative. • 5 X (5 X 2) = (2 X 5) X 5

  13. Identity Property • Any number multiplied by 1 will give you the original number. • 23,487 X 1 = 23,487

  14. Identity Property • 234 X 1 = z • q X 2,567 = 2,567 • 98,765 X d = 98,765 Answers are on the next slide.

  15. Identity Property • 234 X 1 = 234 • 1 X 2,567 = 2,567 • 98,765 X 1 = 98,765

  16. Zero Property • When any number is multiplied with zero, the answer is zero. • 98,756,432 X 0 = 0

  17. Zero Property • 7,547,598,375 X c = 0 • 758,375,937 X 0 = b • z X 75,879,705 = 0

  18. Distributive Property • Multiplying the sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the product. • 9 X (20 - 3) = (9 X 20) – (9 X 3) • 8 X (40 + 5) = (8 X 40) + (8 X 5) • 8 X 45 = (8 X 40) + (8 X 5)

  19. Distributive Property • 4 X 509 = (4 X 500) + (4 X m) • 6 X 310 = (6 X n) + (6 X 10) • s X 205 = (5 X 200) + (5 X 5) • 195 X 5 = (200 X 5) – (5 X t) The answers are on the next slide.

  20. Distributive Property • 4 X 509 = (4 X 500) + (4 X 9) • 6 X 310 = (6 X 300) + (6 X 10) • 5 X 205 = (5 X 200) + (5 X 5) • 195 X 5 = (200 X 5) – (5 X 5)

  21. 9 X 3 = 3 X w 3 X (4 X 2 ) = (n X 4) X 2 234 X 1 = z 56 X p = 11 X 56 7,547,598,375 X c = 0 q X 8 = 8 X 4 5 X (7 X 2) = (5 X 7) X n 4 X 509 = (4 X 500) + (4 X m) 6 X 310 = (6 X n) + (6 X 10) (2 X z) X 5 = 2 X (8 X 5) q X 2,567 = 2,567 195 X 5 = (200 X 5) – (5 X t) z X 75,879,705 = 0 98,765 X d = 98,765 5 X 9 = r X 5 s X 205 = (5 X 200) + (5 X 5) 4 X (p X 7) = (4 X 1) X 7 758,375,937 X 0 = b Test Yourself Rewrite each equation with the correct answer, and write the name of the property.

  22. 9 X 3 = 3 X 9 Commutative 3 X (4 X 2) = (3 X 4) X 2 Associative 234 X 1 = 234 Identity 56 X 11 = 11 X 56 Commutative 7,547,598,375 X 0 = 0 Zero 4 X 8 = 8 X 4 Commutative 5 X (7 X 2) = (5 X 7) X 2 Associative 4 X 509 = (4 X 500) + (4 X 9) Distributive 6 X 310 = (6 X 300) + (6 X 10) Distributive (2 X 8) X 5 = 2 X (8 X 5) Associative 1 X 2,567 = 2,567 Identity 195 X 5 = (200 X 5) – (5 X 5) Distributive 0 X 75,879,705 = 0 Zero 98,765 X 1 = 98,765 Identity 5 X 9 = 9 X 5 Commutative 5 X 205 = (5 X 200) + (5 X 5) Distributive 4 X (1 X 7) = (4 X 1) X 7 Associative 758,375,937 X 0 = 0 Zero Test Yourself Answers

  23. How did you do? • 18 correct Excellent • 17 correct Very Good • 16 - 15 correct Good • 14 - 13 correct Passing • 12 – 0 correct You need more practice.