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Multiplication Properties Shirley Garrett 5th Grade Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive Property 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. Commutative Property The order of the numbers doesn’t change the result (answer to the problem) pXq=qXp Commutative Property 9X3=3Xw 56 X p = 11 X 56 qX8=8X4 5X9=rX5 The answers are on the next slide. Commutative Property 9X3=3X9 56 X 11 = 11 X 56 4X8=8X4 5X9=9X5 Associative Property The grouping of the factors doesn’t change the answer. (p X q) X r = p X (q X r) 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. Associative Property 3 X (4 X 2) 4 X (1 X 7) 5 X (7 X 2) (2 X 8) X 5 = = = = (3 X 4) X 2 (4 X 1) X 7 (5 X 7) X 2 2 X (8 X 5) Is this Associative? No, it’s commutative. 5 X (5 X 2) = (2 X 5) X 5 Identity Property Any number multiplied by 1 will give you the original number. 23,487 X 1 = 23,487 Identity Property 234 X 1 = z q X 2,567 = 2,567 98,765 X d = 98,765 Answers are on the next slide. Identity Property 234 X 1 = 234 1 X 2,567 = 2,567 98,765 X 1 = 98,765 Zero Property When any number is multiplied with zero, the answer is zero. 98,756,432 X 0 = 0 Zero Property 7,547,598,375 X c = 0 758,375,937 X 0 = b z X 75,879,705 = 0 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) 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. Distributive Property 4 X 509 6 X 310 5 X 205 195 X 5 = = = = (4 X 500) (6 X 300) (5 X 200) (200 X 5) + (4 X 9) + (6 X 10) + (5 X 5) – (5 X 5) Test Yourself Rewrite each equation with the correct answer, and write the name of the property. 1. 2. 3. 4. 5. 6. 7. 8. 9. 9X3=3Xw 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 qX8=8X4 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) 10. (2 X z) X 5 = 2 X (8 X 5) 11. q X 2,567 = 2,567 12. 12. 195 X 5 = (200 X 5) – (5 X t) 13. z X 75,879,705 = 0 14. 98,765 X d = 98,765 15. 5 X 9 = r X 5 16. s X 205 = (5 X 200) + (5 X 5) 17. 4 X (p X 7) = (4 X 1) X 7 18. 758,375,937 X 0 = b Test Yourself Answers 1. 9 X 3 = 3 X 9 Commutative 2. 3 X (4 X 2) = (3 X 4) X 2 3. 4. 5. 6. 7. 8. 9. 10. (2 X 8) X 5 = 2 X (8 X 5) Associative Associative 11. 1 X 2,567 = 2,567 Identity 234 X 1 = 234 Identity 12. 195 X 5 = (200 X 5) – (5 X 5) Distributive 56 X 11 = 11 X 56 Commutative 13. 0 X 75,879,705 = 0 Zero 7,547,598,375 X 0 = 0 Zero 14. 98,765 X 1 = 98,765 Identity 4 X 8 = 8 X 4 Commutative 15. 5 X 9 = 9 X 5 Commutative 5 X (7 X 2) = (5 X 7) X 2 Associative 16. 5 X 205 = (5 X 200) + (5 X 5) Distributive 4 X 509 = (4 X 500) + (4 X 9) Distributive 17. 4 X (1 X 7) = (4 X 1) X 7 Associative 6 X 310 = (6 X 300) + (6 X 10) Distributive 18. 758,375,937 X 0 = 0 Zero How did you do? 18 17 16 14 12 correct correct - 15 correct - 13 correct – 0 correct Excellent Very Good Good Passing You need more practice.