1. Multiplication Properties Shirley Garrett 5 th Grade

2. Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive Property

3. 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.

4. Commutative Property The order of the numbers doesnt change the result (answer to the problem) p X q = q X p

5. 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.

6. 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

7. Associative Property The grouping of the factors doesnt change the answer. (p X q) X r = p X (q X r)

8. 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.

9. 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, its commutative. 5 X (5 X 2) = (2 X 5) X 5

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

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

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

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

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

15. 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)

16. 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.

17. 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)

18. Test Yourself 1. 9 X 3 = 3 X w 2. 3 X (4 X 2 ) = (n X 4) X 2 3. 234 X 1 = z 4. 56 X p = 11 X 56 5. 7,547,598,375 X c = 0 6. q X 8 = 8 X 4 7. 5 X (7 X 2) = (5 X 7) X n 8. 4 X 509 = (4 X 500) + (4 X m) 9. 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 Rewrite each equation with the correct answer, and write the name of the property.

19. Test Yourself Answers 1. 9 X 3 = 3 X 9 Commutative 2. 3 X (4 X 2) = (3 X 4) X 2 Associative 3. 234 X 1 = 234 Identity 4. 56 X 11 = 11 X 56 Commutative 5. 7,547,598,375 X 0 = 0 Zero 6. 4 X 8 = 8 X 4 Commutative 7. 5 X (7 X 2) = (5 X 7) X 2 Associative 8. 4 X 509 = (4 X 500) + (4 X 9) Distributive 9. 6 X 310 = (6 X 300) + (6 X 10) Distributive 10. (2 X 8) X 5 = 2 X (8 X 5) Associative 11. 1 X 2,567 = 2,567 Identity 12. 195 X 5 = (200 X 5) – (5 X 5) Distributive 13. 0 X 75,879,705 = 0 Zero 14. 98,765 X 1 = 98,765 Identity 15. 5 X 9 = 9 X 5 Commutative 16. 5 X 205 = (5 X 200) + (5 X 5) Distributive 17. 4 X (1 X 7) = (4 X 1) X 7 Associative 18. 758,375,937 X 0 = 0 Zero

20. How did you do? 18 correctExcellent 17 correctVery Good 16 - 15 correctGood 14 - 13 correctPassing 12 – 0 correctYou need more practice.