Multiplication Properties 7th Grade

Multiplication Properties Commutative Property Associative Property Distributive Property Identity Property Zero 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 in which 2 numbers are added or multiplied does not change the answer. p X q = q X p

Commutative Property What is missing? 9 X 3 = 3 X w 56 X p = 11 X 56 q X 8 = 8 X 4 5 X 9 = r X 5

Commutative Property 9 X 3 = 3 X 9 56 X 11 = 11 X 56 4 X 8 = 8 X 4

Associative Property The grouping of 3 numbers when they are added or multiplied does not change the answer. Parenthesis change; Order does not!! (p X q) X r = p X (q X r)

Associative Property What is missing? 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 (3 X 2) = (3 X 5) X 2

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

Identity Property Any number multiplied by 1 will give you the original number. 23,487 X 1 = 23,487 Any number added to zero will give you the original number. 456 + 0 = 456

Identity Property 234 X 1 = z q X 2,567 = 2,567 98,765 X d = 98,765

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)

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)

Test Yourself Rewrite each equation with the correct answer, and write the name of the property. 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 12. 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 Answers 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

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.