Multiplication Properties Shirley Garrett

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) p X q = q X p

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.

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 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) = (3 X 4) X 2 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 = (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.