Multiplication Properties 5th Grade

Multiplication Properties Associative Property Commutative Property Zero Property Identity 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.

Associative Property The grouping of the factors doesn’t change the answer (the parenthesis are moved). (p X q) X r = p X (q X r) (2 X 3) X 4 = 2 X (3 X 4)

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

Commutative Property The order of the numbers doesn’t change the result (answer to the problem) p X q = q X p 4 X 5 = 5 X 4

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

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

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

Distributive Property To multiply a sum by a number, you can multiply each addend by the number and then add the products. 6 X 23 = 6 X (20+3) = (6X20)+(6X3)

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) 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)

Test Yourself Rewrite each equation with the correct answer, and write the name of the property. 9 X 3 = 3 X 9 3 X (4 X 2 ) = (3 X 4) X 2 234 X 1 = 234 56 X 11 = 11 X 56 7,547,598,375 X 0 = 0 4 X 8 = 8 X 4 5 X (7 X 2) = (5 X 7) X 2 4 X 509 = (4 X 500) + (4 X 9) 6 X 310 = (6 X 300) + (6X 10) (2 X 8) X 5 = 2 X (8 X 5) 1 X 2,567 = 2,567 12. 195 X 5 = (200 X 5) – (5 X 5) 0 X 75,879,705 = 0 98,765 X 1 = 98,765 5 X 9 = 9 X 5 5 X 205 = (5 X 200) + (5 X 5) 4 X (1 X 7) = (4 X 1) X 7 758,375,937 X 0 = 0

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.