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**Multiplication Properties**

5th Grade

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**Multiplication Properties**

Associative Property Commutative Property Zero Property Identity Property Distributive Property

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**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.

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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)

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**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.

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**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

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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

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**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.

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

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

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

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

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

Answers are on the next slide.

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

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**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)

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**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.

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**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)

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**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 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

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**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

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**How did you do? 18 correct Excellent 17 correct Very Good**

correct Good correct Passing 12 – 0 correct You need more practice.

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