multiplication properties

Multiplication Properties

Shirley Garrett5th Grade

Multiplication Properties

Commutative PropertyAssociative PropertyIdentity PropertyZero PropertyDistributive 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 w56 X p = 11 X 56q X 8 = 8 X 45 X 9 = r X 5

The answers are on the next slide.

Commutative Property

9 X 3 = 3 X 956 X 11 = 11 X 564 X 8 = 8 X 45 X 9 = 9 X 5

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 24 X (p X 7) = (4 X 1) X 75 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 24 X (1 X 7) = (4 X 1) X 75 X (7 X 2) = (5 X 7) X 2(2 X 8) X 5 = 2 X (8 X 5)

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 = zq X 2,567 = 2,56798,765 X d = 98,765

Answers are on the next slide.

Identity Property

234 X 1 = 2341 X 2,567 = 2,56798,765 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 = 0758,375,937 X 0 = bz 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

1. 9 X 3 = 3 X w2. 3 X (4 X 2 ) = (n X 4) X 23. 234 X 1 = z4. 56 X p = 11 X 565. 7,547,598,375 X c = 06. q X 8 = 8 X 47. 5 X (7 X 2) = (5 X 7) X n8. 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 = 2,56712.12. 195 X 5 = (200 X 5) – (5

X t)13.z X 75,879,705 = 014.98,765 X d = 98,76515.5 X 9 = r X 516.s X 205 = (5 X 200) + (5 X 5)17.4 X (p X 7) = (4 X 1) X 718.758,375,937 X 0 = b

Rewrite each equation with the correct answer, and write the name of the property.

Test Yourself Answers

1. 9 X 3 = 3 X 9 Commutative2. 3 X (4 X 2) = (3 X 4) X 2

Associative3. 234 X 1 = 234 Identity4. 56 X 11 = 11 X 56

Commutative5. 7,547,598,375 X 0 = 0 Zero6. 4 X 8 = 8 X 4 Commutative7. 5 X (7 X 2) = (5 X 7) X 2

Associative8. 4 X 509 = (4 X 500) + (4 X 9)

Distributive9. 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 Identity12.195 X 5 = (200 X 5) – (5 X 5)

Distributive13.0 X 75,879,705 = 0 Zero14.98,765 X 1 = 98,765 Identity15.5 X 9 = 9 X 5 Commutative16.5 X 205 = (5 X 200) + (5 X

5) Distributive17.4 X (1 X 7) = (4 X 1) X 7

Associative18.758,375,937 X 0 = 0 Zero

How did you do?

18 correct Excellent17 correct Very Good16 - 15 correct Good14 - 13 correct Passing12 – 0 correct You need more practice.