Math Properties

1. Math Properties The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

2. Commutative Properties • Numbers can be added or multiplied in any order. • a + b = b +a 1 + 3 = 3 + 1 • a × b = b × a 2 x 6 = 6 x 2 Why is this important? 15 + 7 + 5 $4. 30 + $10.50 + $0.70 + $0.50 6 x 12 x 5

3. Does Commutative Property work with Subtraction? 10 - 5 = 5 - 10 • Does Commutative Property work with Division? 50 ÷ 10 = 10 ÷ 50

4. Identity Properties • Identity property of addition - the sum of zero and any number or variable is the number or variable itself. • When you add 0 to any number, it will always keep its identity!!!! 5 + 0 = 5 A + 0 = A

5. Identity Properties • Identity property of multiplication - the product of 1 and any number or variable is the number or variable itself. 5 X 1= 5 B x 1 = B

6. Associative Properties • The associative property of addition - when adding more than two numbers the grouping of the numbers does not change the sum. (a + b) + c = a + (b + c) Example:(29 + 13) + 7 = 29 + (13 + 7) Notice how adding the 13 + 7 first makes completing the problem easier mentally

7. Associative Properties • The associative property of multiplication - when multiplying more than two numbers the grouping of the factors does not change the product. (a xb) xc = a x (b xc) Example: (6 x 4) x 5 = 6 x (4 x 5) Notice how multiplying the 4 and 5 first makes completing the problem easier.

8. Distributive Properties • The distributive property lets you multiply a sum by multiplying each number separately and then add the products.

9. 4 ( 45)= 4 (40) + 4(5) • 20(13)=