Addition Order is not important when adding numbers. 4 + 7 = 7 + 4 Multiplication Order is not important when multiplying numbers. 8 x 3 = 3 x 8
Commutative Property
Associative Property: GROUPING Addition: The grouping of numbers is not important when adding numbers. 3 + (4 + 7) = ; (3 + 4) + 7 Multiplication: The grouping of numbers is not important when multiplying numbers. 2 x (8 x 3) = ; (2 x 8) x 3
Neither the associative nor the commutative property works for subtraction or division. Grouping and order make a huge difference when subtracting and dividing!
Associative Property
Identity Property: SELF Addition Any number plus zero equals that number. 4 + 0 = 4 Multiplication Any number times one equals that number. 8 x 1 = 8
These properties are also called the additive identity and the multiplicative identity. The number wants to stay the same; it wants to be itself. Multiplication Any number times zero is zero. 8 x 0 = 0
Identity Property
Question Which number sentence below illustrates the commutative property? A. 5 x 7 x 6 = 210 B. 3 x (6 x 4) = (3 x 6) x 4 = 72 C. 4 + 5 + 0 = 9 D. 9 + 2 + 5 = 9 + 5 + 2 = 16
Distributive Property:
The distributive property combines together addition (or subtraction) and multiplication. The idea behind the distributive property is that it doesn’t matter if you find the product of the sum/difference or the sum/difference of the product. The distributive property comes in handy both in algebraic problems and in solving arithmetic problems mentally. Let’s try a problem: Can you multiply 9 x 47 in your head?
Try it with the distributive property instead of replicating the paper-and-pencil mentally. Did you get 423? It should have worked this way:
First thought: 9 x 40 = 360 Second thought: 9 x 7 = 63 Third thought: 360 + 63 = 423
Distributive Property
Q. Which answer choice shows the expression correctly simplified? 5(3c + 5d) – 2d A. 15c + 23d B. 15c + 25d C. 15c + 3d D. 15c + 27d
Review:
Math properties: Commutative: The order of numbers is not important when adding or multiplying
Associative: grouping of numbers is not important when adding or multiplying
Identity: for addition, adding zero keeps the number the same; for multiplication, multiplying by one keeps the number the same
Multiplicative Property of Zero: anything times zero is zero
Distributive: combines addition/subtraction and multiplication for expanding expressions with parentheses;
