Math Properties
Distributive, Commutative, Associative, Identity
The distributive property helps us how we can distribute multiplication over addition, subtraction, multiplication, division and bracket.
In algebra, the Distributive Property is used to help you simplify algebraic expressions, combine like terms, and find the value of variables.
Commutative Property: ORDER
(Commute or Move)
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
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
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;
a(b + c) = ab + ac
Evaluating Expressions:
We use the order of operations to understand and remember how to evaluate expressions involving two or more operations.PEMDAS is a common acronym that can help us remember the order:
P ( ) parentheses or grouping symbols
E a² exponents
D ➗Divide
A + Add
S - Subtract
m X multiply
We multiply and divide from left to right.
Then we add and subtract from left to right.
Let's evaluate this Expression!
4³ - 36 ÷ 6 + 2 (9 + 12)
9 + 12 = 21
4³ - 36 ÷ 6 + 2 x 21
4³ - 36 ÷ 6 + 42
4³ = 4 x 4 x 4 = 64
64 - 6 + 42
100
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