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The Commutative Property states that when adding or multiplying two or more numbers or terms, order is not important. That is:
2+7=7+2
3×5=5×3
7−2=2−7
50÷10=10÷50
The Associative Property states that when adding or multiplying three or more numbers or terms together, grouping is not important. That is:
(5+2)+6=5+(2+6)
(5×2)×6=5×(2×6)
(5−2)−3=5−(2−3)
(20÷4)÷2=20÷(4÷2)
The Distributive Property states that for any three terms a,b, and c: a(b+c)=ab+ac
Select the answer below that models this
4(3+2)=(4×3)+(4×2)
5(6+7)=56+57
4(3+2)=(4+3)×(4+2)
5(6+7)=5×6×7
The Identity Property of Addition states that adding 0 to any expression leaves the expression unchanged.
3 + 0 = 3
5 + 0 = 0
7 + 0 = 70
3 + 0 = 3
The Identity Property of Multiplication states that multiplying any expression by 1 leaves the expression unchanged.
8(1) = 8
10(1) = 11
5(1) = 51
6(1) = 6
The Additive Inverse Property states that for every number a there is a number −a such that a + (−a) = 0.
5 + (-5) = 0
6 + (-6) = -12
2 + (-2) = 0
8 + (-7) = 0
The Multiplicative Inverse Property states that for every nonzero number a there is a number a1 such that a×a1=1
A common name used for the multiplicative inverse is the reciprocal
8 ×81=1
5×51=0
6×121=1
3×31=1
The Additive Property of Equality states that equality is maintained if the same amount is added to both sides of an equation. That is, if a = b, then a + c = b + c
5x = 10 then 5x + 2 = 12
3x = 9 then 3x + 3 = 9
4x = 8 then 4x - 4 = 4
6x = 12 then 6x - 3 = 6
The Multiplicative Property of Equality states that equality is maintained if both sides of an equation are multiplied by the same amount. That is, if a = b, then a · c = b · c
y = 3 then 4y = 4(3)
x = 2 then 2x = 22
y = 6 then 3y = 3
x = 4 then 2x = 8
A symbol used to represent one or more numbers. Letters of the English alphabet are used as _________. For example, in the expression 3x – (8.6xy + z), the _________ are x, y, and z.
Variables
Expressions
Order of Operations
Combine like terms
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