Name that Property pt 1
Order does not matter when adding and multiplying values.
Example: 3x+4y=4y+3x
Commutative Property
Order does not matter when grouping values using addition and multiplication.
Example: (a+b)+c=a+(b+c)
Associative
Evaluate:
3+5*2
13
2+3*(6-2)
14
Simplify:
2(x+5)
2x+10
Simplify:
3(2x+5)
6x+15
Simplify:
2x+3x
5x
Simplify:
3x+2+5x+6
8x+8
Adding zero to any value with not change the value. Identity means stays the same.
Example: x+0=xAdditive Identity
Adding the Opposite of any value will cancel out the value to zero.
Example: x+(-x)=0
Additive Inverse
Evaluate
(6+4)/2
5
Evaluate:
(5+3)2/4
16
Simplify:
3(2+y)
6+3y
Simplify:
6(y-4)
6y-24
Simplify:
5y+7y
12y
Simplify:
7a-3a+10
4a+10
Multiplying any value by 1 will not change the value.
Example: x*1=x
Multiplying by the reciprocal of any value will cancel out the value to 1.
Example: x*1/x=1
Multiplicative Inverse
Evaluate:
12-32
3
Evaluate
18/3+23
14
Simplify:
4(a-3)
4a-12
Simplify:
2(3x+7)-5
6x+9
Simplify:
4a+6+2a+3
6a+9
Simplify:
2y+3x-y+5x
8x+y
The left and right side of an equal sign are the exact same.
Example: if x=2 then 2=x
Symmetric
You can replace given values with an equivalent value.
Example: if x=2 and y=2 then x=y
Transitive
Evaluate
20/(2*5)
2
Evaluate
4*(10-32)
4
Simplify:
5(x+2)
Simplify:
4(2a-3)+6
8a-6
Simplify:
10x-3x+8
7x+8
Simplify:
8b-2+4b+7
12b+5
A value equals itself
Example: 3=3 x=x
Reflexive
Multiplying a value by and expression inside parentheses.
Example: 4(x-2)=4x-8
Distributive
Evaluate:
(8-2)2+4
40
Evaluate
(12-6)*(22+1)
24
Simplify:
2(3x+4)
6x+8
Simplify:
7(x+2)-3(x-1)
4x+17
Simplify:
6m+2n+4m-n
10m+n
Simplify:
9x+3y-4x+2y
5x+5y