Properties
The order in which numbers are added does not change the sum or product.
Ex. 3 + 5 = 5 + 3
7 x 4 = 4 x 7
Commutative Property of Addition and Multiplication
The quotient of 62 and g
62/g
Simplify the following expression: 12y + 3y
15y
2x + 3x - 6
5x - 6
Evaluate 15/x when x = 3
5
3(7x + 4)
21x + 12
The sum of any number and 0 is that number.
Ex. 17 + 0 = 17
Addition Property of Zero
Twice k
2k or 2(k) or 2 x k or (2)(k)
Simplify the following expression: x + 8y + 2x
3x + 8y
5x - x + 3 +27
4x + 30
Evaluate 24 + x - 9 when x = 6
21
5 (9 - 10p)
45 - 50p
The product of any number and 1 is that number.
EX. 13 x 1 = 13
Multiplication Property of One
The sum of x and 41
x + 41
Simplify the following expression: 8 + 12x - x + 2y
11x + 2y + 8
12x + 7 - 3x + 5
9x +12
Evaluate 9a + 7 when a = 2
25
20g + 35
5( 4g + 7)
Changing the grouping of three or more factors does not change the product or the sum.
Ex. 3 + (5 -2) = (3 + 5 ) -2
(9 x 1) x 2 = 9 x (1 x 2)
Associative Property of Multiplication & Addition
p squared decreased by 9
p2 - 9
Simplify the following expression: 6x + 2y + 9x + 10y -3
15x + 12y -3
6x2 + 18x + 12x2 - 8x
18x2 + 10x
Evaluate x/3 + y when x = 12 and y = 4
42f + 8 - 14k
2( 21f + 4 -7k)
The product of any number and zero is zero.
Ex. 3 x 0 = 0
1,237 x 0 = 0
Multiplication Property of Zero
The product of 3 and y increased by g cubed
3y + g3
Simplify the following expression: 7w + 10x - 3w + 5 + w + 6
5w + 10x + 11
5 + 6x3 - 3x3 + 3 + 4x +7x
3x3 + 11x + 8
Evaluate x2 + z2 when x = 5 z = 8
89
(4s + 12c - 3x) 11
44s + 132c - 33x