Properties of Real Numbers
IN WORDS
ISN Page 32
You have learned properties of real numbers starting in 4th grade. 8th grade math pulls them all together so that we
can justify our steps when solving equations. Let’s review.
1) Addition Property of Equality:
IN WORDS:
If you add the same number on both sides of
an equation, the two sides remain equal.
2) Subtraction Property of Equality:
IN WORDS:
If you subtract the same number on both sides of
an equation, the two sides remain equal.
3) Multiplication Property of Equality:
IN WORDS:
If you multiply the same number on both sides of
an equation, the two sides remain equal.
4) Division Property of Equality:
IN WORDS:
If you divide the same number on both sides of
an equation, the two sides remain equal.
5) Associative Property of Addition:
IN WORDS:
The way in which addends are grouped does not
change the sum.
6) Associative Property of Multiplication:
IN WORDS:
The way in which factors are grouped does not
change the sum.
7) Commutative Property of Addition:
IN WORDS:
The order in which numbers are added does not
change the sum
8) Commutative Property of Multiplication:
IN WORDS:
The order in which numbers are multiplied does
not change the sum
9) Identity Property of Addition (Additive Identity)
IN WORDS:
The sum of an addend and zero
is the addend.
10) Identity Property of Multiplication (Multiplicative Identity)
IN WORDS:
The product of a factor and 1 is
the factor.
11) Inverse Property of Addition (Additive Inverse)
IN WORDS:
The sum of a number and its
additive inverse is zero.
12) Inverse Property of Multiplication (Multiplicative Inverse)
IN WORDS:
The product of a number and its
multiplicative inverse is 1.
13) Distributive Property: Not available in just words. We will practice on the back
14) Zero Product Property:
IN WORDS: The product of a factor and zero is zero.
There are a lot of properties to know. Use flashcards to help you remember them. Always do your assigned
homework, and complete the notes on the back.
Properties of Real Numbers
EXAMPLES
ISN Page 32
Match the property on the left with its example on the right.
1) Addition Property of Equality: Example:
A
a + (b + c) = (a + b) + c
2) Subtraction Property of Equality: Example:
B
2 + (3+4) = (2+3) + 4
a+0=a
4+0=4
3) Multiplication Property of Equality: Example:
4) Division Property of Equality: Example:
D
5) Associative Property of Addition: Example:
a
C
(b c) = (a
a
1=a
b)
c
4
1=4
2 (3 4) = (2 3)
6) Associative Property of Multiplication: Example:
7) Commutative Property of Addition: Example:
E
a
b=b
a
4
8) Commutative Property of Multiplication: Example:
9) Identity Property of Addition (Additive Identity) Example:
a
G
4
2(x + 2) = 2x + 4
4(x – 1) = 4x - 1
F
10) Identity Property of Multiplication (Multiplicative Identity) Example:
3=3
0=0
4
0=0
11) Inverse Property of Addition (Additive Inverse) Example:
12) Inverse Property of Multiplication (Multiplicative Inverse) Example:
H
a + (-a) = 0
3 + (-3) = 0
13) Distributive Property: Example:
J
14) Zero Product Property: Example:
a+b=b+a
1+4=4+1
3x = 6
3 3
K
x-2=6
x-2+2=6+2
L
x+1=5
x + 1 -1 = 5 - 1
M
N
A
a
1
a
=1
x

2  5 2
2

3
1
=1
3
4