Download Number Properties

Properties of Real Numbers
Math 0099
Opposites
Two real numbers that are the same distance
from the origin of the real number line are
opposites of each other.
Examples of opposites:
2 and -2 -100 and 100  15 and
15
Reciprocals
Two numbers whose product is 1 are
reciprocals of each other.
Examples of Reciprocals:
1 and 5
-3 and  1
5
3
5
4
and
4
5
Absolute Value
The absolute value of a number is its
distance from 0 on the number line. The
absolute value of x is written x .
Examples of absolute value:
5  5
3 3

7 7
Commutative Property of
Addition
a+b=b+a
When adding two numbers, the order of the
numbers does not matter.
Examples of the Commutative Property of
Addition
2+3=3+2
(-5) + 4 = 4 + (-5)
Commutative Property of
Multiplication
ab=ba
When multiplying two numbers, the order
of the numbers does not matter.
Examples of the Commutative Property of
Multiplication
23=32
(-3)  24 = 24  (-3)
Associative Property of Addition
a + (b + c) = (a + b) + c
When three numbers are added, it makes no
difference which two numbers are added
first.
Examples of the Associative Property of
Addition
2 + (3 + 5) = (2 + 3) + 5
(4 + 2) + 6 = 4 + (2 + 6)
Associative Property of
Multiplication
a(bc) = (ab)c
When three numbers are multiplied, it
makes no difference which two numbers are
multiplied first.
Examples of the Associative Property of
Multiplication
2  (3  5) = (2  3)  5
(4  2)  6 = 4  (2  6)
Distributive Property
a(b + c) = ab + ac
Multiplication distributes over addition.
Examples of the Distributive Property
2 (3 + 5) = (2  3) + (2  5)
(4 + 2)  6 = (4  6) + (2  6)
Additive Identity Property
The additive identity property states that if 0
is added to a number, the result is that
number.
Example: 3 + 0 = 0 + 3 = 3
Multiplicative Identity Property
The multiplicative identity property states
that if a number is multiplied by 1, the
result is that number.
Example: 5  1 = 1  5 = 5
Additive Inverse Property
The additive inverse property states that
opposites add to zero.
7 + (-7) = 0 and -4 + 4 = 0
Multiplicative Inverse Property
The multiplicative inverse property states
that reciprocals multiply to 1.
5
1
1
5
2 3
 1
3 2
Identify which property that
justifies each of the following.
4  (8  2) = (4  8)  2
Identify which property that
justifies each of the following.
4  (8  2) = (4  8)  2
Associative Property of Multiplication
Identify which property that
justifies each of the following.
6+8=8+6
Identify which property that
justifies each of the following.
6+8=8+6
Commutative Property of Addition
Identify which property that
justifies each of the following.
12 + 0 = 12
Identify which property that
justifies each of the following.
12 + 0 = 12
Additive Identity Property
Identify which property that
justifies each of the following.
5(2 + 9) = (5  2) + (5  9)
Identify which property that
justifies each of the following.
5(2 + 9) = (5  2) + (5  9)
Distributive Property
Identify which property that
justifies each of the following.
5 + (2 + 8) = (5 + 2) + 8
Identify which property that
justifies each of the following.
5 + (2 + 8) = (5 + 2) + 8
Associative Property of Addition
Identify which property that
justifies each of the following.
5 9
 1
9 5
Identify which property that
justifies each of the following.
5 9
 1
9 5
Multiplicative Inverse Property
Identify which property that
justifies each of the following.
5  24 = 24  5
Identify which property that
justifies each of the following.
5  24 = 24  5
Commutative Property of Multiplication
Identify which property that
justifies each of the following.
18 + -18 = 0
Identify which property that
justifies each of the following.
18 + -18 = 0
Additive Inverse Property
Identify which property that
justifies each of the following.
-34 1 = -34
Identify which property that
justifies each of the following.
-34 1 = -34
Multiplicative Identity Property
Least Common Denominator
The least common denominator (LCD) is
the smallest number divisible by all the
denominators.
2
5
and
3
4
Example: The LCD of
is 12 because
12 is the smallest number into which 3 and
4 will both divide.
Adding Two Fractions
To add two fractions you must first find the
LCD. In the problem below the LCD is 12.
Then rewrite the two addends as equivalent
expressions with the LCD. Then add the
numerators and keep the denominator.
3 5
9 10 19
 


4 6 12 12 12