Real Numbers Worksheet Template Page 2
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1
2
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4Practice D
Unit 1
Getting
Real Numbers
continued
Ready
You’ve seen that there are a number of categories of real numbers. Although
each category has its own unique set of properties, there are a handful of
properties that they all share.
Properties of Real Numbers
Addition
Multiplication
Commutative
a + b = b + a
ab = ba
Associative
a + (b + c) = (a + b) + c
a(bc) = (ab)c
Identity
a + 0 = a
a ∙ 1 = a
a ∙ 1
__
Inverse
a + (− a) = 0
a = 1, (a ≠ 0)
Distributive
a(b + c) = ab + ac
EXAMPLE 2
Name the property that justifies the equation −9 + 2 = 2 − 9.
This follows the pattern a + b = b + a, with a = −9 and b = 2.
Solution: commutative property of addition
EXAMPLE 3
Name the property that justifies the equation 5 ∙ 1 = 5.
This follows the pattern a ∙ 1 = a, with a = 5.
Solution: multiplicative identity property
The numbers a and −a are called additive inverses or opposites. Similarly, the
numbers a and 1
__
a , where a ≠ 0, are called multiplicative inverses or reciprocals.
Additive inverses have a special feature in common. They share the same
absolute value. The absolute value of a given number can be thought of as the
distance between the number and 0 on a number line. The following notation
can be used for the absolute value of a number, x: ∙x∙.
D-2
Getting Ready Practice D Real Numbers
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