1. Properties of REAL Numbers
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Properties of REAL Numbers

2. Opposites
Two real numbers that are the same distance from the origin of the real number line are opposites of each other. EXAMPLES -100 AND AND -2
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3. Reciprocals
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4. Absolute Value
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5. Commutative Property of Addition
a + b = b + a
When adding two numbers, the order of the numbers does not matter.
EXAMPLES
2 + 3 = 3 + 2
(-5) + 4 = 4 + (-5)
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6. Commutative Property of Multiplication
a × b = b × a
When multiplying two numbers, the order of the numbers does not matter.
EXAMPLES
2 × 3 = 3 × 2
(-3) × 24 = 24 × (-3)
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7. 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
2 + (3 + 5) = (2 + 3) + 5
(4 + 2) + 6 = 4 + (2 + 6)
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8. Associative Property of Multiplication
a(bc) = (ab)c
When three numbers are multiplied, it makes no difference which two numbers are multiplied first.
EXAMPLES
2 × (3 × 5) = (2 × 3) × 5
(4 × 2) × 6 = 4 × (2 × 6)
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9. Distributive Property
a(b + c) = ab + ac
Multiplication distributes over addition.
EXAMPLES
2 (3 + 5) = (2 × 3) + (2 × 5)
(4 + 2) × 6 = (4 × 6) + (2 × 6)
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10. Additive Identity Property
The additive identity property states that if 0 is added to a number, the result is that number. EXAMPLE = = 3
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11. 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
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12. Additive Inverse Property
The additive inverse property states that opposites add to zero. EXAMPLE 7 + (-7) = 0 and = 0
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13. Multiplicative Inverse Property
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14. PRACTICE EXERCISES
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15. Associative Property of Multiplication
Identify which property justifies each of the following:
4 × (8 × 2) = (4 × 8) × 2
Associative Property of Multiplication
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16. COMMUTATIVE PROPERTY OF ADDITION
Identify which property justifies each of the following:
6 + 8 = 8 + 6
COMMUTATIVE PROPERTY OF ADDITION
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17. ADDITIVE IDENTITY PROPERTY
Identify which property justifies each of the following:
= 12
ADDITIVE IDENTITY PROPERTY
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18. DISTRIBUTIVE PROPERTY
Identify which property justifies each of the following:
5(2 + 9) = (5 × 2) + (5 × 9)
DISTRIBUTIVE PROPERTY
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19. Multiplicative Inverse Property
Multiplicative Inverse Property
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20. Commutative Property of Multiplication
Identify which property justifies each of the following:
5 × 24 = 24 × 5
Commutative Property of Multiplication
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21. Additive Inverse Property
Identify which property justifies each of the following:
18 + (-18) = 0
Additive Inverse Property
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22. Multiplicative Identity Property
Identify which property justifies each of the following:
-34 × 1 = -34
Multiplicative Identity Property
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