Name ____________________________________
Algebra I – Pd ____
Date _____________
Real Number Properties
You may answer the questions on the paper
1. State which property is being shown
a) 3(x + 5) = 3x + 3(5)
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b) (9 + 4) + 5 = 9 + (4 + 5)
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c) 36 * 0 = 0
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d) 8m + 6m = (8 + 6)m
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e) (m * 14) * n = m * (14 * n) ___________________________
f) 162 * 1 = 162
g) 4 *
1
=1
4
h) 5 + 8 = 8 + 5
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____________________________
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2. Complete the matching column
_______ 1) 5(6 + 2) = 5(6) + 5(2)
a) Additive Identity
_______ 2) If 40 = 4(10) then 4(10) = 40
b) Associative Prop of Mult.
_______ 3) 5 + 18 = 18 + 5
c) Commutative Property of Addition
_______ 4) 14 · 1 = 14
d) Distributive Property
_______ 5) 15 + 2 = 15 + 2
e) Transitive Property
_______ 6) (5 + 6) + 8 = 5 + (6 + 8)
f) Multiplicative Identity
_______ 7) If 62 = 36 and 36 = 4(9) then 62 = 4(9)
g) Associative Prop of Addition
_______ 8) 23 · 0 = 0
h) Multiplicative Property of Zero
i) Commutative Property of Mult.
j) Symmetric Property
k) Reflexive Proprty
3. Is the following operation true? If true, which property is being shown. If false, explain why.
(8  4)  2 = 8  (4  2)
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4. Which is an illustration of the commutative property of addition?
(a) a + 0 = a
(b) a(b + c) = ab + ac
(c) a + b = b + a
(d) (a + b) + c = a + (b + c)
5. Which statement illustrates the associative property of multiplication?
1
(a) 2   = 1
(b) 2(3 + 4) = 2(3) + 2(4)
2
(c) 2(3 * 4) = (2 * 3)4
(d) 2(1) = 2
6. Give an example of each:
a) a number that is whole, but not a natural number
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b) a number that is rational, but not a whole number
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c) a number that is rational, but not an integer
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d) a number that is irrational
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e) a number that is a natural number, but not an integer
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f) a number that is an integer, but not a natural number
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7. Write True or False (do not write T or F...you must write out the word
a) all whole numbers are rational
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b) all integers are natural numbers
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c) all real numbers are rational
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d) all irrational numbers are real
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e) all natural numbers are irrational ___________