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Did you grow up using the U.S. customary or the metric system of measurement? Describe two examples in your life when you had to convert between systems of measurement. Which system do you think is easier to use? Explain.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

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Overall, after looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?

Chapter review exercises

Rational and Irrational Numbers

In the following exercises, write as the ratio of two integers.

In the following exercises, determine which of the numbers is rational.

0.42 , 0. 3 , 2.56813…

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0.75319… , 0. 16 , 1.95

0. 16 , 1.95

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In the following exercises, identify whether each given number is rational or irrational.

72 64

  1. irrational
  2. rational

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In the following exercises, list the whole numbers, integers, rational numbers, irrational numbers, real numbers for each set of numbers.

−9 , 0 , 0.361.... , 8 9 , 16 , 9

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−5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4

  1. 4
  2. 5 , 4 , 4
  3. 5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4
  4. none
  5. 5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4

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Commutative and Associative Properties

In the following exercises, use the commutative property to rewrite the given expression.

−14 · 5 = ____

−14·5 = 5(−14)

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a + 8 = ____

a + 8 = 8 + a

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In the following exercises, use the associative property to rewrite the given expression.

( 13 · 5 ) · 2 = _____

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( 22 + 7 ) + 3 = _____

(22 + 7) + 3 = 22 + (7 + 3)

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1 2 ( 22 y ) = _____

1 2 ( 22 y ) = ( 1 2 · 22 ) y

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In the following exercises, evaluate each expression for the given value.

If y = 11 12 , evaluate: y + 0.7 + ( y ) y + ( y ) + 0.7

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If z = 5 3 , evaluate: z + 5.39 + ( z ) z + ( z ) + 5.39

  1. 5.39
  2. 5.39

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If k = 65 , evaluate: 4 9 ( 9 4 k ) ( 4 9 · 9 4 ) k

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If m = −13 , evaluate: 2 5 ( 5 2 m ) ( 2 5 · 5 2 ) m

  1. 13
  2. 13

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In the following exercises, simplify using the commutative and associative properties.

1 4 + 11 15 + ( 1 4 )

11 15

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−18 · 15 · 2 9

−60

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( 3.98 d + 0.75 d ) + 1.25 d

5.98 d

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11 x + 8 y + 16 x + 15 y

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52 m + ( −20 n ) + ( −18 m ) + ( −5 n )

34 m + (−25 n )

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Distributive Property

In the following exercises, simplify using the distributive property.

9 ( u 4 )

9 y − 36

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−8 ( −7 a 12 )

56 a + 96

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( y + 10 ) · p

yp + 10 p

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( a 4 ) ( 6 a + 9 )

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4 ( x + 3 ) 8 ( x 7 )

−4 x + 68

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In the following exercises, evaluate using the distributive property.

If u = 2 , evaluate 3 ( 8 u + 9 ) and 3 · 8 u + 3 · 9 to show that 3 ( 8 u + 9 ) = 3 · 8 u + 3 · 9

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If n = 7 8 , evaluate 8 ( n + 1 4 ) and 8 · n + 8 · 1 4 to show that 8 ( n + 1 4 ) = 8 · n + 8 · 1 4

  1. 9
  2. 9

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If d = 14 , evaluate −100 ( 0.1 d + 0.35 ) and −100 · ( 0.1 d ) + ( −100 ) ( 0.35 ) to show that −100 ( 0.1 d + 0.35 ) = −100 · ( 0.1 d ) + ( −100 ) ( 0.35 )

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If y = −18 , evaluate ( y 18 ) and y + 18 to show that ( y 18 ) = y + 18

  1. 36
  2. 36

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Properties of Identities, Inverses, and Zero

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

29 + 0 = 29

identity property of addition

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( 6 x + 0 ) + 4 x = 6 x + 4 x

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9 · 1 + ( 3 ) = 9 + ( 3 )

identity property of multiplication

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In the following exercises, find the additive inverse.

In the following exercises, find the multiplicative inverse.

In the following exercises, simplify.

( n + 6.75 ) + 0.25

n + 7

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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