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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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Questions & Answers

what is mutation
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what is a cell
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classification of plants, gymnosperm features.
Linsy Reply
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What is Atoms
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urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
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State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
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how is urine formed in human
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how is urine formed in human
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malaria is caused by an insect called mosquito.
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Malaria is cause by female anopheles mosquito
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Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
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a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
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Achiri Reply
in the mouth
EZEKIEL
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stimulates the follicle to release the mature ovum into the oviduct
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endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
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Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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biology is the study of life.
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Biology is the study of how living organisms live and survive in a specific environment
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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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