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the sum of −4 and −17 , increased by 32

( −4 + ( −17 ) ) + 32 ; 11

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the difference of 15 and −7 subtract 15 from −7

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the quotient of −45 and −9

−45 −9 ; 5

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the product of −12 and the difference of c and d

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Use Integers in Applications

In the following exercises, solve.

Temperature The high temperature one day in Miami Beach, Florida, was 76 ° . That same day, the high temperature in Buffalo, New York was 8 ° . What was the difference between the temperature in Miami Beach and the temperature in Buffalo?

84 degrees

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Checking Account Adrianne has a balance of $22 in her checking account. She deposits $301 to the account. What is the new balance?

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Visualize Fractions

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

1 4

2 8 , 3 12 , 4 16 answers may vary

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5 6

10 12 , 15 18 , 20 24 answers may vary

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Simplify Fractions

In the following exercises, simplify.

Multiply Fractions

In the following exercises, multiply.

7 12 ( 8 21 )

2 9

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Divide Fractions

In the following exercises, divide.

2 5 ÷ ( −10 )

1 25

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In the following exercises, simplify.

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

15 · 5 5 2 2 · 10

5 2

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2 + 4 ( 3 ) −3 2 2

−2

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7 + 3 ( 5 ) −2 3 2

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Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

the quotient of c and the sum of d and 9.

c d + 9

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the quotient of the difference of h and k , and −5 .

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Add and Subtract Fractions

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

1 8 + ( 3 8 )

1 2

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In the following exercises, subtract.

y 17 9 17

y 9 17

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8 d 3 d

11 d

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Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

1 5 ( 1 10 )

3 10

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9 16 ( 4 5 )

19 80

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7 20 ( 5 8 )

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Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

2 3 + 1 2 3 4 2 3

14

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Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

x + 1 2 when
x = 1 8
x = 1 2

3 8 0

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x + 2 3 when
x = 1 6
x = 5 3

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4 p 2 q when p = 1 2 and q = 5 9

5 9

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5 m 2 n when m = 2 5 and n = 1 3

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u + v w when
u = −4 , v = −8 , w = 2

−6

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m + n p when
m = −6 , n = −2 , p = 4

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Decimals

Name and Write Decimals

In the following exercises, write as a decimal.

Eight and three hundredths

8.03

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Nine and seven hundredths

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In the following exercises, name each decimal.

7.8

seven and eight tenths

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Round Decimals

In the following exercises, round each number to the nearest hundredth tenth whole number.

5.7932

5.79 5.8 6

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12.4768

12.48 12.5 12

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Add and Subtract Decimals

In the following exercises, add or subtract.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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