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8.7 Decimals: combinations of operations with decimals and fractions

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses combinations of operations with decimals and fractions. By the end of the module students should be able to combine operations with decimals.

Having considered operations with decimals and fractions, we now consider opera­tions that involve both decimals and fractions.

Sample set a

Perform the following operations.

0 . 38 ⋅ 1 4 size 12{0 "." "38" cdot { {1} over {4} } } {} . Convert both numbers to decimals or both numbers to fractions. We’ll convert to decimals.

.25 4 1.00   8   ̲ 20 20 ̲ 0
To convert 1 4 size 12{ { {1} over {4} } } {} to a decimal, divide 1 by 4.

Now multiply 0.38 and .25.

.3 4 1 8 × .25 ̲ 190 76    ̲ .0950

Thus, 0 . 38 ⋅ 1 4 = 0 . 095 size 12{0 "." "38" cdot { {1} over {4} } =0 "." "095"} {} .

In the problems that follow, the conversions from fraction to decimal, or decimal to fraction, and some of the additions, subtraction, multiplications, and divisions will be left to you.

1 . 85 + 3 8 ⋅ 4 . 1 size 12{1 "." "85"+ { {3} over {8} } cdot 4 "." 1} {} Convert 3 8 size 12{ { {3} over {8} } } {} to a decimal.

1 . 85 + 0 . 375 ⋅ 4 . 1 size 12{1 "." "85"+0 "." "375" cdot 4 "." 1} {} Multiply before adding.

1 . 85 + 1 . 5375 size 12{1 "." "85"+1 "." "5375"} {} Now add.

3.3875

5 13 4 5 − 0 . 28 size 12{ { {5} over {"13"} } left ( { {4} over {5} } -0 "." "28" right )} {} Convert 0.28 to a fraction.

5 13 4 5 − 28 100 = 5 13 4 5 − 7 25 = 5 13 20 25 − 7 25 = 5 1 13 1 ⋅ 13 1 25 5 = 1 5

0.125 1 1 3 + 1 16 - 0.1211 = 125 1000 4 3 + 1 16 - 0.1211 = 1 8 4 3 + 1 16 - 0.1211 = 1 8 ⋅ 3 4 + 1 16 - 0.1211 = 3 32 + 1 16 - 0.1211 = 3 32 + 2 32 - 0.1211 = 5 32 - 0.1211 = 0.15625 - 0.1211 = 0.03515 Convert this to fraction form = 3515 100,000 = 703 20,000

Practice set a

Perform the following operations.

3 5 + 1 . 6 size 12{ { {3} over {5} } +1 "." 6} {}

2.2 or 2 1 5 size 12{2 { {1} over {5} } } {}

8 . 91 + 1 5 ⋅ 1 . 6 size 12{8 "." "91"+ { {1} over {5} } cdot 1 "." 6} {}

9.23

1 9 16 6 . 12 + 7 25 size 12{1 { {9} over {"16"} } left (6 "." "12"+ { {7} over {"25"} } right )} {}

10

0 . 156 1 11 15 − 0 . 05 size 12{ { {0 "." "156"} over {1 { {"11"} over {"15"} } } } -0 "." "05"} {}

1 25 or   0 . 04 size 12{ { {1} over {"25"} } " or "0 "." "04"} {}

Exercises

3 10 + 0 . 7 size 12{ { {3} over {"10"} } +0 "." 7} {}

1

1 5 + 0 . 1 size 12{ { {1} over {5} } +0 "." 1} {}

5 8 − 0 . 513 size 12{ { {5} over {8} } -0 "." "513"} {}

0.112

0 . 418 − 67 200 size 12{0 "." "418"- { {"67"} over {"200"} } } {}

0 . 22 ⋅ 1 4 size 12{0 "." "22" cdot { {1} over {4} } } {}

0.055

3 5 ⋅ 8 . 4 size 12{ { {3} over {5} } cdot 8 "." 4} {}

1 25 ⋅ 3 . 19 size 12{ { {1} over {"25"} } cdot 3 "." "19"} {}

0.1276

3 20 ÷  0 . 05 size 12{ { {3} over {"20"} } ÷0 "." "05"} {}

7 40 ÷  0 . 25 size 12{ { {7} over {"40"} } ÷0 "." "25"} {}

0.7

1 1 15 ÷  0 . 9 ⋅ 0 . 12 size 12{1 { {1} over {"15"} } ÷0 "." 9 cdot 0 "." "12"} {}

9 . 26 + 1 4 ⋅ 0 . 81 size 12{9 "." "26"+ { {1} over {4} } cdot 0 "." "81"} {}

9.4625

0 . 588 + 1 40 ⋅ 0 . 24 size 12{0 "." "588"+ { {1} over {"40"} } cdot 0 "." "24"} {}

1 20 + 3 . 62 ⋅ 3 8 size 12{ { {1} over {"20"} } +3 "." "62" cdot { {3} over {8} } } {}

1.4075

7 + 0 . 15 ÷  3 30 size 12{7+0 "." "15"÷ { {3} over {"30"} } } {}

15 16 ⋅ 7 10 − 0 . 5 size 12{ { {"15"} over {"16"} } cdot left ( { {7} over {"10"} } -0 "." 5 right )} {}

0.1875

0 . 2 ⋅ 7 20 + 1 . 1143 size 12{0 "." 2 cdot left ( { {7} over {"20"} } +1 "." "1143" right )} {}

3 4 ⋅ 0 . 875 + 1 8 size 12{ { {3} over {4} } cdot left (0 "." "875"+ { {1} over {8} } right )} {}

0.75

5 . 198 − 0 . 26 ⋅ 14 250 + 0 . 119 size 12{5 "." "198"-0 "." "26" cdot left ( { {"14"} over {"250"} } +0 "." "119" right )} {}

0 . 5 1 4 + 0 . 3 2 size 12{0 "." 5 { {1} over {4} } + left (0 "." 3 right ) rSup { size 8{2} } } {}

0.615

1 . 4 2 − 1 . 6 1 2 size 12{ left (1 "." 4 right ) rSup { size 8{2} } -1 "." 6 { {1} over {2} } } {}

3 8 2 − 0 . 000625 + ( 1 . 1 ) 2 size 12{ left ( { {3} over {8} } right ) rSup { size 8{2} } -0 "." "000625"+ \( 1 "." 1 \) rSup { size 8{2} } } {}

1.35

0 . 6 2 ⋅ 1 20 − 1 25 size 12{ left (0 "." 6 right ) rSup { size 8{2} } cdot left ( { {1} over {"20"} } - { {1} over {"25"} } right )} {}

1 2 2 − 0 . 125 size 12{ left ( { {1} over {2} } right ) rSup { size 8{2} } -0 "." "125"} {}

0.125

0 . 75 4 1 2 + 5 12 size 12{ { {0 "." "75"} over {4 { {1} over {2} } } } + { {5} over {"12"} } } {}

0 . 375 2 1 16 − 1 33 size 12{ left ( { {0 "." "375"} over {2 { {1} over {"16"} } } } - { {1} over {"33"} } right )} {}

0 . 15 ¯ size 12{0 "." {overline {"15"}} } {}

8 1 3 ⋅ 1 1 4 2 . 25 + 9 25 size 12{8 { {1} over {3} } cdot left ( { {1 { {1} over {4} } } over {2 "." "25"} } + { {9} over {"25"} } right )} {}

0 . 32 12 35 0 . 35 size 12{ { { { {0 "." "32"} over { { {"12"} over {"35"} } } } } over {0 "." "35"} } } {}

2 . 6 ¯ size 12{2 "." {overline {6}} } {}

49 64 − 5 0.125 1.375

Exercises for review

( [link] ) Is 21,480 divisible by 3?

yes

( [link] ) Expand 14 4 . Do not find the actual value.

( [link] ) Find the prime factorization of 15,400.

2 3 ⋅ 5 2 ⋅ 7 ⋅ 11

( [link] ) Convert 8.016 to a fraction.

( [link] ) Find the quotient. 16 ÷ 27 size 12{"16 " div "27"} {} .

0 . 592 ¯ size 12{0 "." {overline {"592"}} } {}

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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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