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Decimals: Combinations of Operations with Decimals and Fractions

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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.

Example 1

0.38⋅140.38⋅14 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 .25 4 1.00   8   ̲ 20 20 ̲ 0
To convert 1414 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 .3 4 1 8 × .25 ̲ 190 76   ̲ .0950

Thus, 0.38⋅14=0.0950.38⋅14=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.

Example 2

1.85+38⋅4.11.85+38⋅4.1 size 12{1 "." "85"+ { {3} over {8} } cdot 4 "." 1} {} Convert 3838 size 12{ { {3} over {8} } } {} to a decimal.

1.85+0.375⋅4.11.85+0.375⋅4.1 size 12{1 "." "85"+0 "." "375" cdot 4 "." 1} {} Multiply before adding.

1.85+1.53751.85+1.5375 size 12{1 "." "85"+1 "." "5375"} {} Now add.

3.3875

Example 3

51345−0.2851345−0.28 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 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

Example 4

0.125 113 + 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 0.125 113 + 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.

Exercise 1

35+1.635+1.6 size 12{ { {3} over {5} } +1 "." 6} {}

Solution

2.2 or 215215 size 12{2 { {1} over {5} } } {}

Exercise 2

8.91+15⋅1.68.91+15⋅1.6 size 12{8 "." "91"+ { {1} over {5} } cdot 1 "." 6} {}

Solution

9.23

Exercise 3

19166.12+72519166.12+725 size 12{1 { {9} over {"16"} } left (6 "." "12"+ { {7} over {"25"} } right )} {}

Solution

10

Exercise 4

0.15611115−0.050.15611115−0.05 size 12{ { {0 "." "156"} over {1 { {"11"} over {"15"} } } } -0 "." "05"} {}

Solution

125 or  0.04125 or  0.04 size 12{ { {1} over {"25"} } " or "0 "." "04"} {}

Exercises

Exercise 5

310+0.7310+0.7 size 12{ { {3} over {"10"} } +0 "." 7} {}

Solution

1

Exercise 6

15+0.115+0.1 size 12{ { {1} over {5} } +0 "." 1} {}

Exercise 7

58−0.51358−0.513 size 12{ { {5} over {8} } -0 "." "513"} {}

Solution

0.112

Exercise 8

0.418−672000.418−67200 size 12{0 "." "418"- { {"67"} over {"200"} } } {}

Exercise 9

0.22⋅140.22⋅14 size 12{0 "." "22" cdot { {1} over {4} } } {}

Solution

0.055

Exercise 10

35⋅8.435⋅8.4 size 12{ { {3} over {5} } cdot 8 "." 4} {}

Exercise 11

125⋅3.19125⋅3.19 size 12{ { {1} over {"25"} } cdot 3 "." "19"} {}

Solution

0.1276

Exercise 12

320÷ 0.05320÷ 0.05 size 12{ { {3} over {"20"} } ÷0 "." "05"} {}

Exercise 13

740÷ 0.25740÷ 0.25 size 12{ { {7} over {"40"} } ÷0 "." "25"} {}

Solution

0.7

Exercise 14

1115÷ 0.9⋅0.121115÷ 0.9⋅0.12 size 12{1 { {1} over {"15"} } ÷0 "." 9 cdot 0 "." "12"} {}

Exercise 15

9.26+14⋅0.819.26+14⋅0.81 size 12{9 "." "26"+ { {1} over {4} } cdot 0 "." "81"} {}

Solution

9.4625

Exercise 16

0.588+140⋅0.240.588+140⋅0.24 size 12{0 "." "588"+ { {1} over {"40"} } cdot 0 "." "24"} {}

Exercise 17

120+3.62⋅38120+3.62⋅38 size 12{ { {1} over {"20"} } +3 "." "62" cdot { {3} over {8} } } {}

Solution

1.4075

Exercise 18

7+0.15÷ 3307+0.15÷ 330 size 12{7+0 "." "15"÷ { {3} over {"30"} } } {}

Exercise 19

1516⋅710−0.51516⋅710−0.5 size 12{ { {"15"} over {"16"} } cdot left ( { {7} over {"10"} } -0 "." 5 right )} {}

Solution

0.1875

Exercise 20

0.2⋅720+1.11430.2⋅720+1.1143 size 12{0 "." 2 cdot left ( { {7} over {"20"} } +1 "." "1143" right )} {}

Exercise 21

34⋅0.875+1834⋅0.875+18 size 12{ { {3} over {4} } cdot left (0 "." "875"+ { {1} over {8} } right )} {}

Solution

0.75

Exercise 22

5.198−0.26⋅14250+0.1195.198−0.26⋅14250+0.119 size 12{5 "." "198"-0 "." "26" cdot left ( { {"14"} over {"250"} } +0 "." "119" right )} {}

Exercise 23

0.514+0.320.514+0.32 size 12{0 "." 5 { {1} over {4} } + left (0 "." 3 right ) rSup { size 8{2} } } {}

Solution

0.615

Exercise 24

1.42−1.6121.42−1.612 size 12{ left (1 "." 4 right ) rSup { size 8{2} } -1 "." 6 { {1} over {2} } } {}

Exercise 25

382−0.000625+(1.1)2382−0.000625+(1.1)2 size 12{ left ( { {3} over {8} } right ) rSup { size 8{2} } -0 "." "000625"+ \( 1 "." 1 \) rSup { size 8{2} } } {}

Solution

1.35

Exercise 26

0.62⋅120−1250.62⋅120−125 size 12{ left (0 "." 6 right ) rSup { size 8{2} } cdot left ( { {1} over {"20"} } - { {1} over {"25"} } right )} {}

Exercise 27

122−0.125122−0.125 size 12{ left ( { {1} over {2} } right ) rSup { size 8{2} } -0 "." "125"} {}

Solution

0.125

Exercise 28

0.75412+5120.75412+512 size 12{ { {0 "." "75"} over {4 { {1} over {2} } } } + { {5} over {"12"} } } {}

Exercise 29

0.3752116−1330.3752116−133 size 12{ left ( { {0 "." "375"} over {2 { {1} over {"16"} } } } - { {1} over {"33"} } right )} {}

Solution

0.15¯0.15¯ size 12{0 "." {overline {"15"}} } {}

Exercise 30

813⋅1142.25+925813⋅1142.25+925 size 12{8 { {1} over {3} } cdot left ( { {1 { {1} over {4} } } over {2 "." "25"} } + { {9} over {"25"} } right )} {}

Exercise 31

0.3212350.350.3212350.35 size 12{ { { { {0 "." "32"} over { { {"12"} over {"35"} } } } } over {0 "." "35"} } } {}

Solution

2.6¯2.6¯ size 12{2 "." {overline {6}} } {}

Exercise 32

49 64 − 5 0.125 1.375 49 64 − 5 0.125 1.375

Exercises for Review

Exercise 33

((Reference)) Is 21,480 divisible by 3?

Solution

yes

Exercise 34

((Reference)) Expand 14 4 14 4 . Do not find the actual value.

Exercise 35

((Reference)) Find the prime factorization of 15,400.

Solution

23⋅52⋅7⋅1123⋅52⋅7⋅11

Exercise 36

((Reference)) Convert 8.016 to a fraction.

Exercise 37

((Reference)) Find the quotient. 16 ÷2716 ÷27 size 12{"16 " div "27"} {}.

Solution

0.592¯0.592¯ size 12{0 "." {overline {"592"}} } {}

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