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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to estimate by rounding fractions. By the end of the module students should be able to estimate the sum of two or more fractions using the technique of rounding fractions.

Section overview

  • Estimation by Rounding Fractions

Estimation by rounding fractions is a useful technique for estimating the result of a computation involving fractions. Fractions are commonly rounded to 1 4 size 12{ { {1} over {4} } } {} , 1 2 size 12{ { {1} over {2} } } {} , 3 4 size 12{ { {3} over {4} } } {} , 0, and 1. Remember that rounding may cause estimates to vary.

Sample set a

Make each estimate remembering that results may vary.

Estimate 3 5 + 5 12 size 12{ { {3} over {5} } + { {5} over {"12"} } } {} .

Notice that 3 5 size 12{ { {3} over {5} } } {} is about 1 2 size 12{ { {1} over {2} } } {} , and that 5 12 size 12{ { {5} over {"12"} } } {} is about 1 2 size 12{ { {1} over {2} } } {} .

Thus, 3 5 + 5 12 size 12{ { {3} over {5} } + { {5} over {"12"} } } {} is about 1 2 + 1 2 = 1 size 12{ { {1} over {2} } + { {1} over {2} } =1} {} . In fact, 3 5 + 5 12 = 61 60 size 12{ { {3} over {5} } + { {5} over {"12"} } = { {"61"} over {"60"} } } {} , a little more than 1.

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Estimate 5 3 8 + 4 9 10 + 11 1 5 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } } {} .

Adding the whole number parts, we get 20. Notice that 3 8 size 12{ { {3} over {8} } } {} is close to 1 4 size 12{ { {1} over {4} } } {} , 9 10 size 12{ { {9} over {"10"} } } {} is close to 1, and 1 5 size 12{ { {1} over {5} } } {} is close to 1 4 size 12{ { {1} over {4} } } {} . Then 3 8 + 9 10 + 1 5 size 12{ { {3} over {8} } + { {9} over {"10"} } + { {1} over {5} } } {} is close to 1 4 + 1 + 1 4 = 1 1 2 size 12{ { {1} over {4} } +1+ { {1} over {4} } =1 { {1} over {2} } } {} .

Thus, 5 3 8 + 4 9 10 + 11 1 5 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } } {} is close to 20 + 1 1 2 = 21 1 2 size 12{"20"+1 { {1} over {2} } ="21" { {1} over {2} } } {} .

In fact, 5 3 8 + 4 9 10 + 11 1 5 = 21 19 40 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } ="21" { {"19"} over {"40"} } } {} , a little less than 21 1 2 size 12{"21" { {1} over {2} } } {} .

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Practice set a

Use the method of rounding fractions to estimate the result of each computation. Results may vary.

5 8 + 5 12 size 12{ { {5} over {8} } + { {5} over {"12"} } } {}

Results may vary. 1 2 + 1 2 = 1 size 12{ { {1} over {2} } + { {1} over {2} } =1} {} . In fact, 5 8 + 5 12 = 25 24 = 1 1 24 size 12{ { {5} over {8} } + { {5} over {"12"} } = { {"25"} over {"24"} } =1 { {1} over {"24"} } } {}

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7 9 + 3 5 size 12{ { {7} over {9} } + { {3} over {5} } } {}

Results may vary. 1 + 1 2 = 1 1 2 size 12{1+ { {1} over {2} } =1 { {1} over {2} } } {} . In fact, 7 9 + 3 5 = 1 17 45 size 12{ { {7} over {9} } + { {3} over {5} } =1 { {"17"} over {"45"} } } {}

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8 4 15 + 3 7 10 size 12{8 { {4} over {"15"} } +3 { {7} over {"10"} } } {}

Results may vary. 8 1 4 + 3 3 4 = 11 + 1 = 12 size 12{8 { {1} over {4} } +3 { {3} over {4} } ="11"+1="12"} {} . In fact, 8 4 15 + 3 7 10 = 11 29 30 size 12{8 { {4} over {"15"} } +3 { {7} over {"10"} } ="11" { {"29"} over {"30"} } } {}

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16 1 20 + 4 7 8 size 12{"16" { {1} over {20} } +4 { {7} over {8} } } {}

Results may vary. 16 + 0 + 4 + 1 = 16 + 5 = 21. size 12{ left ("16"+0 right )+ left (4+1 right )="16"+5="21"} {} In fact, 16 1 20 + 4 7 8 = 20 37 40 size 12{"16" { {1} over {"20"} } +4 { {7} over {8} } ="20" { {"37"} over {"40"} } } {}

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Exercises

Estimate each sum or difference using the method of rounding. After you have made an estimate, find the exact value of the sum or difference and compare this result to the estimated value. Result may vary.

5 6 + 7 8 size 12{ { {5} over {6} } + { {7} over {8} } } {}

1 + 1 = 2   1 17 24 size 12{1+1=2 left (1 { {"17"} over {"24"} } right )} {}

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3 8 + 11 12 size 12{ { {3} over {8} } + { {"11"} over {"12"} } } {}

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9 10 + 3 5 size 12{ { {9} over {"10"} } + { {3} over {5} } } {}

1 + 1 2 = 1 1 2 1 1 2 size 12{1+ { {1} over {2} } =1 { {1} over {2} } left (1 { {1} over {2} } right )} {}

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13 15 + 1 20 size 12{ { {"13"} over {"15"} } + { {1} over {"20"} } } {}

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3 20 + 6 25 size 12{ { {3} over {"20"} } + { {6} over {"25"} } } {}

1 4 + 1 4 = 1 2 39 100 size 12{ { {1} over {4} } + { {1} over {4} } = { {1} over {2} } left ( { {"39"} over {"100"} } right )} {}

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1 12 + 4 5 size 12{ { {1} over {"12"} } + { {4} over {5} } } {}

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15 16 + 1 12 size 12{ { {"15"} over {"16"} } + { {1} over {"12"} } } {}

1 + 0 = 1 1 1 48 size 12{1+0=1 left (1 { {1} over {"48"} } right )} {}

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29 30 + 11 20 size 12{ { {"29"} over {"30"} } + { {"11"} over {"20"} } } {}

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5 12 + 6 4 11 size 12{ { {5} over {"12"} } +6 { {4} over {"11"} } } {}

1 2 + 6 1 2 = 7   6 103 132 size 12{ { {1} over {2} } +6 { {1} over {2} } =7 left (6 { {"103"} over {"132"} } right )} {}

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3 7 + 8 4 15 size 12{ { {3} over {7} } +8 { {4} over {"15"} } } {}

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9 10 + 2 3 8 size 12{ { {9} over {"10"} } +2 { {3} over {8} } } {}

1 + 2 1 2 = 3 1 2 3 11 40 size 12{1+2 { {1} over {2} } =3 { {1} over {2} } left (3 { {"11"} over {"40"} } right )} {}

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19 20 + 15 5 9 size 12{ { {"19"} over {"20"} } +"15" { {5} over {9} } } {}

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8 3 5 + 4 1 20 size 12{8 { {3} over {5} } +4 { {1} over {"20"} } } {}

8 1 2 + 4 = 12 1 2 12 13 20 size 12{8 { {1} over {2} } +4="12" { {1} over {2} } left ("12" { {"13"} over {"20"} } right )} {}

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5 3 20 + 2 8 15 size 12{5 { {3} over {"20"} } +2 { {8} over {"15"} } } {}

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9 1 15 + 6 4 5 size 12{9 { {1} over {"15"} } +6 { {4} over {5} } } {}

9 + 7 = 16   15 13 15 size 12{9+7="16" left ("15" { {"13"} over {"15"} } right )} {}

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7 5 12 + 10 1 16 size 12{7 { {5} over {"12"} } +"10" { {1} over {"16"} } } {}

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3 11 20 + 2 13 25 + 1 7 8 size 12{3 { {"11"} over {"20"} } +2 { {"13"} over {"25"} } +1 { {7} over {8} } } {}

3 1 2 + 2 1 2 + 2 = 8   7 189 200 size 12{3 { {1} over {2} } +2 { {1} over {2} } +2=8 left (7 { {"189"} over {"200"} } right )} {}

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6 1 12 + 1 1 10 + 5 5 6 size 12{6 { {1} over {"12"} } +1 { {1} over {"10"} } +5 { {5} over {6} } } {}

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15 16 7 8 size 12{ { {"15"} over {"16"} } - { {7} over {8} } } {}

1 1 = 0   1 16 size 12{1 - 1=0 left ( { {1} over {"16"} } right )} {}

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12 25 9 20 size 12{ { {"12"} over {"25"} } - { {9} over {"20"} } } {}

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Exercises for review

( [link] ) The fact that
( a first number a second number ) a third number = a first number ( a second number a third number )
is an example of which property of multiplication?

associative

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( [link] ) Find the quotient: 14 15 ÷ 4 45 size 12{ { {"14"} over {"15"} } div { {4} over {"45"} } } {} .

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( [link] ) Find the difference: 3 5 9 2 2 3 size 12{3 { {5} over {9} } - 2 { {2} over {3} } } {} .

8 9 size 12{ { {8} over {9} } } {}

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( [link] ) Find the quotient: 4 . 6 ÷ 0 . 11 size 12{4 "." "6 " div " 0" "." "11"} {} .

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( [link] ) Use the distributive property to compute the product: 25 37 size 12{"25 " cdot " 37"} {} .

25 40 3 = 1000 75 = 925 size 12{"25" left ("40" - 3 right )="1000" - "75"="925"} {}

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Questions & Answers

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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