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Estimation by Rounding 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 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 1414 size 12{ { {1} over {4} } } {}, 1212 size 12{ { {1} over {2} } } {}, 3434 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.

Example 1

Estimate 35+51235+512 size 12{ { {3} over {5} } + { {5} over {"12"} } } {}.

Notice that 3535 size 12{ { {3} over {5} } } {} is about 1212 size 12{ { {1} over {2} } } {}, and that 512512 size 12{ { {5} over {"12"} } } {} is about 1212 size 12{ { {1} over {2} } } {}.

Thus, 35+51235+512 size 12{ { {3} over {5} } + { {5} over {"12"} } } {} is about 12+12=112+12=1 size 12{ { {1} over {2} } + { {1} over {2} } =1} {}. In fact, 35+512=616035+512=6160 size 12{ { {3} over {5} } + { {5} over {"12"} } = { {"61"} over {"60"} } } {}, a little more than 1.

Example 2

Estimate 538+4910+1115538+4910+1115 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } } {}.

Adding the whole number parts, we get 20. Notice that 3838 size 12{ { {3} over {8} } } {} is close to 1414 size 12{ { {1} over {4} } } {}, 910910 size 12{ { {9} over {"10"} } } {} is close to 1, and 1515 size 12{ { {1} over {5} } } {} is close to 1414 size 12{ { {1} over {4} } } {}. Then 38+910+1538+910+15 size 12{ { {3} over {8} } + { {9} over {"10"} } + { {1} over {5} } } {} is close to 14+1+14=11214+1+14=112 size 12{ { {1} over {4} } +1+ { {1} over {4} } =1 { {1} over {2} } } {}.

Thus, 538+4910+1115538+4910+1115 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } } {} is close to 20+112=211220+112=2112 size 12{"20"+1 { {1} over {2} } ="21" { {1} over {2} } } {}.

In fact, 538+4910+1115=211940538+4910+1115=211940 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } ="21" { {"19"} over {"40"} } } {}, a little less than 21122112 size 12{"21" { {1} over {2} } } {}.

Practice Set A

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

Exercise 1

58+51258+512 size 12{ { {5} over {8} } + { {5} over {"12"} } } {}

Solution

Results may vary. 12+12=112+12=1 size 12{ { {1} over {2} } + { {1} over {2} } =1} {}. In fact, 58+512=2524=112458+512=2524=1124 size 12{ { {5} over {8} } + { {5} over {"12"} } = { {"25"} over {"24"} } =1 { {1} over {"24"} } } {}

Exercise 2

79+3579+35 size 12{ { {7} over {9} } + { {3} over {5} } } {}

Solution

Results may vary. 1+12=1121+12=112 size 12{1+ { {1} over {2} } =1 { {1} over {2} } } {}. In fact, 79+35=1174579+35=11745 size 12{ { {7} over {9} } + { {3} over {5} } =1 { {"17"} over {"45"} } } {}

Exercise 3

8415+37108415+3710 size 12{8 { {4} over {"15"} } +3 { {7} over {"10"} } } {}

Solution

Results may vary. 814+334=11+1=12814+334=11+1=12 size 12{8 { {1} over {4} } +3 { {3} over {4} } ="11"+1="12"} {}. In fact, 8415+3710=1129308415+3710=112930 size 12{8 { {4} over {"15"} } +3 { {7} over {"10"} } ="11" { {"29"} over {"30"} } } {}

Exercise 4

16120+47816120+478 size 12{"16" { {1} over {20} } +4 { {7} over {8} } } {}

Solution

Results may vary. 16+0+4+1=16+5=21.16+0+4+1=16+5=21. size 12{ left ("16"+0 right )+ left (4+1 right )="16"+5="21"} {} In fact, 16120+478=20374016120+478=203740 size 12{"16" { {1} over {"20"} } +4 { {7} over {8} } ="20" { {"37"} over {"40"} } } {}

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.

Exercise 5

56+7856+78 size 12{ { {5} over {6} } + { {7} over {8} } } {}

Solution

1+1=2  117241+1=2  11724 size 12{1+1=2 left (1 { {"17"} over {"24"} } right )} {}

Exercise 6

38+111238+1112 size 12{ { {3} over {8} } + { {"11"} over {"12"} } } {}

Exercise 7

910+35910+35 size 12{ { {9} over {"10"} } + { {3} over {5} } } {}

Solution

1+12=1121121+12=112112 size 12{1+ { {1} over {2} } =1 { {1} over {2} } left (1 { {1} over {2} } right )} {}

Exercise 8

1315+1201315+120 size 12{ { {"13"} over {"15"} } + { {1} over {"20"} } } {}

Exercise 9

320+625320+625 size 12{ { {3} over {"20"} } + { {6} over {"25"} } } {}

Solution

14+14=123910014+14=1239100 size 12{ { {1} over {4} } + { {1} over {4} } = { {1} over {2} } left ( { {"39"} over {"100"} } right )} {}

Exercise 10

112+45112+45 size 12{ { {1} over {"12"} } + { {4} over {5} } } {}

Exercise 11

1516+1121516+112 size 12{ { {"15"} over {"16"} } + { {1} over {"12"} } } {}

Solution

1+0=111481+0=11148 size 12{1+0=1 left (1 { {1} over {"48"} } right )} {}

Exercise 12

2930+11202930+1120 size 12{ { {"29"} over {"30"} } + { {"11"} over {"20"} } } {}

Exercise 13

512+6411512+6411 size 12{ { {5} over {"12"} } +6 { {4} over {"11"} } } {}

Solution

12+612=7  610313212+612=7  6103132 size 12{ { {1} over {2} } +6 { {1} over {2} } =7 left (6 { {"103"} over {"132"} } right )} {}

Exercise 14

37+841537+8415 size 12{ { {3} over {7} } +8 { {4} over {"15"} } } {}

Exercise 15

910+238910+238 size 12{ { {9} over {"10"} } +2 { {3} over {8} } } {}

Solution

1+212=312311401+212=31231140 size 12{1+2 { {1} over {2} } =3 { {1} over {2} } left (3 { {"11"} over {"40"} } right )} {}

Exercise 16

1920+15591920+1559 size 12{ { {"19"} over {"20"} } +"15" { {5} over {9} } } {}

Exercise 17

835+4120835+4120 size 12{8 { {3} over {5} } +4 { {1} over {"20"} } } {}

Solution

812+4=1212121320812+4=1212121320 size 12{8 { {1} over {2} } +4="12" { {1} over {2} } left ("12" { {"13"} over {"20"} } right )} {}

Exercise 18

5320+28155320+2815 size 12{5 { {3} over {"20"} } +2 { {8} over {"15"} } } {}

Exercise 19

9115+6459115+645 size 12{9 { {1} over {"15"} } +6 { {4} over {5} } } {}

Solution

9+7=16  1513159+7=16  151315 size 12{9+7="16" left ("15" { {"13"} over {"15"} } right )} {}

Exercise 20

7512+101167512+10116 size 12{7 { {5} over {"12"} } +"10" { {1} over {"16"} } } {}

Exercise 21

31120+21325+17831120+21325+178 size 12{3 { {"11"} over {"20"} } +2 { {"13"} over {"25"} } +1 { {7} over {8} } } {}

Solution

312+212+2=8  7189200312+212+2=8  7189200 size 12{3 { {1} over {2} } +2 { {1} over {2} } +2=8 left (7 { {"189"} over {"200"} } right )} {}

Exercise 22

6112+1110+5566112+1110+556 size 12{6 { {1} over {"12"} } +1 { {1} over {"10"} } +5 { {5} over {6} } } {}

Exercise 23

1516−781516−78 size 12{ { {"15"} over {"16"} } - { {7} over {8} } } {}

Solution

1−1=0  1161−1=0  116 size 12{1 - 1=0 left ( { {1} over {"16"} } right )} {}

Exercise 24

1225−9201225−920 size 12{ { {"12"} over {"25"} } - { {9} over {"20"} } } {}

Exercises for Review

Exercise 25

((Reference)) The fact that
 (a first number ⋅ a second number) ⋅ a third number= a first number ⋅ (a second number ⋅ a third number ) (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?

Solution

associative

Exercise 26

((Reference)) Find the quotient: 1415÷4451415÷445 size 12{ { {"14"} over {"15"} } div { {4} over {"45"} } } {}.

Exercise 27

((Reference)) Find the difference: 359−223359−223 size 12{3 { {5} over {9} } - 2 { {2} over {3} } } {}.

Solution

8989 size 12{ { {8} over {9} } } {}

Exercise 28

((Reference)) Find the quotient: 4.6 ÷ 0.114.6 ÷ 0.11 size 12{4 "." "6 " div " 0" "." "11"} {}.

Exercise 29

((Reference)) Use the distributive property to compute the product: 25 ⋅ 3725 ⋅ 37 size 12{"25 " cdot " 37"} {}.

Solution

2540−3=1000−75=9252540−3=1000−75=925 size 12{"25" left ("40" - 3 right )="1000" - "75"="925"} {}

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