Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Derived copy of Fundamentals of Mathematics » Estimation by Rounding Fractions

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCQ display tagshide tags

    This module is included in aLens by: Community College of QatarAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Used as supplemental materials for developmental math courses."

    Click the "CCQ" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "Fundamentals of Mathematics"

    Click the "UniqU content" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

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

151678151678 size 12{ { {"15"} over {"16"} } - { {7} over {8} } } {}

Solution

11=0  11611=0  116 size 12{1 - 1=0 left ( { {1} over {"16"} } right )} {}

Exercise 24

12259201225920 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: 359223359223 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

25403=100075=92525403=100075=925 size 12{"25" left ("40" - 3 right )="1000" - "75"="925"} {}

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks