# 8.4 Estimation by rounding fractions

 Page 1 / 1
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 $\frac{1}{4}$ , $\frac{1}{2}$ , $\frac{3}{4}$ , 0, and 1. Remember that rounding may cause estimates to vary.

## Sample set a

Make each estimate remembering that results may vary.

Estimate $\frac{3}{5}+\frac{5}{\text{12}}$ .

Notice that $\frac{3}{5}$ is about $\frac{1}{2}$ , and that $\frac{5}{\text{12}}$ is about $\frac{1}{2}$ .

Thus, $\frac{3}{5}+\frac{5}{\text{12}}$ is about $\frac{1}{2}+\frac{1}{2}=1$ . In fact, $\frac{3}{5}+\frac{5}{\text{12}}=\frac{\text{61}}{\text{60}}$ , a little more than 1.

Estimate $5\frac{3}{8}+4\frac{9}{\text{10}}+\text{11}\frac{1}{5}$ .

Adding the whole number parts, we get 20. Notice that $\frac{3}{8}$ is close to $\frac{1}{4}$ , $\frac{9}{\text{10}}$ is close to 1, and $\frac{1}{5}$ is close to $\frac{1}{4}$ . Then $\frac{3}{8}+\frac{9}{\text{10}}+\frac{1}{5}$ is close to $\frac{1}{4}+1+\frac{1}{4}=1\frac{1}{2}$ .

Thus, $5\frac{3}{8}+4\frac{9}{\text{10}}+\text{11}\frac{1}{5}$ is close to $\text{20}+1\frac{1}{2}=\text{21}\frac{1}{2}$ .

In fact, $5\frac{3}{8}+4\frac{9}{\text{10}}+\text{11}\frac{1}{5}=\text{21}\frac{\text{19}}{\text{40}}$ , a little less than $\text{21}\frac{1}{2}$ .

## Practice set a

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

$\frac{5}{8}+\frac{5}{\text{12}}$

Results may vary. $\frac{1}{2}+\frac{1}{2}=1$ . In fact, $\frac{5}{8}+\frac{5}{\text{12}}=\frac{\text{25}}{\text{24}}=1\frac{1}{\text{24}}$

$\frac{7}{9}+\frac{3}{5}$

Results may vary. $1+\frac{1}{2}=1\frac{1}{2}$ . In fact, $\frac{7}{9}+\frac{3}{5}=1\frac{\text{17}}{\text{45}}$

$8\frac{4}{\text{15}}+3\frac{7}{\text{10}}$

Results may vary. $8\frac{1}{4}+3\frac{3}{4}=\text{11}+1=\text{12}$ . In fact, $8\frac{4}{\text{15}}+3\frac{7}{\text{10}}=\text{11}\frac{\text{29}}{\text{30}}$

$\text{16}\frac{1}{20}+4\frac{7}{8}$

Results may vary. $\left(\text{16}+0\right)+\left(4+1\right)=\text{16}+5=\text{21.}$ In fact, $\text{16}\frac{1}{\text{20}}+4\frac{7}{8}=\text{20}\frac{\text{37}}{\text{40}}$

## 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.

$\frac{5}{6}+\frac{7}{8}$

$\frac{3}{8}+\frac{\text{11}}{\text{12}}$

$\frac{9}{\text{10}}+\frac{3}{5}$

$1+\frac{1}{2}=1\frac{1}{2}\left(1\frac{1}{2}\right)$

$\frac{\text{13}}{\text{15}}+\frac{1}{\text{20}}$

$\frac{3}{\text{20}}+\frac{6}{\text{25}}$

$\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\left(\frac{\text{39}}{\text{100}}\right)$

$\frac{1}{\text{12}}+\frac{4}{5}$

$\frac{\text{15}}{\text{16}}+\frac{1}{\text{12}}$

$1+0=1\left(1\frac{1}{\text{48}}\right)$

$\frac{\text{29}}{\text{30}}+\frac{\text{11}}{\text{20}}$

$\frac{5}{\text{12}}+6\frac{4}{\text{11}}$

$\frac{3}{7}+8\frac{4}{\text{15}}$

$\frac{9}{\text{10}}+2\frac{3}{8}$

$1+2\frac{1}{2}=3\frac{1}{2}\left(3\frac{\text{11}}{\text{40}}\right)$

$\frac{\text{19}}{\text{20}}+\text{15}\frac{5}{9}$

$8\frac{3}{5}+4\frac{1}{\text{20}}$

$8\frac{1}{2}+4=\text{12}\frac{1}{2}\left(\text{12}\frac{\text{13}}{\text{20}}\right)$

$5\frac{3}{\text{20}}+2\frac{8}{\text{15}}$

$9\frac{1}{\text{15}}+6\frac{4}{5}$

$7\frac{5}{\text{12}}+\text{10}\frac{1}{\text{16}}$

$3\frac{\text{11}}{\text{20}}+2\frac{\text{13}}{\text{25}}+1\frac{7}{8}$

$6\frac{1}{\text{12}}+1\frac{1}{\text{10}}+5\frac{5}{6}$

$\frac{\text{15}}{\text{16}}-\frac{7}{8}$

$\frac{\text{12}}{\text{25}}-\frac{9}{\text{20}}$

## Exercises for review

( [link] ) The fact that
$\left(\text{a first number}\cdot \text{a second number}\right)\cdot \text{a third number}=\text{a first number}\cdot \left(\text{a second number}\cdot \text{a third number}\right)$
is an example of which property of multiplication?

associative

( [link] ) Find the quotient: $\frac{\text{14}}{\text{15}}÷\frac{4}{\text{45}}$ .

( [link] ) Find the difference: $3\frac{5}{9}-2\frac{2}{3}$ .

$\frac{8}{9}$

( [link] ) Find the quotient: $4\text{.}\text{6}÷\text{0}\text{.}\text{11}$ .

( [link] ) Use the distributive property to compute the product: $\text{25}\cdot \text{37}$ .

$\text{25}\left(\text{40}-3\right)=\text{1000}-\text{75}=\text{925}$

#### Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
In the number 779,844,205 how many ten millions are there?
TELLY Reply
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

### Read also:

#### Get Jobilize Job Search Mobile App in your pocket Now!

Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications? By Stephen Voron By OpenStax By OpenStax By John Gabrieli By Olivia D'Ambrogio By OpenStax By John Gabrieli By Janet Forrester By Mary Cohen By OpenStax