# 5.3 Addition and subtraction of mixed numbers

 Page 1 / 1
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add and subtract mixed numbers. By the end of the module students should be able to add and subtract mixed numbers.

## Section overview

• The Method of Converting to Improper Fractions

To add or subtract mixed numbers, convert each mixed number to an improper fraction, then add or subtract the resulting improper fractions.

## Sample set a

Find the following sums and differences.

$8\frac{3}{5}+5\frac{1}{4}$ . Convert each mixed number to an improper fraction.

$8\frac{3}{5}=\frac{5\cdot 8+3}{5}=\frac{\text{40}+3}{5}=\frac{\text{43}}{5}$

$5\frac{1}{4}=\frac{4\cdot 5+1}{4}=\frac{\text{20}+1}{4}=\frac{\text{21}}{4}$ Now add the improper fractions $\frac{\text{43}}{5}\text{and}\frac{\text{21}}{4}$ .

$\frac{43}{5}+\frac{21}{4}$ The LCD = 20.

$\begin{array}{cccc}\hfill \frac{\text{43}}{5}+\frac{\text{21}}{4}& =& \frac{\text{43}\cdot 4}{\text{20}}+\frac{\text{21}\cdot 5}{\text{20}}\hfill & \\ & =& \frac{\text{172}}{\text{20}}+\frac{\text{105}}{\text{20}}\hfill & \\ & =& \frac{\text{172}+\text{105}}{\text{20}}\hfill & \\ & =& \frac{\text{277}}{\text{20}}\hfill & \text{Convert this improper fraction to a mixed number.}\\ & =& \text{13}\frac{\text{17}}{\text{20}}\hfill & \end{array}$

Thus, $8\frac{3}{5}+5\frac{1}{4}=\text{13}\frac{\text{17}}{\text{20}}$ .

$3\frac{1}{8}-\frac{5}{6}$ . Convert the mixed number to an improper fraction.

$3\frac{1}{8}=\frac{3\cdot 8+1}{8}=\frac{\text{24}+1}{8}=\frac{\text{25}}{8}$

$\frac{\text{25}}{8}-\frac{5}{6}$ The LCD = 24.

$\begin{array}{cccc}\hfill \frac{\text{25}}{8}-\frac{5}{6}& =& \frac{\text{25}\cdot 3}{\text{24}}-\frac{5\cdot 4}{\text{24}}\hfill & \\ & =& \frac{\text{75}}{\text{24}}-\frac{\text{20}}{\text{24}}\hfill & \\ & =& \frac{\text{75}-\text{20}}{\text{24}}\hfill & \\ & =& \frac{\text{55}}{\text{24}}\hfill & \text{Convert his improper fraction to a mixed number.}\hfill \\ & =& 2\frac{7}{\text{24}}\hfill & \end{array}$

Thus, $3\frac{1}{8}-\frac{5}{6}=2\frac{7}{\text{24}}$ .

## Practice set a

Find the following sums and differences.

$1\frac{5}{9}+3\frac{2}{9}$

$4\frac{7}{9}$

$\text{10}\frac{3}{4}-2\frac{1}{2}$

$8\frac{1}{4}$

$2\frac{7}{8}+5\frac{1}{4}$

$8\frac{1}{8}$

$8\frac{3}{5}-\frac{3}{\text{10}}$

$8\frac{3}{\text{10}}$

$\text{16}+2\frac{9}{\text{16}}$

$\text{18}\frac{9}{\text{16}}$

## Exercises

For the following problems, perform each indicated opera­tion.

$3\frac{1}{8}+4\frac{3}{8}$

$7\frac{1}{2}$

$5\frac{1}{3}+6\frac{1}{3}$

$\text{10}\frac{5}{\text{12}}+2\frac{1}{\text{12}}$

$\text{12}\frac{1}{2}$

$\text{15}\frac{1}{5}-\text{11}\frac{3}{5}$

$9\frac{3}{\text{11}}+\text{12}\frac{3}{\text{11}}$

$\text{21}\frac{6}{\text{11}}$

$1\frac{1}{6}+3\frac{2}{6}+8\frac{1}{6}$

$5\frac{3}{8}+1\frac{1}{8}-2\frac{5}{8}$

$3\frac{7}{8}$

$\frac{3}{5}+5\frac{1}{5}$

$2\frac{2}{9}-\frac{5}{9}$

$1\frac{2}{3}$

$6+\text{11}\frac{2}{3}$

$\text{17}-8\frac{3}{\text{14}}$

$8\frac{\text{11}}{\text{14}}$

$5\frac{1}{3}+2\frac{1}{4}$

$6\frac{2}{7}-1\frac{1}{3}$

$4\frac{\text{20}}{\text{21}}$

$8\frac{2}{5}+4\frac{1}{\text{10}}$

$1\frac{1}{3}+\text{12}\frac{3}{8}$

$\text{13}\frac{\text{17}}{\text{24}}$

$3\frac{1}{4}+1\frac{1}{3}-2\frac{1}{2}$

$4\frac{3}{4}-3\frac{5}{6}+1\frac{2}{3}$

$\text{2}\frac{7}{12}$

$3\frac{1}{\text{12}}+4\frac{1}{3}+1\frac{1}{4}$

$5\frac{1}{\text{15}}+8\frac{3}{\text{10}}-5\frac{4}{5}$

$7\frac{\text{17}}{\text{30}}$

$7\frac{1}{3}+8\frac{5}{6}-2\frac{1}{4}$

$\text{19}\frac{\text{20}}{\text{21}}+\text{42}\frac{6}{7}-\frac{5}{\text{14}}+\text{12}\frac{1}{7}$

$\text{74}\frac{\text{25}}{\text{42}}$

$\frac{1}{\text{16}}+4\frac{3}{4}+\text{10}\frac{3}{8}-9$

$\text{11}-\frac{2}{9}+\text{10}\frac{1}{3}-\frac{2}{3}-5\frac{1}{6}+6\frac{1}{\text{18}}$

$\text{21}\frac{1}{3}$

$\frac{5}{2}+2\frac{1}{6}+\text{11}\frac{1}{3}-\frac{\text{11}}{6}$

$1\frac{1}{8}+\frac{9}{4}-\frac{1}{\text{16}}-\frac{1}{\text{32}}+\frac{\text{19}}{8}$

$5\frac{\text{21}}{\text{32}}$

$\text{22}\frac{3}{8}-\text{16}\frac{1}{7}$

$\text{15}\frac{4}{9}+4\frac{9}{\text{16}}$

$\text{20}\frac{1}{\text{144}}$

$4\frac{\text{17}}{\text{88}}+5\frac{9}{\text{110}}$

$6\frac{\text{11}}{\text{12}}+\frac{2}{3}$

$7\frac{7}{\text{12}}$

$8\frac{9}{\text{16}}-\frac{7}{9}$

$5\frac{2}{\text{11}}-\frac{1}{\text{12}}$

$5\frac{\text{13}}{\text{132}}$

$\text{18}\frac{\text{15}}{\text{16}}-\frac{\text{33}}{\text{34}}$

$1\frac{\text{89}}{\text{112}}-\frac{\text{21}}{\text{56}}$

$1\frac{\text{47}}{\text{212}}$

$\text{11}\frac{\text{11}}{\text{24}}-7\frac{\text{13}}{\text{18}}$

$5\frac{\text{27}}{\text{84}}-3\frac{5}{\text{42}}+1\frac{1}{\text{21}}$

$3\frac{1}{4}$

$\text{16}\frac{1}{\text{48}}-\text{16}\frac{1}{\text{96}}+\frac{1}{\text{144}}$

A man pours $2\frac{5}{8}$ gallons of paint from a bucket into a tray. After he finishes pouring, there are $1\frac{1}{4}$ gallons of paint left in his bucket. How much paint did the man pour into the tray?

$2\frac{5}{8}\phantom{\rule{4px}{0ex}}\text{gallons}$

A particular computer stock opened at $\text{37}\frac{3}{8}$ and closed at $\text{38}\frac{1}{4}$ . What was the net gain for this stock?

A particular diet program claims that $4\frac{3}{\text{16}}$ pounds can be lost the first month, $3\frac{1}{4}$ pounds can be lost the second month, and $1\frac{1}{2}$ pounds can be lost the third month. How many pounds does this diet program claim a person can lose over a 3-month period?

$8\frac{15}{16}\phantom{\rule{4px}{0ex}}\text{pounds}$

If a person who weighs $\text{145}\frac{3}{4}$ pounds goes on the diet program described in the problem above, how much would he weigh at the end of 3 months?

If the diet program described in the problem above makes the additional claim that from the fourth month on, a person will lose $1\frac{1}{8}$ pounds a month, how much will a person who begins the program weighing $\text{208}\frac{3}{4}$ pounds weight after 8 months?

$194\frac{3}{16}\phantom{\rule{4px}{0ex}}\text{pounds}$

## Exercises for review

( [link] ) Use exponents to write $4\cdot 4\cdot 4$ .

( [link] ) Find the greatest common factor of 14 and 20.

2

( [link] ) Convert $\frac{\text{16}}{5}$ to a mixed number.

( [link] ) Find the sum. $\frac{4}{9}+\frac{1}{9}+\frac{2}{9}$ .

$\frac{7}{9}$

( [link] ) Find the difference. $\frac{\text{15}}{\text{26}}-\frac{3}{\text{10}}$ .

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
7hours 36 min - 4hours 50 min