<< Chapter < Page Chapter >> Page >
7 12 2 12 = 5 12

Let’s use fraction circles to model the same example, 7 12 2 12 .

Start with seven 1 12 pieces. Take away two 1 12 pieces. How many twelfths are left?

The bottom reads 7 twelfths minus 2 twelfths equals 5 twelfths. Above 7 twelfths, there is a circle divided into 12 equal pieces, with 7 pieces shaded in orange. Above 2 twelfths, the same circle is shown, but 2 of the 7 pieces are shaded in grey. Above 5 twelfths, the 2 grey pieces are no longer shaded, so there is a circle divided into 12 pieces with 5 of the pieces shaded in orange.

Again, we have five twelfths, 5 12 .

Doing the Manipulative Mathematics activity "Model Fraction Subtraction" will help you develop a better understanding of subtracting fractions.

Use fraction circles to find the difference: 4 5 1 5 .

Solution

Start with four 1 5 pieces. Take away one 1 5 piece. Count how many fifths are left. There are three 1 5 pieces left.

The bottom reads 4 fifths minus 1 fifth equals 3 fifths. Above 4 fifths, there is a circle divided into 5 equal pieces, with 4 pieces shaded in orange. Above 1 fifth, the same circle is shown, but 1 of the 4 shaded pieces is shaded in grey. Above 3 fifths, the 1 grey piece is no longer shaded, so there is a circle divided into 5 pieces with 3 of the pieces shaded in orange.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Use a model to find each difference. Show a diagram to illustrate your model.

7 8 4 8

3 8 , models may differ.

Got questions? Get instant answers now!

Use a model to find each difference. Show a diagram to illustrate your model.

5 6 4 6

1 6 , models may differ

Got questions? Get instant answers now!

Subtract fractions with a common denominator

We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.

Fraction subtraction

If a , b , and c are numbers where c 0 , then

a c b c = a b c

To subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.

Find the difference: 23 24 14 24 .

Solution

23 24 14 24
Subtract the numerators and place the difference over the common denominator. 23 14 24
Simplify the numerator. 9 24
Simplify the fraction by removing common factors. 3 8
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the difference: 19 28 7 28 .

3 7

Got questions? Get instant answers now!

Find the difference: 27 32 11 32 .

1 2

Got questions? Get instant answers now!

Find the difference: y 6 1 6 .

Solution

y 6 1 6
Subtract the numerators and place the difference over the common denominator. y 1 6

The fraction is simplified because we cannot combine the terms in the numerator.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the difference: x 7 2 7 .

x 2 7

Got questions? Get instant answers now!

Find the difference: y 14 13 14 .

y 13 14

Got questions? Get instant answers now!

Find the difference: 10 x 4 x .

Solution

Remember, the fraction 10 x can be written as −10 x .

10 x 4 x
Subtract the numerators. −10 4 x
Simplify. −14 x
Rewrite with the negative sign in front of the fraction. 14 x
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the difference: 9 x 7 x .

16 x

Got questions? Get instant answers now!

Find the difference: 17 a 5 a .

22 a

Got questions? Get instant answers now!

Now lets do an example that involves both addition and subtraction.

Simplify: 3 8 + ( 5 8 ) 1 8 .

Solution

3 8 + ( 5 8 ) 1 8
Combine the numerators over the common denominator. 3 + ( −5 ) 1 8
Simplify the numerator, working left to right. −2 1 8
Subtract the terms in the numerator. −3 8
Rewrite with the negative sign in front of the fraction. 3 8
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: 2 5 + ( 4 5 ) 3 5 .

−1

Got questions? Get instant answers now!

Simplify: 5 9 + ( 4 9 ) 7 9 .

2 3

Got questions? Get instant answers now!

Key concepts

  • Fraction Addition
    • If a , b , and c are numbers where c 0 , then a c + b c = a + c c .
    • To add fractions, add the numerators and place the sum over the common denominator.
  • Fraction Subtraction
    • If a , b , and c are numbers where c 0 , then a c - b c = a - c c .
    • To subtract fractions, subtract the numerators and place the difference over the common denominator.

Practice makes perfect

Model Fraction Addition

In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model.

Add Fractions with a Common Denominator

In the following exercises, find each sum.

−11 x 5 + 7 x 5

−4 x 5

Got questions? Get instant answers now!

1 8 + ( 5 8 )

3 4

Got questions? Get instant answers now!

5 16 + ( 9 16 )

7 8

Got questions? Get instant answers now!

6 13 + ( 10 13 ) + ( 12 13 )

Got questions? Get instant answers now!

5 12 + ( 7 12 ) + ( 11 12 )

13 12

Got questions? Get instant answers now!

Model Fraction Subtraction

In the following exercises, use a model to subtract the fractions. Show a diagram to illustrate your model.

Subtract Fractions with a Common Denominator

In the following exercises, find the difference.

8 9 16 9

8 3

Got questions? Get instant answers now!

x 19 8 19

x 8 19

Got questions? Get instant answers now!

11 z 13 8 13

11 z 8 13

Got questions? Get instant answers now!

7 c 7 c

14 c

Got questions? Get instant answers now!

29 v 26 v

55 v

Got questions? Get instant answers now!

12 d 11 9 d 11

3 d 11

Got questions? Get instant answers now!

−7 s 3 7 s 3

14 s 3

Got questions? Get instant answers now!

3 7 ( 5 7 )

2 7

Got questions? Get instant answers now!

8 11 ( 5 11 )

3 11

Got questions? Get instant answers now!

Mixed Practice

In the following exercises, perform the indicated operation and write your answers in simplified form.

3 14 · 7 12

1 8

Got questions? Get instant answers now!

6 11 s 11

6 s 11

Got questions? Get instant answers now!

Everyday math

Trail Mix Jacob is mixing together nuts and raisins to make trail mix. He has 6 10 of a pound of nuts and 3 10 of a pound of raisins. How much trail mix can he make?

Got questions? Get instant answers now!

Baking Janet needs 5 8 of a cup of flour for a recipe she is making. She only has 3 8 of a cup of flour and will ask to borrow the rest from her next-door neighbor. How much flour does she have to borrow?

1 4 cup

Got questions? Get instant answers now!

Writing exercises

Greg dropped his case of drill bits and three of the bits fell out. The case has slots for the drill bits, and the slots are arranged in order from smallest to largest. Greg needs to put the bits that fell out back in the case in the empty slots. Where do the three bits go? Explain how you know.

Got questions? Get instant answers now!

After a party, Lupe has 5 12 of a cheese pizza, 4 12 of a pepperoni pizza, and 4 12 of a veggie pizza left. Will all the slices fit into 1 pizza box? Explain your reasoning.

Answers will vary.

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Questions & Answers

what is microbiology
Agebe Reply
What is a cell
Odelana Reply
what is cell
Mohammed
how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask