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

7 8 4 8

3 8 , models may differ.

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

5 6 4 6

1 6 , models may differ

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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
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Find the difference: 19 28 7 28 .

3 7

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Find the difference: 27 32 11 32 .

1 2

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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.

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Find the difference: x 7 2 7 .

x 2 7

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Find the difference: y 14 13 14 .

y 13 14

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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
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Find the difference: 9 x 7 x .

16 x

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Find the difference: 17 a 5 a .

22 a

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

−1

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

2 3

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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

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1 8 + ( 5 8 )

3 4

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5 16 + ( 9 16 )

7 8

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

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

13 12

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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

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x 19 8 19

x 8 19

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11 z 13 8 13

11 z 8 13

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7 c 7 c

14 c

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29 v 26 v

55 v

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12 d 11 9 d 11

3 d 11

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−7 s 3 7 s 3

14 s 3

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3 7 ( 5 7 )

2 7

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8 11 ( 5 11 )

3 11

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Mixed Practice

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

3 14 · 7 12

1 8

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6 11 s 11

6 s 11

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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?

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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

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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.

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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.

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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 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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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