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By the end of this section, you will be able to:
  • Multiply and divide mixed numbers
  • Translate phrases to expressions with fractions
  • Simplify complex fractions
  • Simplify expressions written with a fraction bar

Before you get started, take this readiness quiz.

  1. Divide and reduce, if possible: ( 4 + 5 ) ÷ ( 10 7 ) .
    If you missed this problem, review Add Integers .
  2. Multiply and write the answer in simplified form: 1 8 · 2 3 .
    If you missed this problem, review Multiply and Divide Fractions .
  3. Convert 2 · 3 5 into an improper fraction.
    If you missed this problem, review Visualize Fractions .

Multiply and divide mixed numbers

In the previous section, you learned how to multiply and divide fractions. All of the examples there used either proper or improper fractions. What happens when you are asked to multiply or divide mixed numbers? Remember that we can convert a mixed number    to an improper fraction . And you learned how to do that in Visualize Fractions .

Multiply: 3 1 3 · 5 8

Solution

3 1 3 · 5 8
Convert 3 1 3 to an improper fraction. 10 3 · 5 8
Multiply. 10 · 5 3 · 8
Look for common factors. · 5 · 5 3 · · 4
Remove common factors. 5 · 5 3 · 4
Simplify. 25 12

Notice that we left the answer as an improper fraction, 25 12 , and did not convert it to a mixed number. In algebra, it is preferable to write answers as improper fractions instead of mixed numbers. This avoids any possible confusion between 2 1 12 and 2 · 1 12 .

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Multiply, and write your answer in simplified form: 5 2 3 · 6 17 .

2

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Multiply, and write your answer in simplified form: 3 7 · 5 1 4 .

9 4

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Multiply or divide mixed numbers.

  1. Convert the mixed numbers to improper fractions.
  2. Follow the rules for fraction multiplication or division.
  3. Simplify if possible.

Multiply, and write your answer in simplified form: 2 4 5 ( 1 7 8 ) .

Solution

2 4 5 ( 1 7 8 )
Convert mixed numbers to improper fractions. 14 5 ( 15 8 )
Multiply. 14 · 15 5 · 8
Look for common factors. · 7 · · 3 · · 4
Remove common factors. 7 · 3 4
Simplify. 21 4
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Multiply, and write your answer in simplified form. 5 5 7 ( 2 5 8 ) .

−15

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Multiply, and write your answer in simplified form. −3 2 5 · 4 1 6 .

85 6

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Divide, and write your answer in simplified form: 3 4 7 ÷ 5 .

Solution

3 4 7 ÷ 5
Convert mixed numbers to improper fractions. 25 7 ÷ 5 1
Multiply the first fraction by the reciprocal of the second. 25 7 · 1 5
Multiply. 25 · 1 7 · 5
Look for common factors. · 5 · 1 7 ·
Remove common factors. 5 · 1 7
Simplify. 5 7
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Divide, and write your answer in simplified form: 4 3 8 ÷ 7 .

5 8

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Divide, and write your answer in simplified form: 2 5 8 ÷ 3 .

7 8

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Divide: 2 1 2 ÷ 1 1 4 .

Solution

2 1 2 ÷ 1 1 4
Convert mixed numbers to improper fractions. 5 2 ÷ 5 4
Multiply the first fraction by the reciprocal of the second. 5 2 · 4 5
Multiply. 5 · 4 2 · 5
Look for common factors. · · 2 · 1 ·
Remove common factors. 2 1
Simplify. 2
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Divide, and write your answer in simplified form: 2 2 3 ÷ 1 1 3 .

2

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Divide, and write your answer in simplified form: 3 3 4 ÷ 1 1 2 .

5 2

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Translate phrases to expressions with fractions

The words quotient and ratio are often used to describe fractions. In Subtract Whole Numbers , we defined quotient as the result of division. The quotient of a and b is the result you get from dividing a by b , or a b . Let’s practice translating some phrases into algebraic expressions using these terms.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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
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
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
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
Practice Key Terms 1

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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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