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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

what is the meaning of function in economics
Effah Reply
Pls, I need more explanation on price Elasticity of Supply
Isaac Reply
Is the degree to the degree of responsiveness of a change in quantity supplied of goods to a change in price
Afran
Discuss the short-term and long-term balance positions of the firm in the monopoly market?
Rabindranath Reply
hey
Soumya
hi
Mitiku
how are you?
Mitiku
can you tell how can i economics honurs(BSC) in reputed college?
Soumya
through hard study and performing well than expected from you
Mitiku
what should i prepare for it?
Soumya
prepare first, in psychologically as well as potentially to sacrifice what's expected from you, when I say this I mean that you have to be ready, for every thing and to accept failure as a good and you need to change them to potential for achievement of ur goals
Mitiku
parna kya hai behencho?
Soumya
Hallo
Rabindranath
Hello, dear what's up?
Mitiku
cool
Momoh
good morning
Isaac
pls, is anyone here from Ghana?
Isaac
Hw s every one please
Afran
Ys please I'm in Ghana
Afran
what is firms
Anteyi Reply
A firm is a business entity which engages in the production of goods and aimed at making profit.
Avuwada
What is autarky in Economics.
Avuwada
what is choice
Tia Reply
So how is the perfect competition different from others
Rev Reply
what is choice
Tia
please what type of commodity is 1.Beaf 2.Suagr 3.Bread
Alfred Reply
1
Naziru
what is the difference between short run and long run?
Ukpen Reply
It just depends on how far you would like to run!!!🤣🤣🤣
Anna
meaning? You guys need not to be playing here; if you don't know a question, leave it for he that knows.
Ukpen
pls is question from which subject or which course
Ada
Is this not economics?
Ukpen
This place is meant to be for serious educational matters n not playing ground so pls let's make it a serious place.
Docky
Is there an economics expert here?
Docky
Okay and I was being serous
Anna
The short run is a period of time in which the quantity of at least one inputs is fixed...
Anna
that is the answer that I found online and in my text book
Anna
Elacisity
salihu
Meaning of economics
Suraj Reply
It will creates rooms for an effective demands.
Chinedum Reply
different between production and supply
babsnof
Hii
Suraj
hlo
eshita
What is the economic?
Suraj
Economics is a science which study human behavior as a relationship between ends and scarce means which has an alternative use.
Mr
what is supply
babsnof
what is different between demand and supply
Debless Reply
Demand refers to the quantity of products that consumers are willing to purchase at various prices per time while Supply has to do with the quantity of products suppliers are willing to supply at various prices per time. find the difference in between
Saye
Please what are the effects of rationing Effect of black market Effects of hoarding
Atty Reply
monoply is amarket structure charecrized by asingle seller and produce a unique product in the market
Cali Reply
yes
Niraj
I want to know wen does the demand curve shift to the right
Nana
demand curve shifts to the right when there's an increase in price of a substitute or increase in income
kin
ask me anything in economics, I promise to try and do justice to the question, you can send me an email or message, I will answer
kin
what are the factor that change the curve right
Nana
explain the law of supply in simple .....
freshwater
the Law of supply: states that all factor being equal, when the price of a particular goods increase the supply will also increase, as it decreases the supply will also decrease
kin
@Nana the factor that changes or shift the d demand curve to the right is 1) the increase in price of a substitute good or commodity 2) increase in income
kin
you can send your questions I am Comr. Kin chukwuebuka
kin
different between bill of exchange n treasure bill
Nana
yes
Ada
so would you tell me what means an apportunity cost plz?
Cali
what is true cost
Akiti
your question isn't correct naadi
Anthonia
define an apportunity cost?
Cali
orukpe ,is my question whats wrong or u dont know anything?
Cali
In a simple term, it is an Alternative foregone.
Sule
opportunity cost is the next best value of a scale of preference
Akiti
Both of you are not correct.
Nelly
opportunity cost: is a forgone alternative
kin
Monopoly is where is one producer produces a given product with no close substitute
James
what is income effect?
Qwecou Reply
if you borrow $5000 to buy a car at 12 percent compounded monthly to be repaid over the next 4 year what is monthly payment
Nitish Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Mapo Reply
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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