<< Chapter < Page Chapter >> Page >
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 3 5 + 5 1 4 size 12{8 { {3} over {5} } +5 { {1} over {4} } } {} . Convert each mixed number to an improper fraction.

8 3 5 = 5 8 + 3 5 = 40 + 3 5 = 43 5 size 12{8 { {3} over {5} } = { {5 cdot 8+3} over {5} } = { {"40"+3} over {5} } = { {"43"} over {5} } } {}

5 1 4 = 4 5 + 1 4 = 20 + 1 4 = 21 4 size 12{5 { {1} over {4} } = { {4 cdot 5+1} over {4} } = { {"20"+1} over {4} } = { {"21"} over {4} } } {} Now add the improper fractions 43 5 and 21 4 size 12{ { {"43"} over {5} } " and " { {"21"} over {4} } } {} .

43 5 + 21 4 The LCD = 20.

43 5 + 21 4 = 43 4 20 + 21 5 20 = 172 20 + 105 20 = 172 + 105 20 = 277 20 Convert this improper fraction to a mixed number. = 13 17 20

Thus, 8 3 5 + 5 1 4 = 13 17 20 size 12{8 { {3} over {5} } +5 { {1} over {4} } ="13" { {"17"} over {"20"} } } {} .

3 1 8 5 6 size 12{3 { {1} over {8} } - { {5} over {6} } } {} . Convert the mixed number to an improper fraction.

3 1 8 = 3 8 + 1 8 = 24 + 1 8 = 25 8 size 12{3 { {1} over {8} } = { {3 cdot 8+1} over {8} } = { {"24"+1} over {8} } = { {"25"} over {8} } } {}

25 8 5 6 size 12{ { {"25"} over {8} } - { {5} over {6} } } {} The LCD = 24.

25 8 5 6 = 25 3 24 5 4 24 = 75 24 20 24 = 75 20 24 = 55 24 Convert his improper fraction to a mixed number. = 2 7 24

Thus, 3 1 8 5 6 = 2 7 24 size 12{3 { {1} over {8} } - { {5} over {6} } =2 { {7} over {"24"} } } {} .

Practice set a

Find the following sums and differences.

1 5 9 + 3 2 9 size 12{1 { {5} over {9} } +3 { {2} over {9} } } {}

4 7 9 size 12{4 { {7} over {9} } } {}

10 3 4 2 1 2 size 12{"10" { {3} over {4} } - 2 { {1} over {2} } } {}

8 1 4 size 12{8 { {1} over {4} } } {}

2 7 8 + 5 1 4 size 12{2 { {7} over {8} } +5 { {1} over {4} } } {}

8 1 8 size 12{8 { {1} over {8} } } {}

8 3 5 3 10 size 12{8 { {3} over {5} } - { {3} over {"10"} } } {}

8 3 10 size 12{8 { {3} over {"10"} } } {}

16 + 2 9 16 size 12{"16"+2 { {9} over {"16"} } } {}

18 9 16 size 12{"18" { {9} over {"16"} } } {}

Exercises

For the following problems, perform each indicated opera­tion.

3 1 8 + 4 3 8 size 12{3 { {1} over {8} } +4 { {3} over {8} } } {}

7 1 2 size 12{7 { {1} over {2} } } {}

5 1 3 + 6 1 3 size 12{5 { {1} over {3} } +6 { {1} over {3} } } {}

10 5 12 + 2 1 12 size 12{"10" { {5} over {"12"} } +2 { {1} over {"12"} } } {}

12 1 2 size 12{"12" { {1} over {2} } } {}

15 1 5 11 3 5 size 12{"15" { {1} over {5} } -"11" { {3} over {5} } } {}

9 3 11 + 12 3 11 size 12{9 { {3} over {"11"} } +"12" { {3} over {"11"} } } {}

21 6 11 size 12{"21" { {6} over {"11"} } } {}

1 1 6 + 3 2 6 + 8 1 6 size 12{1 { {1} over {6} } +3 { {2} over {6} } +8 { {1} over {6} } } {}

5 3 8 + 1 1 8 2 5 8 size 12{5 { {3} over {8} } +1 { {1} over {8} } -2 { {5} over {8} } } {}

3 7 8 size 12{3 { {7} over {8} } } {}

3 5 + 5 1 5 size 12{ { {3} over {5} } +5 { {1} over {5} } } {}

2 2 9 5 9 size 12{2 { {2} over {9} } - { {5} over {9} } } {}

1 2 3 size 12{1 { {2} over {3} } } {}

6 + 11 2 3 size 12{6+"11" { {2} over {3} } } {}

17 8 3 14 size 12{"17"-8 { {3} over {"14"} } } {}

8 11 14 size 12{8 { {"11"} over {"14"} } } {}

5 1 3 + 2 1 4 size 12{5 { {1} over {3} } +2 { {1} over {4} } } {}

6 2 7 1 1 3 size 12{6 { {2} over {7} } -1 { {1} over {3} } } {}

4 20 21 size 12{4 { {"20"} over {"21"} } } {}

8 2 5 + 4 1 10 size 12{8 { {2} over {5} } +4 { {1} over {"10"} } } {}

1 1 3 + 12 3 8 size 12{1 { {1} over {3} } +"12" { {3} over {8} } } {}

13 17 24 size 12{"13" { {"17"} over {"24"} } } {}

3 1 4 + 1 1 3 2 1 2 size 12{3 { {1} over {4} } +1 { {1} over {3} } -2 { {1} over {2} } } {}

4 3 4 3 5 6 + 1 2 3 size 12{4 { {3} over {4} } -3 { {5} over {6} } +1 { {2} over {3} } } {}

2 7 12 size 12{"2" { {7} over {12} } } {}

3 1 12 + 4 1 3 + 1 1 4 size 12{3 { {1} over {"12"} } +4 { {1} over {3} } +1 { {1} over {4} } } {}

5 1 15 + 8 3 10 5 4 5 size 12{5 { {1} over {"15"} } +8 { {3} over {"10"} } -5 { {4} over {5} } } {}

7 17 30 size 12{7 { {"17"} over {"30"} } } {}

7 1 3 + 8 5 6 2 1 4 size 12{7 { {1} over {3} } +8 { {5} over {6} } -2 { {1} over {4} } } {}

19 20 21 + 42 6 7 5 14 + 12 1 7 size 12{"19" { {"20"} over {"21"} } +"42" { {6} over {7} } - { {5} over {"14"} } +"12" { {1} over {7} } } {}

74 25 42 size 12{"74" { {"25"} over {"42"} } } {}

1 16 + 4 3 4 + 10 3 8 9 size 12{ { {1} over {"16"} } +4 { {3} over {4} } +"10" { {3} over {8} } -9} {}

11 2 9 + 10 1 3 2 3 5 1 6 + 6 1 18 size 12{"11"- { {2} over {9} } +"10" { {1} over {3} } - { {2} over {3} } -5 { {1} over {6} } +6 { {1} over {"18"} } } {}

21 1 3 size 12{"21" { {1} over {3} } } {}

5 2 + 2 1 6 + 11 1 3 11 6 size 12{ { {5} over {2} } +2 { {1} over {6} } +"11" { {1} over {3} } - { {"11"} over {6} } } {}

1 1 8 + 9 4 1 16 1 32 + 19 8 size 12{1 { {1} over {8} } + { {9} over {4} } - { {1} over {"16"} } - { {1} over {"32"} } + { {"19"} over {8} } } {}

5 21 32 size 12{5 { {"21"} over {"32"} } } {}

22 3 8 16 1 7 size 12{"22" { {3} over {8} } -"16" { {1} over {7} } } {}

15 4 9 + 4 9 16 size 12{"15" { {4} over {9} } +4 { {9} over {"16"} } } {}

20 1 144 size 12{"20" { {1} over {"144"} } } {}

4 17 88 + 5 9 110 size 12{4 { {"17"} over {"88"} } +5 { {9} over {"110"} } } {}

6 11 12 + 2 3 size 12{6 { {"11"} over {"12"} } + { {2} over {3} } } {}

7 7 12 size 12{7 { {7} over {"12"} } } {}

8 9 16 7 9 size 12{8 { {9} over {"16"} } - { {7} over {9} } } {}

5 2 11 1 12 size 12{5 { {2} over {"11"} } - { {1} over {"12"} } } {}

5 13 132 size 12{5 { {"13"} over {"132"} } } {}

18 15 16 33 34 size 12{"18" { {"15"} over {"16"} } - { {"33"} over {"34"} } } {}

1 89 112 21 56 size 12{1 { {"89"} over {"112"} } - { {"21"} over {"56"} } } {}

1 47 212 size 12{1 { {"47"} over {"212"} } } {}

11 11 24 7 13 18 size 12{"11" { {"11"} over {"24"} } -7 { {"13"} over {"18"} } } {}

5 27 84 3 5 42 + 1 1 21 size 12{5 { {"27"} over {"84"} } -3 { {5} over {"42"} } +1 { {1} over {"21"} } } {}

3 1 4 size 12{3 { {1} over {4} } } {}

16 1 48 16 1 96 + 1 144 size 12{"16" { {1} over {"48"} } -"16" { {1} over {"96"} } + { {1} over {"144"} } } {}

A man pours 2 5 8 size 12{2 { {5} over {8} } } {} gallons of paint from a bucket into a tray. After he finishes pouring, there are 1 1 4 size 12{1 { {1} over {4} } } {} gallons of paint left in his bucket. How much paint did the man pour into the tray?

Think about the wording.

2 5 8 gallons

A particular computer stock opened at 37 3 8 size 12{"37" { {3} over {8} } } {} and closed at 38 1 4 size 12{"38" { {1} over {4} } } {} . What was the net gain for this stock?

A particular diet program claims that 4 3 16 size 12{4 { {3} over {"16"} } } {} pounds can be lost the first month, 3 1 4 size 12{3 { {1} over {4} } } {} pounds can be lost the second month, and 1 1 2 size 12{1 { {1} over {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 15 16 pounds

If a person who weighs 145 3 4 size 12{"145" { {3} over {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 1 8 size 12{1 { {1} over {8} } } {} pounds a month, how much will a person who begins the program weighing 208 3 4 size 12{"208" { {3} over {4} } } {} pounds weight after 8 months?

194 3 16 pounds

Exercises for review

( [link] ) Use exponents to write 4 4 4 size 12{4 cdot 4 cdot 4} {} .

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

2

( [link] ) Convert 16 5 size 12{ { {"16"} over {5} } } {} to a mixed number.

( [link] ) Find the sum. 4 9 + 1 9 + 2 9 size 12{ { {4} over {9} } + { {1} over {9} } + { {2} over {9} } } {} .

7 9 size 12{ { {7} over {9} } } {}

( [link] ) Find the difference. 15 26 3 10 size 12{ { {"15"} over {"26"} } - { {3} over {"10"} } } {} .

Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask