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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
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Sherica
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Sherica
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Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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