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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"} } } {} .

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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"} } } {} .

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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} } } {}

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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} } } {}

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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} } } {}

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

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

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

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

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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} } } {}

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

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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} } } {}

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

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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"} } } {}

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

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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} } } {}

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

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

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

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

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

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

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

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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"} } } {}

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

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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"} } } {}

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

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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} } } {}

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

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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"} } } {}

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

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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"} } } {}

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

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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} } } {}

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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} } } {}

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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"} } } {}

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

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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"} } } {}

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

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

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

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

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

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

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

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

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

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

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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} } } {}

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

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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

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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?

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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

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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?

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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

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Exercises for review

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

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

2

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

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( [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} } } {}

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

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Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket 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
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
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
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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