SOLVING PROBLEMS ON ADDING AND SUBTRACTING FRACTIONS

To add and subtract fractions we have to follow the steps given below.

Step 1 :

If the fractions are like fractions, keep the denominator once and add the numerators.

If the fraction are unlike fractions, we have to take the least common multiple make the denominators same and add.

Step 2 :

After adding or subtracting two fractions, even we get the mixed fraction. Using long division, we can convert the improper fraction to mixed number.

Add or subtract the following fractions. Simplify and reduce when possible.

Problem 1 :

27+37=

Solution:

=27+37

The given fractions are like fractions (having same denominator). To add them, take the denominator once and combine the numerators.

=(2+3)7=57

Problem 2 :

914+114=

Solution:

=914+114=(9+1)14=1014=57

Problem 3 :

16+36=

Solution:

=16+36=(1+3)6=46=23

Problem 4 :

35+14=

Solution:

=35+14Least common multiple of (5,4)=2035=3×45×4=122014=1×54×5=520=1220+520=1720

Problem 5 :

23+12=

Solution:

=23+12Least common multiple of (3,2)=623=2×23×2=4612=1×32×3=36=46+36=76

Problem 6 :

45+12=

Solution:

=45+12Least common multiple of (5,2)=1045=4×25×2=81012=1×52×5=510=810+510=1310

Since the denominator is lesser than the numerator, this can be considered as improper fraction.

Quotient RemainderDivisor

Problem 7 :

24+36=

Solution:

=24+36Least common multiple of (4,6)=1224=2×34×3=61236=3×26×2=612=612+612=1212=1

Problem 8 :

56+38=

Solution:

=56+38Least common multiple of (6,8)=2456=5×46×4=202438=3×38×3=924=2024+924=2924

Converting into mixed number

Quotient RemainderDivisor

Problem 9 :

79+23=

Solution:

=79+23Least common multiple of (9,3)=979=7×19×1=7923=2×33×3=69=79+69=139

Converting into mixed number,

Quotient RemainderDivisor

Problem 10 :

34-12=

Solution:

=34-12Least common multiple of (4,2)=434=3×14×1=3412=1×22×2=24=34-24=14

Problem 11 :

35-13=

Solution:

=35-13Least common multiple of (5,3)=1535=3×35×3=91513=1×53×5=515=915-515=415

Problem 12 :

78-23=

Solution:

=78-23Least common multiple of (8,3)=2478=7×38×3=212423=2×83×8=1624=2124-1624=524

Problem 13 :

512-14=

Solution:

=512-14Least common multiple of (12,4)=12512=5×112×1=51214=1×34×3=312=512-312=212=16

Problem 14 :

911-12=

Solution:

=911-12Least common multiple of (11,2)=22911=9×211×2=182212=1×112×11=1122=1822-1122=722

Problem 15 :

1112-56=

Solution:

=1112-56Least common multiple of (12,6)=121112=11×112×1=111256=5×26×2=1012=1112-1012=112

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