ADDING AND SUBTRACTING FRACTIONS

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While adding or subtracting fractions, we have to consider the following.

i) Check if the given fractions are like or unlike fractions.

ii) If they are like fractions, we have to put the denominator once and add or subtract numerators.

iii)  If they are unlike fractions, we have to find the LCM and make the denominator same and follow the step given above.

iv) After adding or subtracting fractions do the possible simplification as much. Incase we find the improper fraction, we have to write it as mixed fraction.

Using the previously shown method, write just the LCD for the following sets of fractions.

Problem 1 : 

Add the following fractions.

12,13

Solution:

=12+13Least common multiple of (2,3)=612=1×32×3=3613=1×23×2=26=36+26=56

Problem 2 :

25+23

Solution:

=25+23Least common multiple of (5,3)=1525=2×35×3=61523=2×53×5=1015=615+1015=1615

Problem 3 :

58+12

Solution:

=58+12Least common multiple of (8,2)=858=5×18×1=5812=1×42×4=48=58+48=98

Problem 4 :

14+13

Solution:

=14+13Least common multiple of (4,3)=1214=1×34×3=31213=1×43×4=412=312+412=712

Problem 5 :

17+25

Solution:

=17+25Least common multiple of (7,5)=3517=1×57×5=53525=2×75×7=1435=535+1435=1935

Problem 6 :

49+13

Solution:

=49+13Least common multiple of (9,3)=949=4×19×1=4913=1×33×3=39=49+39=79

Problem 7 :

34+12

Solution:

=34+12Least common multiple of (4,2)=434=3×14×1=3412=1×22×2=24=34+24=54

Problem 8 :

78+35

Solution:

=78+35Least common multiple of (8,5)=4078=7×58×5=354035=3×85×8=2440=3540+2440=5940

1  59/40 = 1 + 1  19/40

= 2   19/40

So, the answer is 2  19/40

Problem 9 :

310-23

Solution:

=310-23Least common multiple of (10,3)=30310=3×310×3=93023=2×103×10=2030=930-2030=-1130

Problem 10 :

1315-45

Solution:

=1315-45Least common multiple of (15,5)=151315=13×115×1=131545=4×35×3=1215=1315-1215=115

Problem 11 :

12+23+56

Solution:

=12+23+56Least common multiple of (2,3,6)=612=1×32×3=3623=2×23×2=4656=5×16×1=56=36+46+56=126=2

Problem 12 :

34+58+716

Solution:

=34+58+716Least common multiple of (4,8,16)=1634=3×44×4=121658=5×28×2=1016716=7×116×1=716=1216+1016+716=2916

Problem 13 :

38+16-13

Solution:

=38+16-13Least common multiple of (8,6,3)=2438=3×38×3=92416=1×46×4=42413=1×83×8=824=924+424-824=524

Problem 14 :

17+12-13

Solution:

=17+12-13Least common multiple of (7,2,3)=4217=1×67×6=64212=1×212×21=214213=1×143×14=1442=642+2142-1442=1342

Problem 15 :

38+15-13

Solution:

=38+15-13Least common multiple of (8,5,3)=12038=3×158×15=4512015=1×245×24=2412013=1×403×40=40120=45120+24120-40120=29120

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