ADDING AND SUBTRACTING FRACTIONS
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.
1 2 , 1 3
Solution:
= 1 2 + 1 3 Least common multiple of ( 2 , 3 ) = 6 1 2 = 1 × 3 2 × 3 = 3 6 1 3 = 1 × 2 3 × 2 = 2 6 = 3 6 + 2 6 = 5 6
Problem 2 :
2 5 + 2 3
Solution:
= 2 5 + 2 3 Least common multiple of ( 5 , 3 ) = 15 2 5 = 2 × 3 5 × 3 = 6 15 2 3 = 2 × 5 3 × 5 = 10 15 = 6 15 + 10 15 = 16 15
Problem 3 :
5 8 + 1 2
Solution:
= 5 8 + 1 2 Least common multiple of ( 8 , 2 ) = 8 5 8 = 5 × 1 8 × 1 = 5 8 1 2 = 1 × 4 2 × 4 = 4 8 = 5 8 + 4 8 = 9 8
Problem 4 :
1 4 + 1 3
Solution:
= 1 4 + 1 3 Least common multiple of ( 4 , 3 ) = 12 1 4 = 1 × 3 4 × 3 = 3 12 1 3 = 1 × 4 3 × 4 = 4 12 = 3 12 + 4 12 = 7 12
Problem 5 :
1 7 + 2 5
Solution:
= 1 7 + 2 5 Least common multiple of ( 7 , 5 ) = 35 1 7 = 1 × 5 7 × 5 = 5 35 2 5 = 2 × 7 5 × 7 = 14 35 = 5 35 + 14 35 = 19 35
Problem 6 :
4 9 + 1 3
Solution:
= 4 9 + 1 3 Least common multiple of ( 9 , 3 ) = 9 4 9 = 4 × 1 9 × 1 = 4 9 1 3 = 1 × 3 3 × 3 = 3 9 = 4 9 + 3 9 = 7 9
Problem 7 :
3 4 + 1 2
Solution:
= 3 4 + 1 2 Least common multiple of ( 4 , 2 ) = 4 3 4 = 3 × 1 4 × 1 = 3 4 1 2 = 1 × 2 2 × 2 = 2 4 = 3 4 + 2 4 = 5 4
Problem 8 :
7 8 + 3 5
Solution:
= 7 8 + 3 5 Least common multiple of ( 8 , 5 ) = 40 7 8 = 7 × 5 8 × 5 = 35 40 3 5 = 3 × 8 5 × 8 = 24 40 = 35 40 + 24 40 = 59 40
1 59/40 = 1 + 1 19/40
= 2 19/40
So, the answer is 2 19/40
Problem 9 :
3 10 - 2 3
Solution:
= 3 10 - 2 3 Least common multiple of ( 10 , 3 ) = 30 3 10 = 3 × 3 10 × 3 = 9 30 2 3 = 2 × 10 3 × 10 = 20 30 = 9 30 - 20 30 = - 11 30
Problem 10 :
13 15 - 4 5
Solution:
= 13 15 - 4 5 Least common multiple of ( 15 , 5 ) = 15 13 15 = 13 × 1 15 × 1 = 13 15 4 5 = 4 × 3 5 × 3 = 12 15 = 13 15 - 12 15 = 1 15
Problem 11 :
1 2 + 2 3 + 5 6
Solution:
= 1 2 + 2 3 + 5 6 Least common multiple of ( 2 , 3 , 6 ) = 6 1 2 = 1 × 3 2 × 3 = 3 6 2 3 = 2 × 2 3 × 2 = 4 6 5 6 = 5 × 1 6 × 1 = 5 6 = 3 6 + 4 6 + 5 6 = 12 6 = 2
Problem 12 :
3 4 + 5 8 + 7 16
Solution:
= 3 4 + 5 8 + 7 16 Least common multiple of ( 4 , 8 , 16 ) = 16 3 4 = 3 × 4 4 × 4 = 12 16 5 8 = 5 × 2 8 × 2 = 10 16 7 16 = 7 × 1 16 × 1 = 7 16 = 12 16 + 10 16 + 7 16 = 29 16
Problem 13 :
3 8 + 1 6 - 1 3
Solution:
= 3 8 + 1 6 - 1 3 Least common multiple of ( 8 , 6 , 3 ) = 24 3 8 = 3 × 3 8 × 3 = 9 24 1 6 = 1 × 4 6 × 4 = 4 24 1 3 = 1 × 8 3 × 8 = 8 24 = 9 24 + 4 24 - 8 24 = 5 24
Problem 14 :
1 7 + 1 2 - 1 3
Solution:
= 1 7 + 1 2 - 1 3 Least common multiple of ( 7 , 2 , 3 ) = 42 1 7 = 1 × 6 7 × 6 = 6 42 1 2 = 1 × 21 2 × 21 = 21 42 1 3 = 1 × 14 3 × 14 = 14 42 = 6 42 + 21 42 - 14 42 = 13 42
Problem 15 :
3 8 + 1 5 - 1 3
Solution:
= 3 8 + 1 5 - 1 3 Least common multiple of ( 8 , 5 , 3 ) = 120 3 8 = 3 × 15 8 × 15 = 45 120 1 5 = 1 × 24 5 × 24 = 24 120 1 3 = 1 × 40 3 × 40 = 40 120 = 45 120 + 24 120 - 40 120 = 29 120