ADD AND SUBTRACT FRACTIONS WITH LIKE AND UNLIKE DENOMINATORS

Find :

Problem 1 :

5/13 + 7/13

Solution :

In the given fraction, the denominators are same. So, we put only one denominator and combine the numerators.

= (5 + 7)/13

= 12/13

Problem 2 :

9/16 + 2/16

Solution :

In the given fraction, the denominators are same. So, we put only one denominator and combine the numerators.

= (9 + 2)/16

= 11/16

Problem 3 :

3/8 + 1/4

Solution :

In the given fraction, the denominators are not the same.

So, we are taking the Least Common Multiple of 8 and 4.

= 3/8 + (1/4 × 2/2)

= 3/8 + 2/8

= 5/8

Problem 4 :

2/5 + 1/6

Solution :

In the given fraction, the denominators are not same. 

So, we are taking the Least Common Multiple of 5 and 6.

= (2/5 × 6/6) + (1/6 × 5/5)

= 12/30 + 5/30

= 17/30

Problem 5 :

1  1/3 + 5/6  

Solution :

Method 1 :

= 1  1/3 + 5/6

= 1 (1/3 + 5/6)

By taking the least common multiple, we get

= 1  (2 + 5)/6

= 1  7/6

Converting the improper fraction to mixed fraction, we get

= 1  (1 1/6)

= (1 + 1)  1/6

= 2  1/6

Method 2 :

= 1  1/3 + 5/6

Converting the mixed fractions to improper fraction, we get

= 4/3 + 5/6

Here the denominators are not the same. So, we are taking the Least Common Multiple of 3 and 6.

= (4/3 × 2/2) + 5/6 × 1/1)

= [4(2) + 5]/6

= (8 + 5)/6

= 13/6

Converting the improper fraction to mixed fraction, we get

= 2 1/6

Problem 6 :

2  1/3 +  1  1/6

Solution :

Method 1 :

= 2  1/3 +  1  1/6

= (2 + 1)  (1/3 + 1/6)

By taking the least common multiple, we get

= 3  (2 + 1)/6

= 3  1/2

Method 2 :

 = 2  1/3 +  1  1/6

Converting the mixed fractions to improper fraction, we get

= 7/3 + 7/6

Least common multiple of 3 and 6 is 6.

= [7(2) + 7(1)]/6

= (14 + 7)/6

= 21/6

Converting the improper fraction to mixed fraction, we get

= 3  3/6

= 3  1/2

Problem 7 :

1  1/2 +  4  2/3

Solution :

Method 1 :

= 1  1/2 +  4  2/3

= (1+4)  (1/2 + 2/3)

By taking the least common multiple, we get

= 5  (3 + 4)/6

= 5  7/6

Converting the improper fraction to mixed fraction, we get

= 5  (1 1/6)

= (5 + 1)  1/6

= 6  1/6

Method 2 :

= 1  1/2 +  4  2/3

Converting the mixed fractions to improper fraction, we get

= 3/2 + 14/3

Least common multiple of 2 and 3 is 6.

= [3(3) + 14(2)]/6

= (9 + 28)/6

= 37/6

Converting the improper fraction to mixed fraction, we get

= 6  1/6

Find :

Problem 8 :

7/11 - 3/11

Solution :

In the given fraction, the denominators are same. So, we put only one denominator and combine the numerators.

= (7 - 3)/11

= 4/11

Problem 9 :

5/6 - 2/3

Solution :

In the given fraction, the denominators are not same. 

So, we are taking the Least Common Multiple of 6 and 3.

 = 5/6 - (2/3 × 2/2)

= 5/6 - 4/6

= 1/6

Problem 10 :

4/9 - 1/3

Solution :

In the given fraction, the denominators are not same. 

So, we are taking the Least Common Multiple of 9 and 3.

= 4/9 - (1/3 × 3/3)

= 4/9 - 3/9

= 1/9

Problem 11 :

2  3/5  -  1  1/2

Solution :

Method 1 :

= 2  3/5  -  1  1/2

= (2 - 1)  (3/5 - 1/2)

By taking the least common multiple, we get

= 1  (6 - 5)/10

= 1  1/10

Method 2 :

= 2  3/5  -  1  1/2

Converting the mixed fractions to improper fraction, we get

= 13/5  - 3/2

Least common multiple of 5 and 2 is 10.

= [13(2) - 3(5)]/10

= (26 - 15)/10

= 11/10

Converting the improper fraction to mixed fraction, we get

= 1  1/10

Problem 12 :

3  1/3  -  1  1/2

Solution :

Method 1 :

= 3  1/3  -  1  1/2

= (3 - 1)  (1/3 - 1/2)

By taking the least common multiple, we get

= 2  (2 - 3)/6

= 2  (-1)/6

= 11/6

Converting the improper fraction to mixed fraction, we get

= 1  5/6

Method 2 :

= 3 1/3  -  1  1/2

Converting the mixed fractions to improper fraction, we get

= 10/3 - 3/2

Least common multiple of 3 and 2 is 6.

= [10(2) - 3(3)]/6

= (20 - 9)/6

= 11/6

Converting the improper fraction to mixed fraction, we get

= 1  5/6

Problem 13 :

4  3/7  -  2  1/3

Solution :

Method 1 :

= 4  3/7  -  2  1/3

= (4 - 2)  (3/7 - 1/3)

By taking the least common multiple, we get

= 2  (9 - 7)/21

= 2  2/21

Method 2 :

= 4  3/7  -  2  1/3

Converting the mixed fractions to improper fraction, we get

= 31/7 - 7/3

Least common multiple of 7 and 3 is 21.

= [31(3) - 7(7)]/21

= (93 - 49)/21

= 44/21

Converting the improper fraction to mixed fraction, we get

= 2  2/21