# ADD AND SUBTRACT FRACTIONS WITH LIKE AND UNLIKE DENOMINATORS

When we add or subtract two or more fractions with like denominators, we use only one denominator and combine the numerators.

For example,

= 1/3 + 1/3

= (1+1)/3

= 2/3

When we add or subtract two or more fractions with unlike denominators, we can take the Least Common Multiple or use the cross multiplication.

For example,

Using Least Common Multiple :

= 1/4 + 1/5

= (1/4 × 5/5) + (1/5 × 4/4)

= 5/20 + 4/20

= 9/20

Using Cross Multiplication :

= 1/4 + 1/5

= (5 + 4)/20

= 9/20

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

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