# Subtraction of Unlike Fractions

We will learn how to solve subtraction of unlike fractions.

In order to subtract unlike fractions first we convert them as like fractions.

Let us consider some of the examples of subtracting unlike fractions:

1. Subtract 1/10 from 2/5.

Solution:

2/5 - 1/10

The L.C.M. of the denominators 10 and 5 is 10.

2/5 = (2 × 2)/(5 × 2) = 4/10, (because 10 ÷ 5 = 2)

1/10 = (1 × 1)/(10 × 1) = 1/10, (because 10 ÷ 10 = 1)

Thus, 2/5 - 1/10

= 4/10 - 1/10

= (4 - 1)/10

= 3/10

2. Subtract 4/9 from 5/7.

Solution:

5/7 - 4/9

The L.C.M. of the denominators 9 and 7 is 63.

5/7 = (5 × 9)/(7 × 9) = 45/63, (because 63 ÷ 7 = 9)

4/9 = (4 × 7)/(9 × 7) = 28/63, (because 63 ÷ 9 = 7)

Thus, 5/7 - 4/9

= 45/63 - 28/63

= (45 - 28)/63

= 17/63

3. Subtract 5/8 from 1.

Solution:

1 - 5/8

= 1/1 - 5/8

The L.C.M. of the denominators 1 and 8 is 8.

1/1 = (1 × 8)/(1 × 8) = 8/8, (because 8 ÷ 1 = 8)

5/8 = (5 × 1)/(8 × 1) = 5/8, (because 8 ÷ 8 = 1)

Thus, 1/1 - 5/8

= 8/8 - 5/8

= (8 - 5)/8

= 3/8

4. Subtract 19/36 from 23/24.

Solution:

23/24 - 19/36

The L.C.M. of the denominators 24 and 36 is 72.

23/24 = (23 × 3)/(24 × 3) = 69/72, (because 72 ÷ 24 = 3)

19/36 = (19 × 2)/(36 × 2) = 38/72, (because 72 ÷ 36 = 2)

Thus, 23/24 - 19/36

= 69/72 - 38/72

= (69 - 38)/72

= 31/72

5. Subtract 9/35 from 3/7.

Solution:

3/7 - 9/35

The L.C.M. of the denominators 7 and 35 is 35.

3/7 = (3 × 5)/(7 × 5) = 15/35, (because 35 ÷ 7 = 5)

9/35 = (9 × 1)/(35 × 1) = 9/35, (because 35 ÷ 35 = 1)

Thus, 3/7 - 9/35

= 15/35 - 9/35

= (15 - 9)/35

= 6/35

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