How to Subtract Fractions with Unlike Denominators


Subtract Fractions with Unlike Denominators

Fractions with unlike denominators are the fractions having different denominators. 

Fractions with Unlike Denominators

For instance, fractions 1 4 and 1 3 are unlike denominators.

Another example is if Tom has 34 of a pizza and he eats 1 8 We need to take away 1 8 from 34 to work out how much pizza did he eat.

Similarly, if Macy had a half of an apple and she ate one quarter of it in the morning. To work out the remaining portion of the apple left, we need to take away from  1 4 from 1 2 .

Steps to Subtract Fractions with Unlike Denominators:

(i) Identify the unlike fractions we need to subtract.

(ii) Convert both the fractions into their equivalent fractions such that they have like denominators.

(iii) Replace both the fractions in Step (i) by their equivalent fractions obtained in Step(ii).

(iv) As we have fractions with like denominators, we can subtract the numerators directly to obtain the answer and the denominator remains the  same.

(v) Simplify the fraction obtained in Step (iv) if possible.

Case-1: When one of the denominators is a multiple of the other.

Example 1: Work out: 12 28 .

Solution:

Step Number

Observation

Working Out

Step (i)

Unlike Denominators

1 2 2 8

Step (ii) 

The common denominator for the above fractions is 8. Working out the equivalent fractions.

1 × 42 × 4 = 48 ; 2 8 = 2 8

Step (iii)

Replacing the fractions in (i) by equivalent fractions from (ii)

4 8 28

Step (iv)

We have like denominators now. So, we directly take away the numerators.

48 28 = 2 8

Step (v)

Simplifying the answer from (iv)

2 ÷ 2 8 ÷ 2 = 14

Hence, 12 28 = 14

Case-2: When both the denominators are different. 

Example 2: Jack has of 45 of papaya. If he gives 13 of it to Lucy, what fraction of papaya is left with Jack?

Solution:

Step Number

Observation

Working Out

Step (i)

Unlike Denominators

4513

Step (ii)

The common denominator for the above fractions is 15. Working out the equivalent fractions.

4 × 35 × 3 = 1215 ; 1 × 5 3 × 5  =  515

Step (iii)

Replacing the fractions in (i) by equivalent fractions from (ii)

12 15 5 15

Step (iv)

We have like denominators now. So, we directly take away the numerators.

12 15 515 = 715

Step (v)

The answer is already in its simplest form.

2 ÷ 28 ÷ 2 = 14

Hence, Jack has 14  of the papaya left.

Example 3: Allie and Joseph are competing in a bicycle race. If Allie has covered 34 of the total distance and Joseph has covered 15 of the total distance. What is the difference in the distance covered by both of them? 

Solution:

Step Number

ObservationWorking Out
Step (i)Unlike Denominators 34 1 5
Step (ii)The common denominator for the above fractions is 20. Working out the equivalent fractions. 3 × 54 × 5 = 1520 ; 1 × 45 × 4 = 420

Step (iii)

Replacing the fractions in (i) by equivalent fractions from (ii) 1520 420
Step (iv) We have like denominators now. So, we directly take away the numerators. 1520 4 20 = 1120
Step (v) The answer is already in its simplest form. 1120

Hence, the difference between the distance covered by Allie and Joseph is 1120 of the total distance.

Fun Facts

  • Every whole number can be written as a fraction.

For instance:  2 can be written as 2 1 or 3 as 31 and so on.