Subtract Fractions with Unlike Denominators
Fractions with unlike denominators are the fractions having different 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 | 45 – 13 |
| 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 | Observation | Working 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
For instance: 2 can be written as 2 1 or 3 as 31 and so on. |