Adding and subtracting unlike fractions: Class 6 practice
Fractions can only be added when they describe pieces of the same size, so we first rewrite them with a common denominator — usually the LCM of the denominators.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Equivalent fractions
- LCM of small numbers
The idea behind adding and subtracting unlike fractions
Fractions can only be added when they describe pieces of the same size, so we first rewrite them with a common denominator — usually the LCM of the denominators.
Step-by-step method
- Find the LCM of the denominators.
- Convert each fraction to that denominator.
- Add or subtract the numerators.
- Simplify by dividing by the HCF.
Worked example 1 (Basic)
Work out 7/9 + 7/10.
- LCM of 9 and 10 is 90
- 7/9 = 70/90 and 7/10 = 63/90
- Add numerators: 133/90
- Simplify: 133/90
- Answer: 133/90
Worked example 2 (Standard)
Work out 3/6 + 1/4.
- LCM of 6 and 4 is 12
- 3/6 = 6/12 and 1/4 = 3/12
- Add numerators: 9/12
- Simplify: 3/4
- Answer: 3/4
Worked example 3 (Challenge)
Work out 3/8 − 4/9.
- LCM of 8 and 9 is 72
- 3/8 = 27/72 and 4/9 = 32/72
- Subtract numerators: -5/72
- Simplify: -5/72
- Answer: -5/72
Common mistakes and misconceptions
- Adding denominators (1/2 + 1/3 ≠ 2/5)
- Forgetting to simplify the final answer
Practice questions
- (Basic) Work out 8/9 + 4/8.
- (Basic) Work out 1/5 + 7/12.
- (Standard) Work out 4/6 + 11/12.
- (Standard) Work out 2/8 + 2/5.
- (Challenge) Work out 6/9 − 9/10.
- (Challenge) Work out 1/2 − 1/3.
Answer key with full working
- Q1: LCM of 9 and 8 is 72 → 8/9 = 64/72 and 4/8 = 36/72 → Add numerators: 100/72 → Simplify: 25/18 → Answer: 25/18
- Q2: LCM of 5 and 12 is 60 → 1/5 = 12/60 and 7/12 = 35/60 → Add numerators: 47/60 → Simplify: 47/60 → Answer: 47/60
- Q3: LCM of 6 and 12 is 12 → 4/6 = 8/12 and 11/12 = 11/12 → Add numerators: 19/12 → Simplify: 19/12 → Answer: 19/12
- Q4: LCM of 8 and 5 is 40 → 2/8 = 10/40 and 2/5 = 16/40 → Add numerators: 26/40 → Simplify: 13/20 → Answer: 13/20
- Q5: LCM of 9 and 10 is 90 → 6/9 = 60/90 and 9/10 = 81/90 → Subtract numerators: -21/90 → Simplify: -7/30 → Answer: -7/30
- Q6: LCM of 2 and 3 is 6 → 1/2 = 3/6 and 1/3 = 2/6 → Subtract numerators: 1/6 → Simplify: 1/6 → Answer: 1/6
Syllabus note
This skill is listed under "Fractions" for Class 6 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is adding and subtracting unlike fractions in?
"Fractions", Class 6 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.