Word Problems on Fractions
You have learned how to add, subtract, and compare fractions. Now it is time to apply those skills to real-life situations using word problems.
Word problems on fractions appear in everyday life — sharing food, measuring ingredients, dividing time, and calculating distances. The key skill is to read carefully, identify the operation, and solve step by step.
Follow this approach: read, identify, set up, solve, and answer.
What is Word Problems on Fractions?
Steps to solve fraction word problems:
- Read the problem carefully. Underline key numbers and the question.
- Identify the operation: addition (combining), subtraction (difference/remaining), or finding a part ("of" = multiply).
- Set up the fraction equation.
- Solve using fraction rules (LCM for unlike denominators, simplify).
- Answer with correct unit.
Common keywords:
- Addition: total, altogether, combined, in all.
- Subtraction: remaining, left, difference, how much more.
- "Of" means multiply: 1/3 of 12 = 1/3 × 12 = 4.
Types and Properties
1. Addition Word Problems
Combine two or more fractional parts.
- Riya drank 1/4 litre and 1/3 litre. Total = 1/4 + 1/3 = 3/12 + 4/12 = 7/12 litre.
2. Subtraction Word Problems
Find what is left or the difference.
- A tank is 5/6 full. After use, it is 1/3 full. Used = 5/6 − 1/3 = 5/6 − 2/6 = 3/6 = 1/2.
3. "Part of a Whole" Problems
"Of" means multiplication.
- 30 students, 2/5 are girls. Girls = 2/5 × 30 = 12.
4. Comparison Problems
Which fraction is more or less, and by how much.
- 3/4 km vs 2/3 km: 9/12 vs 8/12. Difference = 1/12 km.
Solved Examples
Example 1: Example 1: Addition
Problem: Seema spent 1/4 on books and 1/3 on stationery. What fraction was spent?
Solution:
- LCM of 4 and 3 = 12.
- 1/4 = 3/12, 1/3 = 4/12.
- Total = 3/12 + 4/12 = 7/12.
Answer: Seema spent 7/12 of her money.
Example 2: Example 2: Subtraction
Problem: A bottle was 7/8 full. After drinking, it was 3/8 full. What fraction was consumed?
Solution:
- Consumed = 7/8 − 3/8 = 4/8 = 1/2.
Answer: 1/2 was consumed.
Example 3: Example 3: Part of a whole number
Problem: There are 48 apples. Rahul took 1/6. How many did he take?
Solution:
- 1/6 of 48 = 48 ÷ 6 = 8.
Answer: Rahul took 8 apples.
Example 4: Example 4: Remaining after spending
Problem: Priya had Rs. 600. She spent 2/3. How much is left?
Solution:
- Spent = 2/3 × 600 = 400.
- Left = 600 − 400 = 200.
Answer: Rs. 200 left.
Example 5: Example 5: Unlike fractions
Problem: A recipe needs 1/2 cup flour and 1/5 cup sugar. Total dry ingredient?
Solution:
- LCM of 2 and 5 = 10.
- 1/2 = 5/10, 1/5 = 2/10.
- Total = 7/10 cup.
Answer: 7/10 cup.
Example 6: Example 6: Comparison
Problem: Karan ate 2/5 of a cake and Neha ate 3/10. Who ate more?
Solution:
- 2/5 = 4/10, 3/10 = 3/10.
- 4/10 > 3/10. Karan ate more by 1/10.
Answer: Karan ate more, by 1/10.
Example 7: Example 7: Distance problem
Problem: Anita walked 3/4 km to school and 1/2 km to the library. Total distance?
Solution:
- 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4 km.
Answer: 1 1/4 km.
Example 8: Example 8: Time problem
Problem: Ravi spent 1/3 hour on homework and 1/4 hour reading. Total minutes?
Solution:
- 1/3 of 60 = 20 min. 1/4 of 60 = 15 min.
- Total = 35 minutes.
Answer: 35 minutes.
Example 9: Example 9: Cloth problem
Problem: A cloth is 3 m long. Sita used 3/4 of it. How much is left?
Solution:
- Used = 3/4 × 3 = 9/4 = 2 1/4 m.
- Left = 3 − 2 1/4 = 3/4 m.
Answer: 3/4 metre is left.
Example 10: Example 10: Multi-step
Problem: A full tank: 1/4 used in morning, 1/3 used in afternoon. What fraction remains?
Solution:
- Used = 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
- Remaining = 1 − 7/12 = 5/12.
Answer: 5/12 remains.
Real-World Applications
Cooking: Recipes use fractions — 1/2 cup oil, 3/4 tsp salt. Doubling or halving requires fraction operations.
Shopping: A 1/4 off sale on Rs. 800 shirt means Rs. 200 discount.
Time: Students spend 1/3 of the day sleeping, 1/4 at school — fractions help calculate free time.
Construction: Using 2/5 of cement on Day 1 and 1/5 on Day 2 leaves 2/5 remaining.
Sports: A cricketer scoring 1/3 of 240 team runs scored 80 runs.
Key Points to Remember
- Read carefully and underline key numbers.
- "Of" means multiplication.
- "Total/altogether" means addition. "Remaining/left" means subtraction.
- Convert unlike fractions to like fractions before adding or subtracting.
- Simplify answers to lowest terms.
- Convert improper fractions to mixed numbers.
- Always include the unit in the answer.
- "Fraction remaining" = 1 minus the fraction used.
Practice Problems
- Aman ate 2/7 of a pizza and his sister 3/7. What fraction was eaten? What is left?
- A rope is 5 m long. If 3/5 is cut off, how many metres remain?
- Meera spent 1/4 on a book and 1/6 on a pen. What fraction was spent? What is left?
- 42 students in a class. 3/7 play cricket. How many play cricket?
- Raju walked 5/8 km and Sita 1/2 km. Who walked more and by how much?
- A 2-litre bottle is 3/4 full. How many litres does it contain?
- Priya answered 5/6 of 30 questions correctly. How many did she get right?
- A painter used 1/3 of paint on Monday and 1/4 on Tuesday. What fraction is left?
Frequently Asked Questions
Q1. How do I know whether to add or subtract?
Look for keywords. 'Total', 'altogether' = addition. 'Remaining', 'left', 'how much more' = subtraction.
Q2. What does 'of' mean?
'Of' means multiplication. 1/4 of 20 = 1/4 × 20 = 5.
Q3. How do I find the fraction remaining?
Subtract the used fraction from 1. If 2/5 is used, remaining = 1 − 2/5 = 3/5.
Q4. Can I add fractions with different denominators directly?
No. First convert to like fractions using the LCM.
Q5. What if the answer is an improper fraction?
Convert to a mixed number. 7/4 = 1 3/4.
Q6. How do I check my answer?
Ask: does it make sense? The total should be more than each part; remaining should be less than original.
Q7. What if the problem mixes whole numbers and fractions?
Convert whole numbers to fractions. 3 = 3/1. Then operate normally.
Q8. Are these problems in exams?
Yes. Word problems on fractions are very common in Class 6 NCERT/CBSE exams.
Related Topics
- Addition of Fractions
- Subtraction of Fractions
- Multiplication of Fractions
- Division of Fractions
- Introduction to Fractions
- Proper and Improper Fractions
- Mixed Numbers
- Equivalent Fractions
- Simplest Form of a Fraction
- Comparing Fractions
- Like and Unlike Fractions
- Fractions on Number Line
- Unit Fractions
- Types of Fractions
