Fraction Word Problems (Grade 5)
Fraction word problems test your ability to apply fraction concepts — addition, subtraction, multiplication, and division — to real-life situations. Unlike plain calculation problems, word problems require you to read carefully, understand what is being asked, identify the correct operation, and then solve step by step.
In Class 5, word problems involve sharing food, spending money, measuring distances, comparing weights, and calculating time. The key skill is translating English sentences into mathematical fraction expressions. For example, "Ria ate 2/5 of the cake" becomes the expression 2/5 × (total cake).
This page covers all major types of fraction word problems with detailed solutions. Practice these to build confidence for school exams and competitive assessments.
What is Fraction Word Problems - Class 5 Maths (Fractions)?
A fraction word problem is a question presented as a real-life story that requires one or more fraction operations to solve.
How to identify which operation to use:
| Operation | Keywords to look for | Example phrase |
|---|---|---|
| Addition | total, altogether, combined, in all, sum | "How much milk in total?" |
| Subtraction | remaining, left, difference, how much more, less than | "How much flour is left?" |
| Multiplication | of, times, each (repeated groups), per | "2/3 of the students" |
| Division | shared equally, divided into, how many pieces, per portion | "divided equally among 4 friends" |
Fraction Word Problems (Grade 5) Formula
5-Step approach for word problems:
1. Read carefully → 2. Identify the operation → 3. Set up the expression → 4. Solve step by step → 5. Check the answer
Key formulas used in fraction word problems:
- Addition of unlike fractions: Find the LCM of denominators, convert to like fractions, then add the numerators.
- Subtraction: Same process as addition, but subtract the numerators.
- Fraction of a number: p/q × n = (p × n) / q
- Division of fractions: a/b ÷ c/d = a/b × d/c (Keep-Change-Flip)
- Finding the whole: If p/q of a number = N, then the number = (N ÷ p) × q.
Solved Examples
Example 1: Example 1: Addition of Fractions
Problem: Ria drinks 2/5 litre of milk in the morning and 1/4 litre in the evening. How much milk does she drink in a day?
Solution:
Identify: "How much in total" → Addition.
Step 1: Total = 2/5 + 1/4. LCM of 5 and 4 = 20.
Step 2: Convert: 2/5 = 8/20, 1/4 = 5/20
Step 3: Add: 8/20 + 5/20 = 13/20
Check: 13/20 is less than 1 (less than the total in a litre). Reasonable for daily milk intake.
Answer: Ria drinks 13/20 litre of milk in a day.
Example 2: Example 2: Subtraction of Fractions
Problem: Kavi had 5/6 kg of sugar. He used 1/3 kg for making sweets. How much sugar is left?
Solution:
Identify: "How much is left" → Subtraction.
Step 1: Remaining = 5/6 − 1/3. LCM of 6 and 3 = 6.
Step 2: Convert: 1/3 = 2/6
Step 3: Subtract: 5/6 − 2/6 = 3/6 = 1/2
Check: 1/3 + 1/2 = 2/6 + 3/6 = 5/6. Correct!
Answer: 1/2 kg of sugar is left.
Example 3: Example 3: Fraction of a Number (Multiplication with Money)
Problem: Aditi earns Rs.1200 per month from tutoring. She saves 3/8 of her earnings. How much does she save each month?
Solution:
Identify: "3/8 of" → Multiplication.
Step 1: Savings = 3/8 of 1200 = (1200 ÷ 8) × 3
Step 2: 1200 ÷ 8 = 150
Step 3: 150 × 3 = 450
Check: 450 is less than 1200 (since 3/8 < 1). Rs.450 out of Rs.1200 is reasonable savings.
Answer: Aditi saves Rs.450 each month.
Example 4: Example 4: Division (Sharing Equally)
Problem: Rahul has 3/4 kg of paneer. He divides it equally among 3 friends. How much does each friend get?
Solution:
Identify: "Divides equally among" → Division.
Step 1: Each share = 3/4 ÷ 3 = 3/4 × 1/3
Step 2: Cancel: 3 and 3 = 1. Result = 1/4
Check: 3 friends × 1/4 kg = 3/4 kg. Correct!
Answer: Each friend gets 1/4 kg of paneer.
Example 5: Example 5: Multi-step Problem (Money)
Problem: Meera had Rs.600. She spent 1/3 on books and 1/4 on a school bag. How much money is left?
Solution:
Identify: "How much is left" after two expenditures → Multiplication + Subtraction.
Step 1: Spent on books = 1/3 of 600 = 200
Step 2: Spent on bag = 1/4 of 600 = 150
Step 3: Total spent = 200 + 150 = Rs.350
Step 4: Money left = 600 − 350 = Rs.250
Alternative using fractions: Total fraction spent = 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Fraction left = 5/12. Money left = 5/12 × 600 = (600 ÷ 12) × 5 = 50 × 5 = Rs.250.
Answer: Meera has Rs.250 left.
Example 6: Example 6: Comparing Fractions in Context
Problem: Dev reads 3/7 of a book on Monday and 2/5 of the same book on Tuesday. On which day did he read more?
Solution:
Identify: "Which day more" → Compare fractions.
Step 1: Compare 3/7 and 2/5. LCM of 7 and 5 = 35.
Step 2: 3/7 = 15/35, 2/5 = 14/35
Step 3: 15/35 > 14/35, so 3/7 > 2/5.
Also: Total read = 15/35 + 14/35 = 29/35. Remaining = 6/35 of the book.
Answer: Dev read more on Monday (3/7 > 2/5).
Example 7: Example 7: Repeated Groups (Multiplication)
Problem: A recipe needs 2/3 cup of oil. Neha wants to make 6 batches of the recipe for a school fair. How much oil does she need in total?
Solution:
Identify: "6 batches, each needing 2/3 cup" → Multiplication.
Step 1: Total oil = 6 × 2/3
Step 2: Cancel: 6 and 3 share factor 3. 6 ÷ 3 = 2.
Step 3: 2 × 2/1 = 4
Check: 6 × 2/3 = 12/3 = 4 cups. Correct!
Answer: Neha needs 4 cups of oil.
Example 8: Example 8: Finding the Whole from a Part
Problem: 4/9 of the students in a class are girls, and there are 16 girls. How many students are in the class?
Solution:
Identify: "4/9 of total = 16" → Find the whole.
Step 1: 4/9 of total = 16
Step 2: 1/9 of total = 16 ÷ 4 = 4
Step 3: Total students = 4 × 9 = 36
Verification: 4/9 of 36 = (36 ÷ 9) × 4 = 4 × 4 = 16 girls. Correct!
Answer: There are 36 students in the class.
Example 9: Example 9: Fraction of Remaining (Two-step)
Problem: Aman has 40 mangoes. He gives 1/4 to his neighbour. Then he gives 1/2 of the remaining mangoes to his cousin. How many mangoes does Aman have left?
Solution:
Step 1: Given to neighbour = 1/4 of 40 = 40 ÷ 4 = 10 mangoes
Step 2: Remaining after neighbour = 40 − 10 = 30 mangoes
Step 3: Given to cousin = 1/2 of 30 (NOT 1/2 of 40!) = 30 ÷ 2 = 15 mangoes
Step 4: Left with Aman = 30 − 15 = 15 mangoes
Common mistake: Taking 1/2 of the original 40 instead of the remaining 30. Read carefully: "1/2 of the remaining", not "1/2 of the total".
Answer: Aman has 15 mangoes left.
Example 10: Example 10: Division Word Problem (Cutting)
Problem: Priya has a ribbon 9/10 metre long. She cuts it into equal pieces of 3/20 metre each for craft work. How many pieces does she get?
Solution:
Identify: "Cut into equal pieces" → Division.
Step 1: Number of pieces = 9/10 ÷ 3/20
Step 2: KCF: 9/10 × 20/3
Step 3: Cancel: 9 and 3 share factor 3 (gives 3/1). 20 and 10 share factor 10 (gives 2/1).
Step 4: 3/1 × 2/1 = 6
Check: 6 × 3/20 = 18/20 = 9/10. Correct!
Answer: Priya gets 6 pieces.
Real-World Applications
Where do fraction word problems appear in daily life?
- Cooking: Scaling recipes up or down by multiplying ingredient quantities by a fraction. "Make half the recipe" means multiply each ingredient by 1/2.
- Money and budgets: Calculating how much to save, spend on different categories, or how much remains after expenses.
- Time management: If homework takes 3/4 hour and you have 3 subjects, total time = 3 × 3/4 = 2 1/4 hours.
- Measurement and construction: Cutting fabric, rope, or wood into fractional lengths for projects.
- Sports and statistics: Comparing scores, calculating averages, and finding what fraction of matches were won.
- Shopping: Finding discounts ("1/3 off"), comparing prices, and calculating total cost of items sold by fractional weight.
Key Points to Remember
- Read the problem carefully to identify the correct operation (add, subtract, multiply, or divide).
- "Of" means multiply. "Shared equally" or "divided into" means divide. "Total" or "altogether" means add. "Remaining" or "left" means subtract.
- For unlike fractions, find the LCM of denominators before adding or subtracting.
- For multi-step problems, solve one step at a time. Write down intermediate answers.
- "Fraction of remaining" is different from "fraction of total". Read carefully which quantity the fraction applies to.
- Always simplify answers and convert improper fractions to mixed numbers.
- Check your answer: Does it make sense? Is it less than the total (for proper fractions)? Does it satisfy the original conditions?
- To find the whole from a part: if p/q of x = N, then x = (N ÷ p) × q.
Practice Problems
- Arjun walks 3/8 km to school and 1/4 km to the library after school. What is the total distance he walks?
- A water tank is 7/10 full. After using some water, it is 2/5 full. What fraction of the tank was used?
- Ria has Rs.800. She spends 3/8 on books and 1/4 on stationery. How much money is left?
- A baker has 5/6 kg of flour. Each cake needs 1/12 kg of flour. How many cakes can he bake?
- 3/5 of the children in a park are boys. There are 24 boys. How many children are there in total?
- Dev has 48 marbles. He gives 1/6 to Aman and 1/4 to Kavi. How many marbles are left with Dev?
- Neha reads 2/7 of a book on Saturday and 3/7 on Sunday. What fraction of the book is left to read?
- A ribbon is 2 1/2 metres long. Priya cuts pieces of 5/8 metre each. How many full pieces can she cut?
Frequently Asked Questions
Q1. How do I know which operation to use in a fraction word problem?
Look for keywords: 'total/altogether' means add, 'remaining/left' means subtract, 'of/each/times' means multiply, 'shared equally/divided into' means divide. Practice with many problems builds this instinct.
Q2. What is the most common mistake in fraction word problems?
Taking a fraction of the wrong quantity. In multi-step problems, pay close attention to whether the fraction applies to the original total or to the remaining amount after a previous step.
Q3. How do I solve a multi-step fraction word problem?
Break it into smaller steps. Solve each step separately, write down intermediate results, and use the result of one step as the starting point for the next. Never try to do everything at once.
Q4. What if the fractions in the problem have different denominators?
For addition and subtraction, find the LCM of the denominators and convert to equivalent fractions with the same denominator. For multiplication and division, you can work directly without finding the LCM.
Q5. How do I find the whole number when a fraction of it is given?
If p/q of a number is N, then: 1/q of the number = N ÷ p, and the whole number = (N ÷ p) × q. For example, if 2/5 of a number is 20, the number = (20 ÷ 2) × 5 = 50.
Q6. Should I always simplify the answer in word problems?
Yes. Always express fractions in lowest terms. Convert improper fractions to mixed numbers when the answer represents a physical quantity (kg, litres, metres, rupees) to make it meaningful.
Q7. How do I check if my answer is correct?
Substitute your answer back into the problem. For example, if the problem says 5/6 − 1/3 and you got 1/2, verify: 5/6 − 2/6 = 3/6 = 1/2. Also check: does the answer make sense in the real-life context?
Q8. Can a word problem involve more than one operation?
Yes. Many Class 5 problems are multi-step, combining addition with subtraction, or multiplication with subtraction. The key is to identify and solve each operation in the correct order.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Fraction word problems are a major part of the NCERT/CBSE Class 5 Maths curriculum. They carry higher marks in exams because they test understanding, not just calculation.
Related Topics
- Adding Unlike Fractions
- Multiplying Fractions
- Fractions Revision (Grade 5)
- Subtracting Unlike Fractions
- Adding Mixed Numbers
- Subtracting Mixed Numbers
- Multiplying a Fraction by a Whole Number
- Fraction of a Number
- Reciprocal of a Fraction
- Dividing Fractions
- Proper, Improper and Mixed Fractions
- Comparing and Ordering Fractions (Grade 5)
