Fraction Word Problems (Grade 3)
Fraction word problems use real-life situations where things are divided into equal parts. In Class 3, these problems involve finding a fraction of a number, adding or subtracting like fractions, and comparing fractions.
These problems combine your knowledge of fractions with reading comprehension. You need to understand what the problem is asking, identify the fraction, and calculate the answer.
What is Fraction Word Problems - Class 3 Maths (Fractions (Grade 3))?
A fraction word problem is a story-based maths question that involves fractions.
Common types in Class 3:
- Finding a fraction of a number: 1/4 of 20 = 20 ÷ 4 = 5
- Adding like fractions in context: Ria ate 2/8 and Aman ate 3/8 of a pizza
- Subtracting like fractions: 5/6 of a cake is left after eating 1/6
- Comparing fractions: Who ate more?
Fraction of a number = Number ÷ Denominator × Numerator
Solved Examples
Example 1: Example 1: Finding a Fraction of a Number
Question: Ria has 24 crayons. She gives 1/4 of them to her friend. How many crayons does she give?
Think:
- 1/4 of 24 = 24 ÷ 4 = 6
Answer: Ria gives 6 crayons.
Example 2: Example 2: Adding Fractions in Context
Question: Dev eats 2/6 of a cake. Priya eats 3/6 of the same cake. What fraction did they eat together?
Think:
- Same denominator → add numerators
- 2/6 + 3/6 = 5/6
Answer: They ate 5/6 of the cake.
Example 3: Example 3: Subtracting Fractions
Question: A tank is 7/8 full. Aman uses 3/8 of the water. What fraction is left?
Think:
- 7/8 − 3/8 = 4/8
Answer: 4/8 (or 1/2) of the water is left.
Example 4: Example 4: Comparing Fractions
Question: Aditi reads 3/5 of a book. Meera reads 2/5 of the same book. Who has read more?
Think:
- Same denominator → compare numerators
- 3 > 2, so 3/5 > 2/5
Answer: Aditi has read more.
Example 5: Example 5: Fraction of a Collection
Question: There are 30 students in a class. 1/3 of them wear spectacles. How many students wear spectacles?
Think:
- 1/3 of 30 = 30 ÷ 3 = 10
Answer: 10 students wear spectacles.
Example 6: Example 6: Finding Remaining Fraction
Question: Rahul spends 2/5 of his pocket money. What fraction does he save?
Think:
- Whole = 5/5
- Saved = 5/5 − 2/5 = 3/5
Answer: Rahul saves 3/5 of his pocket money.
Example 7: Example 7: Multi-Part Fraction
Question: Kavi has 40 marbles. 1/4 are red, 1/2 are blue, and the rest are green. How many green marbles does he have?
Think:
- Red = 1/4 of 40 = 10
- Blue = 1/2 of 40 = 20
- Green = 40 − 10 − 20 = 10
Answer: Kavi has 10 green marbles.
Example 8: Example 8: Fraction of Money
Question: Neha has ₹60. She spends 1/3 on a book. How much does she spend?
Think:
- 1/3 of 60 = 60 ÷ 3 = ₹20
Answer: Neha spends ₹20.
Example 9: Example 9: Two Children Sharing
Question: A chocolate bar is divided into 10 equal pieces. Ria takes 3 pieces and Arjun takes 4 pieces. What fraction is left?
Think:
- Taken: 3/10 + 4/10 = 7/10
- Left: 10/10 − 7/10 = 3/10
Answer: 3/10 of the chocolate is left.
Example 10: Example 10: Finding the Whole
Question: 1/5 of a number is 8. What is the number?
Think:
- 1/5 of number = 8
- Number = 8 × 5 = 40
Answer: The number is 40.
Real-World Applications
Where Do We Use Fraction Word Problems?
- Sharing food: Dividing pizza, cake, or fruit among people.
- Money: Spending a fraction of savings or pocket money.
- Time: A quarter of an hour = 15 minutes, half an hour = 30 minutes.
- School: Finding what fraction of students passed, or what fraction of a book is read.
- Recipes: Using 1/2 cup of sugar or 1/4 kg of flour.
Key Points to Remember
- Fraction of a number = number ÷ denominator × numerator.
- For 1/n of a number, simply divide by n.
- Add like fractions by adding numerators (keep denominator same).
- Subtract like fractions by subtracting numerators.
- To find the remaining fraction: whole − used fraction.
- To find the whole from a fraction: given value × denominator ÷ numerator.
- Always check: does the answer make sense? (A fraction of 24 cannot be more than 24.)
Practice Problems
- Find 1/3 of 27.
- Ria eats 3/8 of a pizza. What fraction is left?
- There are 36 chocolates. 1/6 are dark chocolate. How many dark chocolates are there?
- Dev reads 4/7 of a story and Priya reads 2/7. How much did they read together?
- A bottle is 5/6 full. Aditi drinks 2/6. What fraction is left?
- 1/4 of a number is 9. What is the number?
- Meera has 50 beads. 2/5 are red and 1/5 are blue. How many beads are neither red nor blue?
Frequently Asked Questions
Q1. How do I find a fraction of a number?
Divide the number by the denominator (bottom number) and multiply by the numerator (top number). For example, 2/3 of 15 = 15 ÷ 3 × 2 = 10.
Q2. How do I find what fraction is left?
Subtract the used fraction from the whole (1). Write 1 as a fraction with the same denominator. For example, if 3/5 is used, left = 5/5 − 3/5 = 2/5.
Q3. Can I add fractions in word problems?
Yes, if the fractions have the same denominator. Add the numerators and keep the denominator. For example, 2/8 + 3/8 = 5/8.
Q4. How do I find the whole number when given a fraction?
If 1/n of a number is x, the whole number is x × n. For example, if 1/4 of a number is 7, the number is 7 × 4 = 28.
Q5. What if the problem has fractions with different denominators?
In Class 3, most problems use like fractions (same denominator). If denominators are different, you would need to find a common denominator, which is taught in higher classes.
Q6. How do I compare fractions in a word problem?
If the denominators are the same, compare the numerators. The fraction with the larger numerator is greater. For example, 5/8 > 3/8.
Q7. What clue words indicate fraction problems?
Look for words like 'half of', 'one-third of', 'quarter of', 'shared equally', 'fraction left', 'part of' — these all suggest fraction operations.
Q8. Can fractions be used with money?
Yes. For example, 1/2 of ₹100 = ₹50, and 3/4 of ₹80 = ₹60. Fractions are useful for calculating discounts, shares, and portions.
Q9. Should I simplify my answer?
In Class 3, simplifying is encouraged when possible. For example, 4/8 can be written as 1/2. But it is not always required.
