Fraction of a Number
Fraction of a number means finding a part of a given quantity. When we say "1/3 of 24", we are dividing 24 into 3 equal groups and taking 1 group. This gives us 8.
In daily life, we use this concept constantly: eating half a pizza, spending one-fourth of our pocket money, filling two-thirds of a water bottle, or using three-eighths of a ribbon. Every time you hear the word "of" with a fraction, you are finding a fraction of a number.
In Class 5, you will learn to calculate fractions of whole numbers using a simple multiplication method, handle multi-step problems where you find the remaining part, and even reverse the process to find the whole number when a fraction is given. This concept connects directly to percentages, ratios, and algebra in higher classes.
What is Fraction of a Number - Class 5 Maths (Fractions)?
Fraction of a number means multiplying the fraction by that number.
The word "of" in mathematics means multiplication (×).
p/q of n = (p × n) / q
For example: 3/4 of 20 = (3 × 20) / 4 = 60/4 = 15.
This works because finding 3/4 of 20 means dividing 20 into 4 equal parts (each part = 5) and taking 3 parts (3 × 5 = 15).
Fraction of a Number Formula
Fraction of a Number = (Numerator × Number) ÷ Denominator
Two methods to calculate:
Method 1 (Divide first): If the number is exactly divisible by the denominator, divide first, then multiply.
- Divide the number by the denominator of the fraction.
- Multiply the result by the numerator.
Example: 3/5 of 45 = (45 ÷ 5) × 3 = 9 × 3 = 27.
Method 2 (Multiply first): If the number is NOT exactly divisible by the denominator, multiply first, then divide.
- Multiply the number by the numerator.
- Divide the result by the denominator.
Example: 2/3 of 10 = (2 × 10) / 3 = 20/3 = 6 2/3.
Tip: Method 1 keeps numbers small and is preferred when possible.
Types and Properties
Different situations where you find a fraction of a number:
- Unit fraction of a number: When the numerator is 1, just divide. Example: 1/5 of 35 = 35 ÷ 5 = 7.
- Non-unit fraction of a number: Divide first, then multiply. Example: 3/7 of 42 = (42 ÷ 7) × 3 = 6 × 3 = 18.
- Fraction of money: Commonly used for budgets and discounts. Example: 2/5 of Rs.500 = (500 ÷ 5) × 2 = Rs.200.
- Fraction of a collection: Finding how many items from a group. Example: 3/8 of 40 marbles = (40 ÷ 8) × 3 = 15 marbles.
- Fraction of measurement: Converting parts of length, weight, or volume. Example: 1/4 of 2 km = 2000 m ÷ 4 = 500 m.
- Finding the remaining part: If you know the fraction used, the remaining = Total − Part used.
- Finding the whole from a part: If p/q of a number = N, then the number = (N ÷ p) × q.
Solved Examples
Example 1: Example 1: Unit Fraction of a Number
Problem: Find 1/6 of 54.
Solution:
Step 1: Since the numerator is 1, simply divide the number by the denominator.
Step 2: 1/6 of 54 = 54 ÷ 6 = 9
Check: 9 × 6 = 54. Correct!
Answer: 1/6 of 54 = 9
Example 2: Example 2: Non-unit Fraction
Problem: Find 3/5 of 45.
Solution:
Step 1: Check: Is 45 divisible by 5? Yes. So divide first: 45 ÷ 5 = 9
Step 2: Multiply by the numerator: 9 × 3 = 27
Meaning: Divide 45 into 5 equal groups of 9 each. Take 3 groups = 27.
Answer: 3/5 of 45 = 27
Example 3: Example 3: Fraction of Money
Problem: Aditi has Rs.360. She spends 2/9 of it on books. How much does she spend on books?
Solution:
Step 1: Calculate 2/9 of 360. Is 360 divisible by 9? Yes. 360 ÷ 9 = 40.
Step 2: Multiply by numerator: 40 × 2 = 80
Interpretation: Aditi spends Rs.80 on books out of her Rs.360.
Answer: Aditi spends Rs.80 on books.
Example 4: Example 4: Fraction of a Collection
Problem: There are 56 mangoes in a basket. Rahul takes 3/8 of them. How many mangoes does he take?
Solution:
Step 1: Calculate 3/8 of 56. 56 ÷ 8 = 7.
Step 2: 7 × 3 = 21
Check: 21 is less than 56 (since 3/8 is less than 1). Makes sense!
Answer: Rahul takes 21 mangoes.
Example 5: Example 5: Finding the Remaining Part
Problem: A school has 240 students. 5/12 of them are girls. How many boys are there?
Solution:
Step 1: Find number of girls = 5/12 of 240 = (240 ÷ 12) × 5 = 20 × 5 = 100
Step 2: Number of boys = Total − Girls = 240 − 100 = 140
Alternative: Boys = (1 − 5/12) of 240 = 7/12 of 240 = (240 ÷ 12) × 7 = 20 × 7 = 140. Same answer!
Answer: There are 140 boys.
Example 6: Example 6: Fraction of Weight
Problem: A bag of rice weighs 30 kg. Meera uses 2/5 of it for cooking. How much rice is left?
Solution:
Step 1: Rice used = 2/5 of 30 = (30 ÷ 5) × 2 = 6 × 2 = 12 kg
Step 2: Rice left = 30 − 12 = 18 kg
Check: 12 + 18 = 30. Correct!
Answer: 18 kg of rice is left.
Example 7: Example 7: Fraction of Distance
Problem: Kavi cycles 4/7 of a 21 km trail before stopping for water. How far has he cycled?
Solution:
Step 1: Calculate 4/7 of 21. 21 ÷ 7 = 3.
Step 2: 3 × 4 = 12
Remaining distance: 21 − 12 = 9 km still to go.
Answer: Kavi has cycled 12 km.
Example 8: Example 8: Fraction of Time
Problem: A cricket match lasts 480 minutes. Rain stops play for 1/8 of the total time. How many minutes is the rain delay?
Solution:
Step 1: Rain delay = 1/8 of 480 = 480 ÷ 8 = 60 minutes
Step 2: 60 minutes = 1 hour.
Playing time: 480 − 60 = 420 minutes = 7 hours of actual play.
Answer: The rain delay is 60 minutes (1 hour).
Example 9: Example 9: Two-step Problem
Problem: Dev has Rs.600. He gives 1/3 to his sister and 1/4 to his brother. How much money does he have left?
Solution:
Step 1: Amount given to sister = 1/3 of 600 = 600 ÷ 3 = Rs.200
Step 2: Amount given to brother = 1/4 of 600 = 600 ÷ 4 = Rs.150
Step 3: Total given away = 200 + 150 = Rs.350
Step 4: Money left = 600 − 350 = Rs.250
Alternative using fractions: Fraction given = 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Fraction left = 1 − 7/12 = 5/12. Money left = 5/12 of 600 = (600 ÷ 12) × 5 = 50 × 5 = Rs.250.
Answer: Dev has Rs.250 left.
Example 10: Example 10: Finding the Whole from a Fraction
Problem: 3/5 of a number is 27. Find the number.
Solution:
Step 1: If 3/5 of the number = 27, then 3 parts out of 5 equal parts = 27.
Step 2: Value of 1 part = 27 ÷ 3 = 9
Step 3: The whole number = 5 parts = 9 × 5 = 45
Verification: 3/5 of 45 = (45 ÷ 5) × 3 = 9 × 3 = 27. Correct!
Answer: The number is 45.
Real-World Applications
Where do we use fraction of a number in daily life?
- Shopping discounts: "1/4 off" on a Rs.800 item means the discount is 1/4 of 800 = Rs.200. You pay Rs.600.
- Cooking and recipes: Using 2/3 of a 750 ml bottle of oil means you use 500 ml.
- School attendance: If 3/10 of 40 students are absent, then 12 students are absent and 28 are present.
- Sports statistics: A cricket team scored 2/5 of its total runs (say 200) in the powerplay, meaning 80 runs came in the first 6 overs.
- Travel planning: Completing 5/8 of a 160 km journey means you have covered 100 km, with 60 km remaining.
- Savings and budgets: If you save 1/5 of your Rs.1000 pocket money each month, you save Rs.200 per month.
Key Points to Remember
- The word "of" in fractions always means multiplication.
- Formula: p/q of n = (p × n) ÷ q.
- Quick method: Divide the number by the denominator first (if exactly divisible), then multiply by the numerator. This keeps numbers small.
- To find the remaining part, subtract the fraction found from the total. Or find (1 − fraction) of the total.
- To find the whole when a fraction of it is known: divide by the numerator and multiply by the denominator.
- Unit fractions (numerator = 1) need only one division step: 1/n of x = x ÷ n.
- Always check: the answer must be less than the original number when the fraction is proper (less than 1).
- This concept is the foundation for percentages: finding 25% of a number is the same as finding 1/4 of it.
Practice Problems
- Find 4/9 of 72.
- What is 5/6 of 180?
- Ria has 150 stickers. She gives 2/5 of them to her friend. How many stickers does she give away?
- A farmer has 84 cows. 3/7 of them are brown. How many cows are NOT brown?
- Find 7/10 of Rs.500.
- Arjun reads 5/8 of a 200-page book. How many pages are left to read?
- 3/4 of a number is 36. What is the number?
- A rope is 56 metres long. Priya cuts off 3/8 of it. How long is the remaining piece?
Frequently Asked Questions
Q1. What does 'fraction of a number' mean?
It means finding a part of a given number using multiplication. For example, 2/3 of 15 means dividing 15 into 3 equal parts (5 each) and taking 2 parts, which gives 10.
Q2. Why does 'of' mean multiplication in fractions?
In mathematics, 'of' indicates multiplication. Saying '3/4 of 20' is the same as writing 3/4 × 20. This is a standard mathematical convention used in NCERT textbooks and across all branches of maths.
Q3. Should I multiply first or divide first?
If the number is exactly divisible by the denominator, divide first to get smaller numbers. For example, for 3/8 of 64: divide 64 ÷ 8 = 8, then multiply 8 × 3 = 24. If not exactly divisible, multiply the numerator by the number first.
Q4. Can the answer be bigger than the original number?
No, not when the fraction is a proper fraction (less than 1). The answer is always smaller than the original number. Only improper fractions (greater than 1) give a result larger than the original.
Q5. How do I find the whole number if I know a fraction of it?
Divide the given value by the numerator, then multiply by the denominator. For example, if 2/5 of a number is 18, the number = (18 ÷ 2) × 5 = 9 × 5 = 45.
Q6. What if the number is not divisible by the denominator?
Multiply the numerator by the number first, then divide by the denominator. The answer may be a fraction or decimal. For example, 2/3 of 10 = (2 × 10)/3 = 20/3 = 6 2/3.
Q7. Is finding 1/2 of a number the same as dividing by 2?
Yes, exactly. Finding 1/2 of any number means dividing by 2. Similarly, 1/4 of a number = dividing by 4, 1/10 of a number = dividing by 10. This is because the unit fraction 1/n of x always equals x ÷ n.
Q8. How is this different from multiplying a fraction by a whole number?
They are the same operation written differently. '3/5 of 20' and '3/5 × 20' both equal 12. The word 'of' is just another way to express multiplication.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Finding a fraction of a number is a key topic in the NCERT/CBSE Class 5 Maths curriculum under the Fractions chapter. It appears in school exams and standardised tests, and forms the basis for percentage calculations.
Related Topics
- Multiplying a Fraction by a Whole Number
- Fraction Word Problems (Grade 5)
- Fractions Revision (Grade 5)
- Adding Unlike Fractions
- Subtracting Unlike Fractions
- Adding Mixed Numbers
- Subtracting Mixed Numbers
- Multiplying Fractions
- Reciprocal of a Fraction
- Dividing Fractions
- Proper, Improper and Mixed Fractions
- Comparing and Ordering Fractions (Grade 5)
