Converting Percentage to Fraction
A percentage is a number expressed as a fraction of 100. The word 'percent' comes from the Latin 'per centum', meaning 'out of hundred'. Converting a percentage to a fraction is straightforward: write the percentage number over 100 and simplify.
For example, 25% means 25 out of 100, which equals 25/100 = 1/4. This conversion is essential for solving problems involving discounts, marks, and data analysis.
What is Converting Percentage to Fraction - Class 5 Maths (Percentage)?
To convert a percentage to a fraction:
- Write the percentage number as the numerator with 100 as the denominator.
- Simplify the fraction to its lowest terms by dividing by the HCF.
x% = x/100
Converting Percentage to Fraction Formula
Percentage to Fraction: x% = x/100 (then simplify)
Common conversions:
| Percentage | Fraction |
|---|---|
| 50% | 1/2 |
| 25% | 1/4 |
| 75% | 3/4 |
| 20% | 1/5 |
| 10% | 1/10 |
| 33 1/3% | 1/3 |
Solved Examples
Example 1: Example 1: Convert 50% to a fraction
Problem: Convert 50% to a fraction.
Solution:
50% = 50/100 = 1/2 (divide by HCF 50)
Answer: 50% = 1/2
Example 2: Example 2: Convert 75% to a fraction
Problem: Convert 75% to a fraction.
Solution:
75% = 75/100 = 3/4 (divide by HCF 25)
Answer: 75% = 3/4
Example 3: Example 3: Convert 40% to a fraction
Problem: Convert 40% to a fraction.
Solution:
40% = 40/100 = 2/5 (divide by HCF 20)
Answer: 40% = 2/5
Example 4: Example 4: Convert 12.5% to a fraction
Problem: Convert 12.5% to a fraction.
Solution:
Step 1: 12.5% = 12.5/100
Step 2: Multiply numerator and denominator by 2 to remove the decimal: 25/200
Step 3: Simplify: 25/200 = 1/8
Answer: 12.5% = 1/8
Example 5: Example 5: Convert 5% to a fraction
Problem: Convert 5% to a fraction.
Solution:
5% = 5/100 = 1/20
Answer: 5% = 1/20
Example 6: Example 6: Convert 125% to a fraction
Problem: Convert 125% to a fraction.
Solution:
125% = 125/100 = 5/4 = 1 1/4
Answer: 125% = 5/4 = 1 1/4
Example 7: Example 7: Word problem — Test score
Problem: Ria scored 80% in her maths test. Express her score as a fraction.
Solution:
80% = 80/100 = 4/5
Answer: Ria scored 4/5 of the total marks.
Example 8: Example 8: Word problem — Discount
Problem: A shop offers a 30% discount on a bag priced at ₹500. What fraction of the price is the discount?
Solution:
30% = 30/100 = 3/10
Answer: The discount is 3/10 of the price.
Example 9: Example 9: Convert 66 2/3% to a fraction
Problem: Convert 66 2/3% to a fraction.
Solution:
Step 1: 66 2/3 = 200/3
Step 2: 200/3 ÷ 100 = 200/300 = 2/3
Answer: 66 2/3% = 2/3
Key Points to Remember
- To convert percentage to fraction: divide by 100 (write as x/100) and simplify.
- Memorise common conversions: 50% = 1/2, 25% = 1/4, 75% = 3/4, 20% = 1/5, 10% = 1/10.
- For percentages with decimals, multiply numerator and denominator by 10 (or 100) to remove the decimal, then simplify.
- Percentages greater than 100% give improper fractions (e.g., 150% = 3/2).
- 0% = 0 and 100% = 1 (the whole).
Practice Problems
- Convert 60% to a fraction in simplest form.
- Convert 15% to a fraction.
- Convert 37.5% to a fraction.
- Convert 200% to a fraction and mixed number.
- Dev scored 85% in Science. Express as a fraction.
- A tank is 45% full. What fraction of the tank is full?
- Convert 8% to a fraction.
- Convert 33 1/3% to a fraction.
Frequently Asked Questions
Q1. How do I convert a percentage to a fraction?
Write the percentage number over 100 and simplify. For example, 40% = 40/100 = 2/5.
Q2. What if the percentage has a decimal, like 12.5%?
Write 12.5/100, then multiply both by 2 (or 10) to clear the decimal: 25/200 = 1/8. The goal is to get whole numbers in the fraction.
Q3. Can a percentage be greater than 100%?
Yes. 150% means 150/100 = 3/2 = 1 1/2. A percentage greater than 100% means more than the whole. For example, if prices increased by 150%, the new price is 1.5 times the original.
Q4. What is 100% as a fraction?
100% = 100/100 = 1. It represents the whole or the complete amount.
Q5. Why should I memorise common percentage-fraction conversions?
Memorising common conversions (25% = 1/4, 50% = 1/2, etc.) speeds up mental calculations in exams and daily life. It helps quickly estimate discounts, tips, and test scores.
Q6. How is this different from converting fraction to percentage?
Converting fraction to percentage is the reverse: multiply the fraction by 100. For example, 3/4 × 100 = 75%. Percentage to fraction divides by 100.
Q7. What percentage equals 1/3?
1/3 × 100 = 33.33...% or 33 1/3%. This is a repeating decimal, which is why the fraction form (1/3) is more precise.
Q8. Is this topic in the NCERT Class 5 syllabus?
Yes. Converting between percentages and fractions is part of the Percentage chapter in NCERT Class 5 Maths.
