Converting Percentage to Fraction
A percentage means “per hundred.” Converting a percentage to a fraction is straightforward: divide by 100 and simplify. For example, 45% = 45/100 = 9/20.
This conversion is useful when you need to perform calculations with fractions instead of percentages.
What is Converting Percentage to Fraction - Grade 7 Maths (Comparing Quantities)?
Rule:
x% = x/100 (simplify if possible)
Converting Percentage to Fraction Formula
Steps to convert % to fraction:
- Write the percentage as a fraction with denominator 100.
- Find the HCF of numerator and denominator.
- Simplify by dividing both by the HCF.
Types and Properties
Common percentages as fractions:
- 10% = 1/10
- 20% = 1/5
- 25% = 1/4
- 30% = 3/10
- 33⅓% = 1/3
- 40% = 2/5
- 50% = 1/2
- 60% = 3/5
- 75% = 3/4
- 80% = 4/5
- 100% = 1
Solved Examples
Example 1: Simple Conversion
Problem: Convert 45% to a fraction.
Solution:
- 45% = 45/100
- HCF of 45 and 100 = 5
- 45/100 = 9/20
Answer: 9/20.
Example 2: Percentage Greater Than 100
Problem: Convert 125% to a fraction.
Solution:
- 125% = 125/100 = 5/4 (or 1¼)
Answer: 5/4.
Example 3: Decimal Percentage
Problem: Convert 12.5% to a fraction.
Solution:
- 12.5% = 12.5/100 = 125/1000 = 1/8
Answer: 1/8.
Example 4: Small Percentage
Problem: Convert 2% to a fraction.
Solution:
- 2% = 2/100 = 1/50
Answer: 1/50.
Real-World Applications
Real-world uses:
- Recipes: “Use 25% of the flour” = use 1/4 of it.
- Exams: “80% marks” = 4/5 of total marks.
- Discounts: Understanding “20% off” as “1/5 off” for mental math.
Key Points to Remember
- x% = x/100 — always simplify to lowest terms.
- If the percentage has a decimal, multiply both numerator and denominator by 10 (or 100) to remove it first.
- Percentages > 100% give improper fractions (> 1).
- Memorise common % ↔ fraction equivalents for speed.
Practice Problems
- Convert 65% to a fraction.
- Convert 37.5% to a fraction.
- Convert 150% to a fraction.
- Convert 5% to a fraction.
Frequently Asked Questions
Q1. How do you convert percentage to fraction?
Write the percentage over 100 and simplify. For example, 40% = 40/100 = 2/5.
Q2. What if the percentage has a decimal?
First remove the decimal by multiplying numerator and denominator by 10. For example, 7.5% = 7.5/100 = 75/1000 = 3/40.
Q3. Can percentages over 100 be converted to fractions?
Yes. They become improper fractions. For example, 200% = 200/100 = 2/1 = 2.
Related Topics
- Introduction to Percentage
- Converting Between %, Fraction and Decimal
- Equivalent Fractions
- Simplest Form of a Fraction
- Percentage Increase and Decrease
- Profit and Loss
- Discount Calculation
- Simple Interest
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Word Problems on Comparing Quantities
