Converting Fractions to Percentage
Converting fractions to percentage means expressing a fraction as a number out of 100 with the % symbol. For example, 3/4 = 75% and 2/5 = 40%.
This skill connects two important mathematical concepts — fractions and percentage. In real life, you convert fractions to percentages to understand exam scores, sports statistics, survey results, and much more.
If Ria answered 18 out of 25 questions correctly, her fraction is 18/25. But saying "she scored 72%" is much easier to understand and compare with other scores.
There are two main methods to convert a fraction to a percentage: the equivalent fraction method (make the denominator 100) and the multiplication method (multiply by 100). Both give the same answer — choose whichever is easier for the given fraction.
What is Converting Fractions to Percentage - Class 5 Maths (Percentage)?
A fraction shows a part of a whole (e.g., 3/5 means 3 parts out of 5 equal parts). A percentage shows a part out of 100 (e.g., 60% means 60 parts out of 100).
Converting a fraction to a percentage answers the question: "If the whole were divided into 100 equal parts, how many parts would this fraction represent?"
Fraction to Percentage: Multiply the fraction by 100 and add %
Converting Fractions to Percentage Formula
Percentage = (Numerator ÷ Denominator) × 100%
Method 1: Multiply by 100
- Divide the numerator by the denominator (or keep as a fraction).
- Multiply the result by 100.
- Add the % symbol.
Example: 3/5 → 3 ÷ 5 = 0.6 → 0.6 × 100 = 60%
Or: 3/5 × 100 = 300/5 = 60%
Method 2: Equivalent fraction with denominator 100
- Ask: what number multiplied by the denominator gives 100?
- Multiply both numerator and denominator by that number.
- The new numerator is the percentage.
Example: 3/5 = (3 × 20)/(5 × 20) = 60/100 = 60%
Which denominators work easily with Method 2?
| Denominator | × What = 100 | Example |
|---|---|---|
| 2 | × 50 | 1/2 = 50/100 = 50% |
| 4 | × 25 | 3/4 = 75/100 = 75% |
| 5 | × 20 | 4/5 = 80/100 = 80% |
| 10 | × 10 | 7/10 = 70/100 = 70% |
| 20 | × 5 | 9/20 = 45/100 = 45% |
| 25 | × 4 | 17/25 = 68/100 = 68% |
| 50 | × 2 | 23/50 = 46/100 = 46% |
For other denominators (3, 6, 7, 8, 9, etc.), use Method 1 (divide then multiply by 100).
Types and Properties
Type 1: Fractions with "friendly" denominators (2, 4, 5, 10, 20, 25, 50)
These denominators divide into 100 evenly, so use the equivalent fraction method for quick conversion.
- 3/4 = 75/100 = 75%
- 7/10 = 70/100 = 70%
- 11/20 = 55/100 = 55%
Type 2: Fractions with other denominators (3, 6, 7, 8, 9, etc.)
Use division: divide the numerator by the denominator, then multiply by 100.
- 5/8 → 5 ÷ 8 = 0.625 → 0.625 × 100 = 62.5%
- 1/3 → 1 ÷ 3 = 0.333... → 33.33% (approximately 33 1/3%)
Type 3: Fractions that can be simplified first
Always simplify before converting — it makes the numbers smaller and easier to work with.
- 12/16 → simplify to 3/4 → 75%
- 18/24 → simplify to 3/4 → 75%
Type 4: Mixed numbers to percentage
Convert the mixed number to an improper fraction first, then multiply by 100.
- 1 1/2 = 3/2 → 3/2 × 100 = 150%
- 2 1/4 = 9/4 → 9/4 × 100 = 225%
Note: Mixed numbers always give percentages greater than 100%.
Type 5: Unit fractions
These are fractions with numerator 1. They are useful benchmarks:
- 1/2 = 50%, 1/3 ≈ 33.3%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/10 = 10%
Solved Examples
Example 1: Using Equivalent Fraction — Denominator 4
Problem: Convert 3/4 to a percentage.
Solution:
Step 1: The denominator is 4. What × 4 = 100? Answer: 25.
Step 2: Multiply both numerator and denominator by 25:
3/4 = (3 × 25)/(4 × 25) = 75/100
Step 3: 75/100 = 75%
Answer: 3/4 = 75%
Example 2: Using Equivalent Fraction — Denominator 5
Problem: Convert 2/5 to a percentage.
Solution:
Step 1: The denominator is 5. What × 5 = 100? Answer: 20.
Step 2: 2/5 = (2 × 20)/(5 × 20) = 40/100
Step 3: 40/100 = 40%
Verification: 40% of 5 = (40/100) × 5 = 2 ✓
Answer: 2/5 = 40%
Example 3: Using Division Method — Denominator 8
Problem: Convert 5/8 to a percentage.
Solution:
Step 1: 8 does not divide into 100 evenly (100 ÷ 8 = 12.5, not a whole number). Use the division method.
Step 2: Divide: 5 ÷ 8 = 0.625
Step 3: Multiply by 100: 0.625 × 100 = 62.5
Step 4: Add %: 62.5%
Answer: 5/8 = 62.5%
Example 4: Word Problem — Test Score
Problem: Ria scored 18 out of 25 in a maths test. What is her percentage score?
Solution:
Step 1: Fraction = 18/25. Denominator is 25, which is a friendly number (25 × 4 = 100).
Step 2: 18/25 = (18 × 4)/(25 × 4) = 72/100
Step 3: 72/100 = 72%
Answer: Ria scored 72%.
Example 5: Unit Fraction — 1/2
Problem: Convert 1/2 to a percentage.
Solution:
Step 1: 2 × 50 = 100.
Step 2: 1/2 = (1 × 50)/(2 × 50) = 50/100 = 50%
Real-life meaning: Half of anything is 50%. Half a pizza, half a litre, half the class — all are 50%.
Answer: 1/2 = 50%
Example 6: Simplify First, Then Convert
Problem: A cricket team won 9 out of 12 matches. Express the wins as a percentage.
Solution:
Step 1: Fraction = 9/12. Simplify: HCF of 9 and 12 = 3. So 9/12 = 3/4.
Step 2: Now convert 3/4: 3/4 = 75/100 = 75%.
Why simplify first? Working with 3/4 is much easier than working with 9/12.
Answer: The team won 75% of their matches.
Example 7: Attendance Percentage
Problem: In a class of 40 students, 36 were present on Monday. What percentage of students were present?
Solution:
Step 1: Fraction present = 36/40. Simplify: 36/40 = 9/10.
Step 2: 9/10 × 100 = 900/10 = 90%.
Follow-up: Percentage absent = 100% − 90% = 10%. That means 4 students (10% of 40) were absent.
Answer: 90% of students were present.
Example 8: Mixed Number to Percentage
Problem: Convert 1 1/4 to a percentage.
Solution:
Step 1: Convert to improper fraction: 1 1/4 = (4 + 1)/4 = 5/4.
Step 2: 5/4 × 100 = 500/4 = 125%.
Note: The answer is more than 100% because 1 1/4 is greater than 1 (a whole). This happens when an amount exceeds the original quantity.
Answer: 1 1/4 = 125%
Example 9: Fraction with Denominator 20
Problem: Convert 7/20 to a percentage.
Solution:
Step 1: 20 × 5 = 100. Multiply both by 5.
Step 2: 7/20 = (7 × 5)/(20 × 5) = 35/100 = 35%.
Answer: 7/20 = 35%
Example 10: Common Fractions — Reference Table
Problem: Convert each fraction to a percentage: 1/4, 1/5, 2/5, 3/10, 4/5.
Solution:
| Fraction | Equivalent (/100) | Percentage |
|---|---|---|
| 1/4 | 25/100 | 25% |
| 1/5 | 20/100 | 20% |
| 2/5 | 40/100 | 40% |
| 3/10 | 30/100 | 30% |
| 4/5 | 80/100 | 80% |
Tip: Memorise the percentages for fractions with denominators 2, 3, 4, 5, 8, and 10. They appear frequently in exams.
Real-World Applications
Where do we convert fractions to percentages?
- Exam results: If Kavi scored 36 out of 40, his fraction is 36/40 = 9/10, which is 90%. Percentages let you compare performance across different tests.
- Sports statistics: A team winning 7 out of 10 games has a 70% win rate. Commentators always report statistics in percentages.
- Surveys and polls: If 3 out of 5 people prefer chocolate, that is 60%. Newspapers and TV news report survey results in percentages.
- Cooking and recipes: Using 1/4 of a recipe = 25% of the recipe. Helps when scaling recipes up or down.
- Progress tracking: Completing 4/5 of homework = 80% done. Progress bars on computers show completion as a percentage.
- Attendance records: Schools track attendance as a percentage. If a student attends 180 out of 200 school days, that is 90% attendance.
Key Points to Remember
- To convert a fraction to a percentage, multiply the fraction by 100 and add %.
- If the denominator is 2, 4, 5, 10, 20, 25, or 50, use the equivalent fraction method (make denominator = 100).
- For other denominators (3, 6, 7, 8, 9), divide the numerator by the denominator first, then multiply by 100.
- Always simplify the fraction before converting — smaller numbers are easier to work with.
- A fraction greater than 1 (improper fraction or mixed number) gives a percentage greater than 100%.
- A fraction less than 1 always gives a percentage between 0% and 100%.
- Memorise key conversions: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 1/3 ≈ 33.3%.
- Always write the % symbol in your answer — 75 and 75% mean very different things.
Practice Problems
- Convert 4/5 to a percentage.
- Express 7/10 as a percentage.
- Aman scored 22 out of 25 in a test. What is his percentage?
- Convert 3/8 to a percentage.
- In a class of 50 students, 35 passed. What percentage of students passed?
- Express 1/3 as a percentage (round to one decimal place).
- Convert 9/20 to a percentage.
- Priya completed 11 out of 25 questions in a puzzle. What percentage has she completed?
Frequently Asked Questions
Q1. How do you convert a fraction to a percentage?
Multiply the fraction by 100 and add the % symbol. For example, 3/5 × 100 = 60%. Alternatively, find an equivalent fraction with 100 as the denominator: 3/5 = 60/100 = 60%.
Q2. What is 1/4 as a percentage?
1/4 = 25%. This is because 1/4 × 100 = 25, or equivalently 1/4 = 25/100.
Q3. What is 1/3 as a percentage?
1/3 = 33.33% (repeating). Since 100 ÷ 3 = 33.333..., it does not give a whole number percentage. It is often written as 33 1/3% or approximately 33.3%.
Q4. Can a percentage be more than 100%?
Yes. When the fraction is greater than 1 (an improper fraction), the percentage exceeds 100%. For example, 5/4 = 125% and 3/2 = 150%.
Q5. Why should you simplify the fraction before converting?
Simplifying makes the numbers smaller and the calculation easier. For example, 18/24 can be simplified to 3/4, and 3/4 = 75% is much easier to compute than working with 18/24 directly.
Q6. What if the denominator does not divide 100 evenly?
Use the division method: divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 5/8: 5 ÷ 8 = 0.625, and 0.625 × 100 = 62.5%.
Q7. What is the difference between a fraction and a percentage?
A fraction can have any denominator (e.g., 3/7, 5/12). A percentage always expresses the value out of 100. Percentage is a special kind of fraction where the denominator is always 100.
Q8. Which fractions give whole number percentages?
Fractions whose simplified denominator divides 100 evenly give whole number percentages. These include denominators 1, 2, 4, 5, 10, 20, 25, 50, and 100. For example, 3/4 = 75% (whole), but 1/3 = 33.33% (not whole).
