Introduction to Percentage
Percentage means "per hundred" or "out of 100." The word comes from the Latin per centum, where per means "for every" and centum means "hundred." The symbol for percentage is %.
When we say 25%, we mean 25 out of 100. If Ria scored 80% in a test, it means she got 80 marks out of every 100 marks.
Percentage is one of the most widely used mathematical concepts in daily life. You see it everywhere — exam scores ("scored 92%"), shopping discounts ("30% off"), cricket statistics ("win rate of 65%"), battery levels ("battery at 45%"), and even weather forecasts ("70% chance of rain").
In this topic, you will learn what percentage means, how to calculate it, and how it connects to fractions and decimals. Understanding percentage is the foundation for topics like discount, profit-loss, and data interpretation that you will study in higher classes.
What is Introduction to Percentage - Class 5 Maths (Percentage)?
A percentage is a way of expressing a number as a fraction of 100. It answers the question: "If the total were 100, how many parts would this be?"
Percentage = (Part / Whole) × 100
The percentage symbol is %. Here are some important benchmark values:
- 0% means none of the total — zero parts out of 100.
- 25% means one quarter — 25 out of 100.
- 50% means half — 50 out of 100.
- 75% means three quarters — 75 out of 100.
- 100% means the entire thing — all 100 out of 100.
Percentage as a fraction and decimal:
Every percentage can be written as a fraction (with denominator 100) and as a decimal:
- 25% = 25/100 = 1/4 = 0.25
- 50% = 50/100 = 1/2 = 0.50
- 75% = 75/100 = 3/4 = 0.75
Introduction to Percentage Formula
Percentage = (Part ÷ Whole) × 100
How to calculate percentage step by step:
- Identify the part (the quantity you are finding the percentage of).
- Identify the whole (the total amount).
- Divide the part by the whole to get a decimal or fraction.
- Multiply the result by 100.
- Write the answer with the % symbol.
Key relationships — The Percentage Triangle:
| Percentage | Fraction | Decimal | Meaning |
|---|---|---|---|
| 1% | 1/100 | 0.01 | 1 out of 100 |
| 5% | 5/100 = 1/20 | 0.05 | 5 out of 100 |
| 10% | 10/100 = 1/10 | 0.1 | 10 out of 100 |
| 20% | 20/100 = 1/5 | 0.2 | 20 out of 100 |
| 25% | 25/100 = 1/4 | 0.25 | 25 out of 100 |
| 50% | 50/100 = 1/2 | 0.5 | 50 out of 100 |
| 75% | 75/100 = 3/4 | 0.75 | 75 out of 100 |
| 100% | 100/100 = 1 | 1.0 | The whole thing |
Converting between forms:
- Percentage to fraction: divide by 100 → 45% = 45/100 = 9/20
- Percentage to decimal: divide by 100 → 45% = 0.45
- Fraction to percentage: multiply by 100 → 3/5 × 100 = 60%
- Decimal to percentage: multiply by 100 → 0.7 × 100 = 70%
Types and Properties
Understanding percentage through different models:
Model 1: The 100-square grid
Imagine a grid with 100 small squares (10 rows × 10 columns). If you colour 40 squares, then 40% of the grid is coloured. This is the most visual way to understand percentage.
- Colour 25 squares → 25% shaded
- Colour 50 squares → 50% shaded (exactly half)
- Colour all 100 squares → 100% shaded
Model 2: Fraction form
Any percentage can be immediately written as a fraction with 100 in the denominator:
- 25% = 25/100 = 1/4
- 40% = 40/100 = 2/5
- 75% = 75/100 = 3/4
Model 3: Decimal form
Divide the percentage by 100 to get the decimal:
- 25% = 0.25
- 50% = 0.50
- 10% = 0.10
Model 4: Percentage greater than 100
Sometimes a percentage is more than 100%. This means the quantity is greater than the original whole.
- 150% means 150 out of 100, which equals 1.5 or 1 1/2 times the whole.
- 200% means twice the original amount.
- This happens during price increases, population growth, etc.
Model 5: Percentage less than 1%
Very small quantities can have percentages less than 1%:
- 0.5% means half of one percent — very small.
- If 3 out of 1000 students were late, that is 0.3%.
Solved Examples
Example 1: Understanding What 30% Means
Problem: What does 30% mean? Express it as a fraction and a decimal.
Solution:
Step 1: 30% means 30 out of 100.
Step 2: As a fraction: 30/100. Simplify: HCF of 30 and 100 = 10. So 30/100 = 3/10.
Step 3: As a decimal: 30 ÷ 100 = 0.30 = 0.3.
Real-life meaning: If a class has 100 students and 30% are wearing blue shirts, then 30 students are wearing blue shirts.
Answer: 30% = 3/10 = 0.3, meaning 30 out of every 100.
Example 2: Calculating Percentage from a Score
Problem: Aman got 18 out of 20 in a spelling test. What is his percentage?
Solution:
Step 1: Part = 18, Whole = 20.
Step 2: Percentage = (18/20) × 100
Step 3: Simplify: 18/20 = 9/10. Then 9/10 × 100 = 90.
Verification: 90% of 20 = (90/100) × 20 = 18 ✓
Answer: Aman scored 90%.
Example 3: Percentage from a Grid
Problem: In a 100-square grid, 65 squares are coloured blue and the rest are white. What percentage is blue? What percentage is white?
Solution:
Step 1: Blue squares = 65 out of 100 = 65%.
Step 2: White squares = 100 − 65 = 35 out of 100 = 35%.
Step 3: Check: 65% + 35% = 100% ✓ (the total must always be 100%).
Answer: 65% is blue and 35% is white.
Example 4: Percentage of a Class
Problem: In a class of 50 students, 30 are girls. What percentage of the class are girls? What percentage are boys?
Solution:
Step 1: Fraction of girls = 30/50.
Step 2: Percentage of girls = (30/50) × 100 = 60%.
Step 3: Boys = 50 − 30 = 20. Percentage of boys = (20/50) × 100 = 40%.
Step 4: Check: 60% + 40% = 100% ✓
Answer: 60% are girls and 40% are boys.
Example 5: What Does 100% Mean?
Problem: What fraction and decimal does 100% represent?
Solution:
Step 1: 100% = 100/100 = 1.
Step 2: As a decimal: 1.0.
Meaning: 100% means the entire quantity — the complete whole. If you ate 100% of a pizza, you ate the entire pizza. If 100% of students passed, every single student passed.
Answer: 100% = 1 (the whole amount).
Example 6: Cricket Winning Percentage
Problem: A cricket team played 10 matches and won 7. What is their winning percentage?
Solution:
Step 1: Part = 7 wins. Whole = 10 matches.
Step 2: Winning percentage = (7/10) × 100 = 70%.
Real-life context: Sports commentators often say "the team has a 70% win rate" — this means they win 7 out of every 10 matches they play.
Answer: The winning percentage is 70%.
Example 7: Small Percentage
Problem: Out of 1000 students in a school, 5 were absent on Monday. What percentage were absent?
Solution:
Step 1: Part = 5 absent. Whole = 1000 students.
Step 2: Percentage = (5/1000) × 100 = 500/1000 = 0.5%.
Note: 0.5% is less than 1%. This means very few students were absent — only 5 in every thousand.
Answer: 0.5% of students were absent.
Example 8: Word Problem — Water Consumption
Problem: A water bottle holds 1 litre. Priya drank 250 ml. What percentage of the water did she drink?
Solution:
Step 1: Convert to the same unit: 1 litre = 1000 ml.
Step 2: Part = 250 ml. Whole = 1000 ml.
Step 3: Percentage = (250/1000) × 100 = 25%.
Alternative: 250/1000 = 1/4, and 1/4 = 25%.
Answer: Priya drank 25% of the water.
Example 9: Comparing Scores Using Percentage
Problem: Aditi scored 36 out of 40 in Maths and 42 out of 50 in Science. In which subject did she score a higher percentage?
Solution:
Step 1: Maths percentage = (36/40) × 100 = 90%.
Step 2: Science percentage = (42/50) × 100 = 84%.
Step 3: Compare: 90% > 84%.
Why percentage is useful here: Aditi's raw Science score (42) is higher than her Maths score (36), but the totals are different. Percentage levels the comparison.
Answer: Aditi scored a higher percentage in Maths (90%).
Example 10: Finding the Remaining Percentage
Problem: In a survey of students about their favourite sport, 45% chose cricket and 30% chose football. What percentage chose other sports?
Solution:
Step 1: Total percentage accounted for = 45% + 30% = 75%.
Step 2: The total must be 100% (everyone is counted). Remaining = 100% − 75% = 25%.
Key rule: When a quantity is divided into groups, all the percentages must add up to 100%.
Answer: 25% chose other sports.
Real-World Applications
Where is percentage used in daily life?
- Exam scores: "Kavi scored 85% in the final exam" — this is the most common use students encounter. It allows comparing scores across tests with different totals.
- Shopping discounts: "30% off on all items" — means the price is reduced by 30 out of every 100 rupees.
- Nutrition labels: "This cereal has 10% dietary fibre" — tells you how much of the daily requirement is in one serving.
- Cricket and sports: "Strike rate of 140%" or "win percentage of 65%."
- Banking: "Fixed deposit gives 7% interest per year" — for every ₹100 deposited, you earn ₹7.
- Weather: "70% chance of rain today" — out of 100 similar weather days, 70 would have rain.
- Elections: "Candidate A got 52% of votes" — more than half the voters chose them.
- Battery and progress: "Phone battery at 45%" or "download 80% complete."
Key Points to Remember
- Percentage means "out of 100." The symbol is %.
- To calculate percentage: (Part ÷ Whole) × 100.
- Key benchmarks: 50% = half, 25% = one quarter, 75% = three quarters, 10% = one tenth.
- Any fraction can be converted to a percentage by multiplying by 100.
- Any decimal can be converted to a percentage by multiplying by 100.
- 100% means the complete amount. 0% means nothing.
- More than 100% means exceeding the original amount (e.g., 150% = 1.5 times).
- Percentages make it easy to compare quantities that have different totals.
- Percentage, fraction, and decimal are three different ways to express the same value: 75% = 3/4 = 0.75.
- All percentages in a group must add up to 100% of the total.
Practice Problems
- What is 45% as a fraction in simplest form?
- Rahul scored 35 out of 50 in a test. What is his percentage?
- In a class of 40 students, 16 got full marks. What percentage of students got full marks?
- Express 3/5 as a percentage.
- A shop offers a 15% discount. If an item costs ₹100, how much discount do you get?
- Dev ate 4 out of 8 chapatis. What percentage of chapatis did he eat?
- What percentage of 1 kg is 350 g?
- If 60% of students in a school are boys, what percentage are girls?
Frequently Asked Questions
Q1. What does percentage mean?
Percentage means "out of 100." It tells how much of something there is if the total were counted as 100 parts. For example, 40% means 40 out of every 100.
Q2. What is the symbol for percentage?
The symbol is %. It is written after the number. For example, twenty-five percent is written as 25%.
Q3. How do you calculate percentage?
Use the formula: Percentage = (Part ÷ Whole) × 100. For example, if you scored 45 out of 60, your percentage = (45/60) × 100 = 75%.
Q4. What is 100%?
100% means the complete amount — everything, the whole. 100/100 = 1. If you ate 100% of a cake, you ate the entire cake.
Q5. Can percentage be more than 100?
Yes. Percentages above 100% mean the amount exceeds the original whole. For example, if a plant grew from 10 cm to 25 cm, its height is now 250% of the original (25/10 × 100 = 250%).
Q6. How are fraction, decimal, and percentage related?
They are three ways of expressing the same value. For example: 1/2 = 0.5 = 50%. To convert fraction to percentage, multiply by 100. To convert decimal to percentage, multiply by 100. To convert percentage to fraction, divide by 100.
Q7. Why is percentage useful for comparing?
Percentage converts different totals to a common base of 100, making comparison fair. Scoring 36/40 (90%) is clearly better than 42/50 (84%), even though 42 is a larger raw number than 36.
Q8. What is 0%?
0% means none of the total — zero parts out of 100. If 0% of students failed, it means every student passed.
Q9. How do you convert a decimal to a percentage?
Multiply the decimal by 100 and add the % symbol. For example, 0.35 × 100 = 35%. Moving the decimal point two places to the right achieves the same result.
