Understand the meaning of percentage (per cent = per hundred)
Recognise the percentage symbol (%)
Convert fractions to percentage
Convert decimals to percentage
Convert percentage to fractions and decimals
Find the percentage of a given number
Find what percentage one number is of another
Solve real-life word problems involving percentage
Introduction — Percentage Is Everywhere!
Have you ever heard someone say "I scored 85% in my Maths exam" or "There is a 20% discount on this toy"? The word percentage is used everywhere in our daily life. When your phone shows 75% battery, it means 75 parts out of 100 are still charged. When a shopkeeper says "Diwali Sale — 30% off!", it means for every ₹100, you save ₹30.
In news, we hear things like: "52% voters chose Party A" or "Milk contains about 3.5% fat" or "GST on this item is 18%". All of these use the idea of percentage. In this chapter, we will learn what percentage really means, how to calculate it, and how to use it in real-life situations.
What Does Percentage Mean?
The word "per cent" comes from the Latin words "per centum", which means "per hundred" or "out of hundred".
Definition
Percentage means "out of 100".
The symbol for percentage is %.
25% means 25 out of every 100.
If you score 85 marks out of 100 in a test, your percentage is 85%.
Think of a 10 × 10 grid with 100 small squares. If you colour 40 squares out of 100, you have coloured 40% of the grid.
Image needed: Three 10×10 grids (100 squares each) side by side. First grid: 25 squares shaded blue (labelled "25%"). Second grid: 50 squares shaded green (labelled "50%"). Third grid: 75 squares shaded orange (labelled "75%"). Each grid clearly showing the fraction and percentage below it. Style: Clean flat illustration, bright colours, child-friendly, labelled clearly Size: 800×350px
Understanding with examples:
Statement
What it means
100% battery
Full battery — 100 out of 100 parts charged
50% marks
Half marks — 50 out of every 100
0% chance of rain
No chance at all — 0 out of 100
25% discount
Save ₹25 for every ₹100 spent
18% GST
Pay ₹18 extra tax for every ₹100 of price
Think About It: Can percentage be more than 100%? Yes! If a shopkeeper buys something for ₹100 and sells it for ₹150, he made a profit of 50%. If he sells it for ₹250, that is 150% of the cost price — more than 100%!
Converting Fractions to Percentage
To convert a fraction to a percentage, we use this simple method:
Method: Fraction → Percentage
Multiply the fraction by 100 and add the % symbol.
Formula: Percentage = (Fraction) × 100%
Example 1: Convert 1/2 to percentage.
1/2 × 100 = 100/2 = 50%
Example 2: Convert 3/4 to percentage.
3/4 × 100 = 300/4 = 75%
Example 3: Convert 2/5 to percentage.
2/5 × 100 = 200/5 = 40%
Example 4: Convert 7/10 to percentage.
7/10 × 100 = 700/10 = 70%
Example 5: Convert 1/8 to percentage.
1/8 × 100 = 100/8 = 12.5%
Example 6: Convert 5/6 to percentage.
5/6 × 100 = 500/6 = 83.33% (approximately 83⅓%)
Quick Trick: If the denominator is already a factor of 100, just adjust the fraction to have 100 as the denominator!
For example: 3/5 → multiply top and bottom by 20 → 60/100 = 60%
Similarly: 7/25 → multiply top and bottom by 4 → 28/100 = 28%
Converting Decimals to Percentage
Converting a decimal to a percentage is very simple:
Method: Decimal → Percentage
Multiply the decimal by 100 and add the % symbol.
Shortcut: Move the decimal point 2 places to the right.
Example 1: Convert 0.5 to percentage.
0.5 × 100 = 50% (or move decimal 2 places right: 0.50 → 50)
Example 2: Convert 0.75 to percentage.
0.75 × 100 = 75%
Example 3: Convert 0.08 to percentage.
0.08 × 100 = 8% (move decimal: 0.08 → 8)
Example 4: Convert 0.125 to percentage.
0.125 × 100 = 12.5%
Example 5: Convert 1.5 to percentage.
1.5 × 100 = 150% (Yes, more than 100% is possible!)
Example 6: Convert 0.005 to percentage.
0.005 × 100 = 0.5%
Converting Percentage to Fractions
To convert a percentage to a fraction, we reverse the process:
Method: Percentage → Fraction
Write the percentage number over 100 (as a fraction with denominator 100).
Then simplify the fraction to its lowest terms.
Example 1: Convert 25% to a fraction.
25% = 25/100 = 1/4 (divide both by 25)
Example 2: Convert 60% to a fraction.
60% = 60/100 = 3/5 (divide both by 20)
Example 3: Convert 75% to a fraction.
75% = 75/100 = 3/4 (divide both by 25)
Example 4: Convert 40% to a fraction.
40% = 40/100 = 2/5 (divide both by 20)
Example 5: Convert 12.5% to a fraction.
12.5% = 12.5/100 = 125/1000 = 1/8 (divide both by 125)
Example 6: Convert 33⅓% to a fraction.
33⅓% = (100/3)/100 = 100/(3×100) = 1/3
Converting Percentage to Decimals
To convert a percentage to a decimal:
Method: Percentage → Decimal
Divide the percentage by 100 (remove the % symbol).
Shortcut: Move the decimal point 2 places to the left.
Example 1: Convert 45% to a decimal.
45 ÷ 100 = 0.45
Example 2: Convert 8% to a decimal.
8 ÷ 100 = 0.08 (move decimal 2 places left: 08. → 0.08)
Example 3: Convert 150% to a decimal.
150 ÷ 100 = 1.5
Example 4: Convert 3% to a decimal.
3 ÷ 100 = 0.03
Example 5: Convert 62.5% to a decimal.
62.5 ÷ 100 = 0.625
Example 6: Convert 100% to a decimal.
100 ÷ 100 = 1.0 (the whole thing!)
Fraction — Decimal — Percentage Equivalence Table
This table shows common fractions and their equivalent decimals and percentages. Memorise these — they will help you in many calculations!
Fraction
Decimal
Percentage
1/2
0.5
50%
1/4
0.25
25%
3/4
0.75
75%
1/5
0.2
20%
2/5
0.4
40%
3/5
0.6
60%
4/5
0.8
80%
1/10
0.1
10%
3/10
0.3
30%
7/10
0.7
70%
9/10
0.9
90%
1/8
0.125
12.5%
1/3
0.333...
33⅓%
2/3
0.666...
66⅔%
1/1
1.0
100%
Image needed: A triangle diagram showing the relationship between Fraction, Decimal, and Percentage. Each corner has one form. Arrows between them show the conversion method: "×100" from decimal to %, "÷100" from % to decimal, "write over 100" from % to fraction, "÷ numerator by denominator" from fraction to decimal. Style: Colourful triangle infographic, bold text, child-friendly, clear arrows Size: 600×500px
Finding Percentage of a Number
This is one of the most useful skills. "Finding 25% of 200" means finding 25 parts out of every 100, when the total is 200.
Method: Finding Percentage of a Number
Formula: Percentage of Number = (Percentage / 100) × Number
Or simply: write the percentage as a fraction over 100 and multiply by the number.
Example 1: Find 25% of 200.
= (25/100) × 200 = 25 × 2 = 50
Example 2: Find 10% of 450.
= (10/100) × 450 = 1/10 × 450 = 45
Example 3: Find 15% of 600.
= (15/100) × 600 = 15 × 6 = 90
Example 4: Find 75% of 80.
= (75/100) × 80 = 3/4 × 80 = 60
Example 5: Find 33⅓% of 900.
= 1/3 × 900 = 300
Example 6: Find 12.5% of 480.
= (12.5/100) × 480 = 1/8 × 480 = 60
Image needed: Step-by-step visual showing "Find 25% of 200". Step 1: Write as fraction (25/100). Step 2: Multiply by number (×200). Step 3: Calculate (= 50). Use colourful boxes for each step with arrows connecting them. Also show a visual of a bar divided into 4 parts with 1 part (50) highlighted. Style: Step-by-step process diagram, colourful, child-friendly, with bar model visual Size: 700×400px
Quick Tricks for Finding Percentages
To find...
Quick method
Example (of 360)
10% of a number
Divide by 10
360 ÷ 10 = 36
20% of a number
Find 10%, then double it
36 × 2 = 72
5% of a number
Find 10%, then halve it
36 ÷ 2 = 18
25% of a number
Divide by 4
360 ÷ 4 = 90
50% of a number
Divide by 2
360 ÷ 2 = 180
1% of a number
Divide by 100
360 ÷ 100 = 3.6
Finding What Percentage One Number is of Another
Sometimes we know two numbers and want to find what percentage one is of the other. For example: "Arjun scored 42 out of 50. What is his percentage?"
Method
Formula: Percentage = (Part / Whole) × 100%
The "part" is what you have, and the "whole" is the total.
Example 1: Arjun scored 42 out of 50 in his Maths test. What is his percentage?
= (42/50) × 100 = 42 × 2 = 84%
Example 2: In a class of 40 students, 32 students passed. What percentage passed?
= (32/40) × 100 = 32 × 2.5 = 80%
Example 3: Meena saved ₹150 out of her pocket money of ₹500. What percentage did she save?
= (150/500) × 100 = 150/5 = 30%
Example 4: Out of 25 days in a month, Ravi was present for 22 days. What is his attendance percentage?
= (22/25) × 100 = 22 × 4 = 88%
Example 5: A cricket team won 9 out of 12 matches. What is their win percentage?
= (9/12) × 100 = (3/4) × 100 = 75%
Percentage in Real Life (Indian Context)
Percentage is used in many real-life situations in India. Let us look at some common examples:
1. Marks and Exams
Problem: Priya got the following marks in her Class 5 exams:
Maths: 45/50 | Science: 38/50 | English: 42/50 | Hindi: 40/50 | GK: 48/50
Find her percentage in each subject and total percentage.
Problem: In a school captain election, there are 500 students. 260 students voted for Arjun and 240 voted for Meena. What percentage of votes did each candidate get?
Problem: A school has 240 working days in a year. Dhruv attended 216 days. What is his attendance percentage?
Solution:
Attendance % = (216/240) × 100 = 90%
Since most schools require 75% attendance, Dhruv is well above the minimum!
Image needed: An infographic showing 4 real-life percentage examples: (1) Battery icon showing 75% charged, (2) A sale tag showing "20% OFF" on ₹800 with discounted price ₹640, (3) An exam scorecard showing 85%, (4) A GST receipt showing 18% tax on ₹2000. All in a 2×2 grid layout. Style: Colourful infographic with icons, Indian context (rupee symbol, Indian brand feel), child-friendly Size: 800×500px
Key Words
Term
Meaning
Per cent
"Per hundred" — out of every 100
Percentage (%)
A number expressed as a fraction of 100
Fraction
A part of a whole (e.g., 3/4)
Decimal
A number with a decimal point (e.g., 0.75)
Convert
To change from one form to another
Discount
Reduction in price (expressed as a percentage)
GST
Goods and Services Tax — a percentage added to price
Profit
When selling price is more than cost price
Loss
When selling price is less than cost price
Attendance
Number of days present out of total working days
Key Points to Remember
Percentage means "out of 100". The symbol is %.
Fraction → Percentage: Multiply the fraction by 100.
Decimal → Percentage: Multiply the decimal by 100 (move decimal 2 places right).
Percentage → Fraction: Write over 100, then simplify.
Image needed: A colourful pie chart showing how a Class 5 student spends their day: Sleeping 33% (blue), School 29% (green), Homework 13% (yellow), Playing 13% (red), Other 12% (purple). Each slice labelled with activity name and percentage. Title: "How Arjun Spends His Day" Style: Clean, colourful pie chart with labels, child-friendly, vibrant colours Size: 600×500px
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
Answer these questions right here. You get instant feedback — no paper needed!
Score: 0 / 8
1. What does "percent" mean?
Per cent means "per hundred" — out of 100.
2. 50% of 80 is:
50% = half, and half of 80 is 40.
3. 25% is the same as which fraction?
25/100 = 1/4.
4. 10% of 250 is:
10% = 1/10, and 250 ÷ 10 = 25.
5. What is 30% of 50?
30% of 50 = (30/100) × 50 = 15.
6. Write 3/4 as a percentage (number only):
3/4 = 75/100 = 75%.
7. Ravi scored 20 out of 25 in a test. What percentage did he get?
20/25 = 80/100 = 80%.
8. A shirt costs ₹500. In a 10% off sale, how much do you pay? (₹, digits only)
10% of 500 = 50 discount, so you pay 500 − 50 = ₹450.
Practice Questions
A. Convert the following fractions to percentage:
1. 3/5 = %
2. 7/10 = %
3. 1/4 = %
4. 9/20 = %
5. 5/8 = %
6. 11/25 = %
B. Convert the following decimals to percentage:
1. 0.35 = %
2. 0.7 = %
3. 0.04 = %
4. 0.625 = %
5. 1.25 = %
C. Convert the following percentages to fractions (simplest form):
1. 45% =
2. 80% =
3. 35% =
4. 62.5% =
5. 16% =
D. Convert the following percentages to decimals:
1. 72% =
2. 5% =
3. 125% =
4. 0.5% =
5. 33.3% =
E. Find the percentage of the given number:
1. 20% of 350 =
2. 15% of 600 =
3. 75% of 240 =
4. 8% of 1,500 =
5. 33⅓% of 450 =
6. 12.5% of 800 =
F. Find what percentage the first number is of the second:
1. 36 is what % of 90? = %
2. 18 is what % of 72? = %
3. 125 is what % of 500? = %
4. 7 is what % of 28? = %
5. 45 is what % of 60? = %
G. Fill in the blanks:
1. 50% is the same as (fraction).
2. 0.75 as a percentage is %.
3. 1/5 as a percentage is %.
4. If 30% of a number is 90, the number is .
5. 100% of any number is itself.
H. True or False:
1. 25% is the same as 1/4.
2. 50% of 100 is 25.
3. A percentage can never be more than 100%.
4. 10% of 500 is the same as 50% of 100.
5. 0.08 is the same as 8%.
I. Choose the correct answer (MCQ):
1. What is 25% of 400?
a) 25b) 100c) 200d) 75
2. 3/5 expressed as a percentage is:
a) 35%b) 60%c) 53%d) 30%
3. If a shirt costs ₹500 and there is a 10% discount, how much do you save?
a) ₹10b) ₹100c) ₹50d) ₹5
4. 0.02 as a percentage is:
a) 20%b) 0.2%c) 2%d) 0.02%
J. Word Problems:
1. Arjun scored 38 out of 50 in his Science test. What is his percentage?
2. A book costs ₹450. During a book fair, there is a 15% discount. How much does Priya pay for the book?
3. In a school of 800 students, 92% attended the Annual Day function. How many students attended?
4. Ravi's father earns ₹40,000 per month. He saves 20% of his salary. How much does he save each month?
5. In an election, Candidate A got 1,200 votes and Candidate B got 800 votes out of 2,000 total votes. What percentage of votes did each candidate get?
6. A class has 50 students. On Monday, 5 students were absent. What was the attendance percentage on Monday?
Activity — Class Attendance Tracker
Here is the attendance data for Class 5-B for one week. Calculate the attendance percentage for each day!
Day
Total Students
Students Present
Attendance %
Monday
40
36
Tuesday
40
38
Wednesday
40
40
Thursday
40
34
Friday
40
30
Questions:
a) On which day was the attendance 100%?
b) On which day was the attendance the lowest? What was the percentage?
c) What was the average attendance percentage for the whole week?
Hint: For average, add all present students for 5 days, divide by total possible (40 × 5 = 200), then multiply by 100.
Want to review the lesson again?
Mathematics
Introduction to Percentage
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Learning Objectives
Understand the meaning of percentage (per cent = per hundred)
Convert fractions to percentage and decimals to percentage
Convert percentage to fractions and decimals
Find percentage of a number
Find what percentage one number is of another
Solve real-life word problems involving percentage
Introduction — Percentage Is Everywhere!
The word "per cent" means "per hundred" or "out of 100". The symbol is %. When we say 85%, it means 85 out of every 100. Percentage is used in exam marks, discounts, GST, battery levels, election results, and much more!
What Does Percentage Mean?
Percentage = Out of 100. The symbol is %. 25% means 25 out of every 100. If you colour 40 squares in a 10×10 grid (100 squares), you have coloured 40%.
[Image: Three 10×10 grids showing 25%, 50%, and 75% shaded with labels]
Statement
Meaning
100% battery
Full — all 100 parts charged
50% marks
Half marks — 50 out of 100
25% discount
Save ₹25 for every ₹100
18% GST
₹18 extra tax per ₹100
0%
Nothing at all
Converting Fractions to Percentage
Method: Multiply the fraction by 100 and add % symbol.
Formula: Percentage = Fraction × 100%
Attendance: 216 of 240 days → (216/240) × 100 = 90%
[Image: Infographic — Battery 75%, Sale tag 20% off, Exam scorecard 85%, GST receipt 18%]
Key Words
Term
Meaning
Per cent
"Per hundred" — out of 100
% (symbol)
The percentage symbol
Discount
Reduction in price (as a %)
GST
Tax added to price (as a %)
Convert
Change from one form to another
Key Points to Remember:
• Percentage means "out of 100". Symbol: %
• Fraction → %: multiply by 100 | Decimal → %: multiply by 100
• % → Fraction: write over 100, simplify | % → Decimal: divide by 100
• Finding % of number: (% ÷ 100) × number
• Finding what % A is of B: (A ÷ B) × 100
• 10% = ÷10 | 50% = ÷2 | 25% = ÷4 | 1% = ÷100
• Percentage CAN be more than 100%
• 0% = nothing | 100% = the whole thing
Practice Questions
A. Convert the following fractions to percentage:
1. 3/5 = %
2. 7/10 = %
3. 1/4 = %
4. 9/20 = %
5. 5/8 = %
6. 11/25 = %
B. Convert the following decimals to percentage:
1. 0.35 = %
2. 0.7 = %
3. 0.04 = %
4. 0.625 = %
5. 1.25 = %
C. Convert the following percentages to fractions (simplest form):
1. 45% =
2. 80% =
3. 35% =
4. 62.5% =
5. 16% =
D. Convert the following percentages to decimals:
1. 72% =
2. 5% =
3. 125% =
4. 0.5% =
5. 33.3% =
E. Find the percentage of the given number:
1. 20% of 350 =
2. 15% of 600 =
3. 75% of 240 =
4. 8% of 1,500 =
5. 33⅓% of 450 =
6. 12.5% of 800 =
F. Find what percentage the first number is of the second:
1. 36 is what % of 90? = %
2. 18 is what % of 72? = %
3. 125 is what % of 500? = %
4. 7 is what % of 28? = %
5. 45 is what % of 60? = %
G. Fill in the blanks:
1. 50% is the same as (fraction).
2. 0.75 as a percentage is %.
3. 1/5 as a percentage is %.
4. If 30% of a number is 90, the number is .
5. 100% of any number is itself.
H. True or False:
1. 25% is the same as 1/4.
2. 50% of 100 is 25.
3. A percentage can never be more than 100%.
4. 10% of 500 is the same as 50% of 100.
5. 0.08 is the same as 8%.
I. Choose the correct answer (MCQ):
1. What is 25% of 400?
a) 25b) 100c) 200d) 75
2. 3/5 expressed as a percentage is:
a) 35%b) 60%c) 53%d) 30%
3. If a shirt costs ₹500 and there is a 10% discount, how much do you save?
a) ₹10b) ₹100c) ₹50d) ₹5
4. 0.02 as a percentage is:
a) 20%b) 0.2%c) 2%d) 0.02%
J. Word Problems:
1. Arjun scored 38 out of 50 in his Science test. What is his percentage?
2. A book costs ₹450. During a book fair, there is a 15% discount. How much does Priya pay?
3. In a school of 800 students, 92% attended the Annual Day function. How many attended?
4. Ravi's father earns ₹40,000/month. He saves 20%. How much does he save?
5. Candidate A got 1,200 votes and Candidate B got 800 votes out of 2,000. What % did each get?
6. A class has 50 students. On Monday, 5 were absent. What was the attendance percentage?
Pie Chart — Visualising Percentage
[Image: Pie chart showing how Arjun spends his day — Sleeping 33%, School 29%, Homework 13%, Playing 13%, Other 12%]
Activity — Class Attendance Tracker
Calculate the attendance percentage for each day:
Day
Total
Present
Attendance %
Monday
40
36
Tuesday
40
38
Wednesday
40
40
Thursday
40
34
Friday
40
30
a) Which day had 100% attendance?
b) Which day had the lowest attendance? What %?
c) Average attendance for the week:
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