Introduction to Percentage

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

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:
StatementWhat it means
100% batteryFull battery — 100 out of 100 parts charged
50% marksHalf marks — 50 out of every 100
0% chance of rainNo chance at all — 0 out of 100
25% discountSave ₹25 for every ₹100 spent
18% GSTPay ₹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!

FractionDecimalPercentage
1/20.550%
1/40.2525%
3/40.7575%
1/50.220%
2/50.440%
3/50.660%
4/50.880%
1/100.110%
3/100.330%
7/100.770%
9/100.990%
1/80.12512.5%
1/30.333...33⅓%
2/30.666...66⅔%
1/11.0100%
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 methodExample (of 360)
10% of a numberDivide by 10360 ÷ 10 = 36
20% of a numberFind 10%, then double it36 × 2 = 72
5% of a numberFind 10%, then halve it36 ÷ 2 = 18
25% of a numberDivide by 4360 ÷ 4 = 90
50% of a numberDivide by 2360 ÷ 2 = 180
1% of a numberDivide by 100360 ÷ 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.

Solution:
Maths: (45/50) × 100 = 90%
Science: (38/50) × 100 = 76%
English: (42/50) × 100 = 84%
Hindi: (40/50) × 100 = 80%
GK: (48/50) × 100 = 96%

Total marks: 45 + 38 + 42 + 40 + 48 = 213 out of 250
Total percentage: (213/250) × 100 = 85.2%

2. Discounts and Shopping

Problem: A school bag costs ₹800. During the Diwali sale, there is a 20% discount. How much will Ravi pay?

Solution:
Discount amount = 20% of ₹800 = (20/100) × 800 = ₹160
Price after discount = ₹800 − ₹160 = ₹640

So Ravi pays ₹640 instead of ₹800.

3. GST (Goods and Services Tax)

Problem: Sita buys a watch for ₹2,000. GST on watches is 18%. What is the total amount she pays?

Solution:
GST amount = 18% of ₹2,000 = (18/100) × 2,000 = ₹360
Total price = ₹2,000 + ₹360 = ₹2,360

4. Election Results

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?

Solution:
Arjun: (260/500) × 100 = 52%
Meena: (240/500) × 100 = 48%

Arjun won with 52% of the votes!

5. Attendance

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

TermMeaning
Per cent"Per hundred" — out of every 100
Percentage (%)A number expressed as a fraction of 100
FractionA part of a whole (e.g., 3/4)
DecimalA number with a decimal point (e.g., 0.75)
ConvertTo change from one form to another
DiscountReduction in price (expressed as a percentage)
GSTGoods and Services Tax — a percentage added to price
ProfitWhen selling price is more than cost price
LossWhen selling price is less than cost price
AttendanceNumber 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.
  • Percentage → Decimal: Divide by 100 (move decimal 2 places left).
  • Finding % of a number: (Percentage/100) × Number.
  • Finding what % one number is of another: (Part/Whole) × 100.
  • 10% of any number = divide the number by 10.
  • 50% of any number = half the number.
  • 25% of any number = one-fourth of the number.
  • Percentage can be more than 100% (e.g., 150% means 1.5 times).
  • 0% means nothing, 100% means the whole thing.

Visualising Percentage with Pie Charts

A pie chart (also called a circle graph) is a great way to show percentages. The whole circle represents 100%. Each slice shows a part of the total.

Example: Arjun spends his 24-hour day like this:
Sleeping: 8 hours = (8/24) × 100 = 33⅓%
School: 7 hours = (7/24) × 100 ≈ 29%
Homework: 3 hours = (3/24) × 100 = 12.5%
Playing: 3 hours = (3/24) × 100 = 12.5%
Eating & other: 3 hours = (3/24) × 100 = 12.5%
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!