Percentages • Topic 3 of 3

Finding Percent of a Quantity

Three Methods to Find Percent of a Number:

Method 1: Convert to Decimal

20% of 60 = 0.2 × 60 = 12

Method 2: Use Fraction

20% = (1)/(5), so (1)/(5) of 60 = 12

Method 3: Use Proportion

20/100 = x/60
Cross multiply: 100x = 1200, x = 12

Real-World Applications:

Sales tax: 8% tax on 50 = 0.08 × 50 =4
Tips: 15% tip on 40 = 0.15 × 40 =6
Discounts: 25% off 80 = 0.25 × 80 =20 saved

FINDING 20% OF 60 (VISUAL):

 0% 20% 100%
 ├──────────────────────┼──────────────────────┤
 │ │ │
 0 12 60
 
 20% of 60 = 12


PERCENT OF A NUMBER - BAR MODEL:

 60 total (100%)
 ┌────┬────┬────┬────┬────┐
 │ 12 │ 12 │ 12 │ 12 │ 12 │
 └────┴────┴────┴────┴────┘
 20% 20% 20% 20% 20%
 
 Each 20% = 12


DISCOUNT CALCULATION:

 Original Price: 80 (100%)
 
 25% Discount = 20 saved
 ┌─────────────┬─────────────┐
 │ 20 saved │ 60 pay │
 │ (25%) │ (75%) │
 └─────────────┴─────────────┘
 
 Final Price: 60

Solved Examples

Worked Example

Find 15% of 200

Solution

Decimal: 0.15 × 200 = 30
Fraction: 15/100 × 200 = 3000/100 = 30
Answer: 30

Worked Example

A shirt costs 40. It is 30% off. How much do you save?

Solution

30% of 40 = 0.3 × 40 = 12
Answer: 12 saved

Worked Example

There are 25 students. 40% are girls. How many are girls?

Solution

40% = 0.4
0.4 × 25 = 10
Answer: 10 girls

Key Points

"Percent of" means multiply
Convert percent to decimal or fraction first
Of = multiplication (×)
Is = equals (=)
Check if answer makes sense (part < whole for % < 100%)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.To find a percent of a number, multiply by the percent as a:

Explanation: Fraction/decimal.

Q2.$10\%$ of $200$ is:

Explanation: $\tfrac{10}{100}\times200$.

Q3.$50\%$ of a number is ___ of it.

Explanation: Half.

Q4.$25\%$ of a number is ___ of it.

Explanation: A quarter.

Practice more MCQs → 📝 Assignment · 35 marks