Finding a percentage of a whole

Introduction

Percentages are a fast way to describe a part of a whole. In many exam questions, you are given the total quantity and asked to find a certain percent of it. The key idea is simple: convert the percentage into a fraction or decimal, then multiply by the whole.

Core idea

To find x% of a number N, use:

x% of N = (x/100) × N

You can also think of it as:

x% = x per 100

So x% of N means x out of every 100 parts of N.

Step-by-step method

1. Write the percentage as a fraction over 100.
2. Multiply it by the whole.
3. Simplify the answer.

Worked example 1

Find 15% of 240.

15% of 240 = (15/100) × 240

= 15 × 2.4

= 36

So, 15% of 240 is 36.

Worked example 2

Find 8% of 375.

8% of 375 = (8/100) × 375

= 0.08 × 375

= 30

So, 8% of 375 is 30.

Common mistakes

• Dividing by the percentage instead of multiplying: 20% of 50 is not 50 ÷ 20.
• Forgetting to divide by 100: 25% means 25/100, not 25.
• Using the wrong whole: always identify the total quantity first.

Practice

Try these on your own:

1. Find 12% of 500.
2. Find 7% of 260.
3. Find 40% of 95.

Recap

• x% of N = (x/100) × N
• Convert the percentage first.
• Multiply by the whole to get the part.

Analogy

Finding 15% of 240 is like taking 15 parts out of every 100 parts of that 240. The cut is a multiplication: (15/100) x 240 = 36. Dividing 240 by 15 would be a different question.

Quick reference

• x% of N = (x/100) x N.
• 15% of 240 = 36. 8% of 375 = 30.
• 20% of 50 is 10, not 50 divided by 20.