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Everyday arithmetic

Percentage: think in hundreds

Turn percentages into pictures, compare changes fairly, and recover an original value after a percentage change.

BeginnerAbout 13 min3 worked examples
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01 / THE STARTING POINT

Before you begin

What you need: Fractions, decimals and multiplication.

  • Find a percentage of a quantity
  • Calculate percentage increase or decrease
  • Reverse a percentage change
02 / BUILD THE CONCEPT

Understand the idea

Percent means per hundred

25% means 25 out of 100, or 1/4. A percentage compares a part with a chosen whole; always identify what counts as 100%.

The original value is the comparison base

An increase from 80 to 100 is 20 out of the original 80, so it is 25%. Reversing the journey is a decrease of 20 out of 100, or 20%.

Multipliers make changes easier

An increase of r% multiplies a value by 1 + r/100; a decrease multiplies it by 1 − r/100. Reverse a change by dividing by that multiplier.

03 / A DIFFERENT WAY TO SEE IT

25% is one quarter

25%

25 / 100
= 1 / 4
= 0.25

25 of the 100 equal squares are highlighted. The whole grid represents 100%.
04 / FROM IDEA TO ANSWER

A method you can reuse

KEEP THIS HANDY

Percentage change = (new − original) ÷ original × 100%

The original value must be nonzero. A negative result indicates a decrease for a positive original.
  1. Identify the whole or original quantity.
  2. Convert the percentage to a fraction or decimal multiplier.
  3. Multiply for a forward change; divide by the multiplier to recover the original.
A useful insight

x% of y equals y% of x. For example, 8% of 25 is 25% of 8 = 2.

05 / WATCH THE METHOD WORK

Worked examples

Read the question first. Try a step yourself, then compare your reasoning.

EXAMPLE 01

Find a part

Find 18% of 250.

  1. 10% of 250 is 25.
  2. 8% of 250 is 20.
  3. 25 + 20 = 45.
Answer45
EXAMPLE 02

Compare two values

A score rises from 80 to 100. Find the percentage increase.

  1. Increase = 100 − 80 = 20.
  2. Use the original 80 as the base.
  3. 20/80 × 100% = 25%.
Answer25% increase
EXAMPLE 03

Work backwards

A price after a 20% discount is ₹640. Find the original price.

  1. After the discount, 80% of the original remains.
  2. Write 0.8 × original = 640.
  3. Original = 640 ÷ 0.8.
Answer₹800
06 / YOUR TURN

Check your understanding

Quick questions, with explanations. These are for self-study and do not affect your account score.

0 of 3 questions checked

QUESTION 1What is 15% of 200?

See the explanation

30. 10% is 20 and 5% is 10, giving 30.

QUESTION 2A value rises from 200 to 250. What is the increase?

See the explanation

25%. 50/200 × 100% = 25%.

QUESTION 3₹500 increases by 10%, then decreases by 10%. What remains?

See the explanation

₹495. 500 × 1.1 × 0.9 = 495. The decrease uses the new, larger base.

07 / TAKE THE NEXT STEP

Put your understanding to work

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EXPLORE THE NUMBERS

Percentage Calculator

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Percentage Practice Quiz 1

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Percentage Practice Quiz 2

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Percentage Practice Quiz 3

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Percentage practice

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NEXT LESSONRatio and Proportion
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