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← Back to Commercial Maths & Proportion
1Percentage2Unitary Method3Percentage of a Quantity4Ratio & Proportion5Speed, Distance & Time6Simple Interest7Counting Principle

Concept 1 of 7

Percentage: Out of 100

1

Today's big idea

Per cent means per hundred, so a percentage is a fraction with 100 fixed underneath.

A bigger top does not mean a bigger share, because the bottom counts too.

2

How it works

👀 What's going on?

Marks come as 18 out of 20, a discount comes as 15 percent, and a battery comes as a bar. All three are the same idea wearing different clothes.

💡 Here's the trick

Percentage = out of 10025 of 100 squares shaded = 25%25% = 25/100 = 1/4 = 0.25Same value, three forms

Look at the grid above. Per cent means per hundred, so a percentage is just a fraction whose bottom is fixed at 100. Rewriting anything with 100 underneath turns it into a percentage.

🪄 How to do it

  1. 1.Read the value off the grid above as a fraction.
  2. 2.Rescale that fraction so its bottom becomes 100.
  3. 3.The top of the rescaled fraction is the percentage.

✍️ Try it

Write 21 out of 25 as a percentage. Then: write 0.35 as a percentage.

Multiplying top and bottom of 21 out of 25 by 4 gives 84 out of 100, so it is 84 percent. For the decimal, 0.35 times 100 gives 35 percent.

⚠️ Watch out

You might be thinking a bigger top always means a bigger percentage. It does not, because the bottom matters just as much. 18 out of 20 beats 24 out of 30, even though 24 is the larger number.

🌟 Why this matters

Discounts, battery levels and interest rates are all quoted this way, so reading them fluently is ordinary literacy rather than a school skill.
Exam tip: Learn 1/4, 1/5, 1/8 and 1/3 as percentages, since they turn up constantly.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Express 3/5 as a percentage.”

  1. 1

    Multiply by 100

    3/5 × 100

  2. 2

    Compute

    = 300/5 = 60.

  3. 3

    Add the '%' sign

    60%

  4. 4

    Answer ✓

    60%

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Multiply a fraction by 100 to get a percentage. Divide a percentage by 100 to get a fraction.

CONVERT · ROUND 1 OF 3

Express 1/4 as a percentage.

5

Quick check

✅ VERIFICATION

Which score is the highest?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Unitary Method

Divide for one, multiply for many.

Concept 2 of 7 →