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Mathematics: relationships for creating · Lesson 04 / 08

Percentage: of what?

An imaginary energy display shows 100 units. Saving 20% leaves 80. But what happens when it starts at 150? The base changes the result.

Learning paths9 min

Let's discover together

  1. 1

    20% means 20 out of every 100, or 20 ÷ 100 = 0.2. Find 20% of a quantity by multiplying it by 20 and dividing by 100.

  2. 2

    Of 150 units, 20% is 30. After the reduction, 150 − 30 = 120 remain. Do not subtract just 20 units: 20% is a relationship to the base.

  3. 3

    Reducing 100 by 20% gives 80. Increasing those 80 by 20% adds 16 and gives 96, not 100. The second percentage uses a different base.

  4. 4

    A fixed part is not automatically reduced. If a rule reduces only materials, calculate the percentage of the materials and then add the fixed part.

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YOUR MISSION

Calculate a percentage and identify the quantity it applies to.

Now it's your turn

Discovery workshop

Always identify the base

Trial A: reduce 150 units by 20%. Trial B: increase 80 units by 20%.
Build your answers and check when you are ready.
A moment to understand

Why might reducing by 20% and increasing by 20% not restore the start?

I need a hint

Ask “20% of which quantity?” at each step.

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Take it with you

Show two ways to calculate 25% of 80. Then explain why a 25% reduction in materials need not affect fixed preparation.

At your own pace

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