Lesson 3 of 4

Percentages.

About 20 minutes · 5 practice questions

A percentage is a part per hundred: how to find a percentage of an amount, why a discount is a multiplication, and why a fifty per cent rise and a fifty per cent fall do not bring you back to the start.

Step 1 of 5 · Out of a hundred

Step 1 of 5

Out of a hundred

Per cent means “per hundred”: $1\%$ ⁠ is $\frac{1}{100}$ ⁠, and $37\%$ ⁠ is $\frac{37}{100} = 0.37$ ⁠. The grid has $100$ ⁠ squares, so each square is one per cent. Move Shaded squares and notice how the fraction, the decimal and the percentage change together.

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Step 2 of 5

A percentage of an amount

When the whole grid stands for an amount, each square is a hundredth of it. If the grid is $80$ ⁠ shekels, one square is worth $\frac{80}{100} = 0.8$ ⁠ shekels. To find a percentage of an amount you multiply: $30\%$ ⁠ of $80$ ⁠ is $0.3 \times 80$ ⁠. Answer, then drag Look inside to check.

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Step 3 of 5

A rise, then a fall

Here each bar is an amount, and its length matches its size. The violet bar is the starting price, and the dashed line marks its length on the bars below it too. Predict what happens to the price after a rise and a fall by the same percentage.

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Step 4 of 5

A discount is a multiplication

A $20\%$ ⁠ discount leaves $80\%$ ⁠ of the price, so you can work it out in one step: multiply by $0.8$ ⁠. A $20\%$ ⁠ rise is a multiplication by $1.2$ ⁠. Each bar shows the number it multiplies by.

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Step 5 of 5

Undoing a rise

A percentage change is always worked out from the amount there at that moment. So to get back after a rise, a fall by the same percentage is not always enough. Try different values of Second change.

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Interactive scene

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Each step sets up the Scene for you, and a control marked “fixed” stays put for that step.

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Practice · Reach the target

Use Shaded squares to shade three quarters of the grid, then press Check.

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Practice · Calculate

The whole grid stands for $80$ ⁠ shekels, and $30$ ⁠ squares are shaded. What is $30\%$ ⁠ of $80$ ⁠?

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Practice · Predict, then look

A price of $100$ ⁠ shekels rose by $50\%$ ⁠, then fell by $50\%$ ⁠. What is the price at the end?

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Practice · Calculate

A coat that costs $200$ ⁠ shekels is reduced by $20\%$ ⁠. What does it cost after the discount?

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Practice · Reach the target

The price rose by $25\%$ ⁠, from $100$ ⁠ to $125$ ⁠. Choose a Second change that brings it back to exactly $100$ ⁠, then press Check.