A percentage of a quantity

What you will learn

• Find a percentage of a quantity
• Use 10% and 1% as stepping stones
• Solve discount problems and check the whole being used

Models used: percentage bars, hundred grids, bar models, stories.

Before you start

• Percentage means per hundred

Two reliable methods

This grid is one whole. It has 100 equal squares.

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   This grid is one whole. It has 100 equal squares.

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   0/100 = 0 = 0%

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Shade 25 squares. We have shaded one quarter of the whole.

   25 out of 100 = 25%

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

3. The full bar represents $80, which is 100%. The shaded share is 25%.

   Now the whole is $80. One quarter of $80 is $20.

   25% of $80 = $20

   Each section: 5% = $4

   0%100% = $80

   25% of $80 = $20

4. The complete bar is the whole. Each labelled section is one part of it.

   The fraction, decimal and percentage describe the same share.

   1/4 = 0.25 = 25%

   80

   20one quarter60three quarters

Worked example

15% of 60

1. Start with 10%.

   10% of 60 = 6

   What is 10% of 60?

   6

2. 5% is half of 10%.

   5% of 60 = 3

3. Add the steps.

   15% = 10% + 5% = 6 + 3

   What is 15% of 60?

   9

4. So 15% of 60 is 9.

   Each section: 5% = 3

   0%100% = 60

   20% of 60 = 12

5. Check with 1%: 60 ÷ 100 = 0.6, and 15 × 0.6 = 9.

   15% of 60 = 9 ✓

Common mistakes to discuss

• Using the percentage as the answer. 25% of 80 is not 25. The percentage tells you how much of the whole to take: 25% of 80 is 20.
• Adding percentages of different wholes. 50% off, then 50% off again, is not 100% off: the second discount is taken from the reduced price.

Check your understanding

• find 25% of 80 with a bar or by using 10%
• work out a discount and a sale price
• say which amount is the whole in a percentage question

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.