Year 7 · Unit 2 Percentages · Lesson 1 of 6

What does per cent count?

Per cent means out of 100. Shade squares on a hundred grid, then on wholes that are not cut into 100 parts, and see how one share gets its percentage.

Number and AlgebraNo calculator

Warm-up

Three quick ones from earlier work. Try each in your head or on paper before you open the answer.

  1. (Unit 1, lesson 1) What is the value of the 3 in 0.37?
    Answer0.3, three tenths.
  2. (Unit 1, lesson 1) What is 3.6 × 100?
    Answer360. Each digit moves two places to the left.
  3. (Unit 1, lesson 5) What is the greatest common factor of 20 and 100?
    Answer20, because 20 divides 100 exactly.
Words used in this lesson
per cent (%)
out of 100. For example: 35% means 35 out of 100.
percentage
an amount written as a number of hundredths. For example: a percentage of 25 is 25 out of 100.
whole
the full amount a share is taken from. For example: the whole grid is 100 squares.
part
one piece of the whole. For example: one slice of 8 equal slices.
equal parts
pieces that are all the same size. For example: a bar cut into 20 equal parts.
benchmark
a percentage worth knowing by heart. For example: 50%, 25%, 10% and 1%.

Out of 100, every time

Your phone shows 35% battery. A friend's phone shows 35% as well, though her battery is much bigger. What is the same about the two phones? Not the amount of charge: the share. Per cent means out of 100, so 35% says “35 hundredths of this phone's own full battery”. The size of the whole can be anything.

Predict first: if 35 squares of a hundred grid are shaded, what fraction of the grid is that, in its simplest form? Then slide to check. Keep going past 100 and see what happens.

35
35%percentage
7/20fraction, simplest form
0.35decimal

35 squares out of 100 are shaded: 35%, which is 7/20 or 0.35 of the whole.

Show me the steps
  1. 1 square shaded: 1%, which is 1/100 or 0.01.
  2. 10 squares: 10%, which is 1/10 or 0.1.
  3. 25 squares: 25%, which is 1/4 or 0.25.
  4. 50 squares: 50%, which is 1/2 or 0.5.
  5. 100 squares, the whole grid: 100%, which is 1 whole.
  6. 150 squares: a full grid and half of a second one. 150% is 3/2, or 1.5 wholes: more than the whole.

Per cent means out of 100. 1% is one hundredth of the whole, 100% is the whole, and 35% is 35 hundredths: 35/100 = 7/20 = 0.35. A percentage can be more than 100%: 150% is one whole and half of another.

Four to remember: 50% = 1/2, 25% = 1/4, 10% = 1/10 and 1% = 1/100.

A percentage is a share of a whole. Without the whole it says nothing about an amount: 30% of a small bottle and 30% of a large bottle are not the same volume.

When the whole is not 100 parts

Real wholes come in 20 pieces, 8 slices or 25 beds. Cut the whole into equal parts and one part is 100 ÷ (number of parts) per cent. Then count the parts you want. Move both sliders.

8
3
12.5%one part is
37.5%shaded share

The whole is cut into 8 equal parts, so one part is 100 ÷ 8 = 12.5%. 3 parts are 3 × 12.5 = 37.5%.

Show me the steps
  1. 4 equal parts, 1 shaded: each part is 100 ÷ 4 = 25%, so the share is 25%.
  2. 5 equal parts, 2 shaded: each is 20%, so 2 parts are 40%.
  3. 8 equal parts, 3 shaded: each is 12.5%, so 3 parts are 37.5%.
  4. 20 equal parts, 7 shaded: each is 5%, so 7 parts are 35%.
  5. 40 equal parts, 7 shaded: each is 2.5%, so 7 parts are 17.5%.
  6. 50 equal parts, all 50 shaded: each is 2%, so the whole is 100%.

A common mistake: “8 out of 20 is 8%.” The 8 counts parts. A percentage counts hundredths of the whole. Each of 20 parts is 5%, so 8 parts are 8 × 5 = 40%.

Worked example: from parts to a percentage

A school garden has 25 beds and 7 are planted with beans. What percentage is planted with beans?

  1. One bed is 100 ÷ 25 = 4% of the garden.
  2. 7 beds are 7 × 4 = 28%.
  3. Check: 7/25 = 28/100, because 25 × 4 = 100 and 7 × 4 = 28. 28%.

Your go. The first step is given. A netball team scored in 12 of its 20 matches. What percentage of its matches did it score in?

  1. One match is 100 ÷ 20 = 5% of the season.
  2. Now find 12 matches yourself, then check.
Check the answer

12 × 5 = 60, so the team scored in 60% of its matches. In fractions: 12/20 = 60/100.

Check before you go on

1. A bar is cut into 20 equal parts and 5 of them are shaded. What percentage of the bar is shaded?

Your turn

Start at Level 1 and go as far as you can. A wrong answer gets a reason, not just a cross: read it, then try again.

Level 1 · Getting started

2. In a class of 25 students, 9 walk to school. What percentage of the class walks?

3. Which of these is the same as 7%?

Level 2 · Building

4. 135% is shaded using two hundred grids: the first is full. How many squares of the second grid are shaded?

5. Kofi scored 36 out of 40 in a quiz. What percentage did he score?

6. A flatbread is cut into 8 equal slices. What percentage of the flatbread is one slice? Give your answer to one decimal place.

Level 3 · Stretch

7. On a hundred grid, 24 squares are shaded. On a grid of 50 squares, how many must be shaded to show the same percentage?

8. A cloth strip has 20 equal parts. 30% of it is dyed red and 45% is dyed blue. The rest is white. How many parts are white?

Something to think about

A bean plant was 20 cm tall and is now 50 cm tall. The new height is what percentage of the old height? Can a percentage be more than 100%?

One way to think about it

50 ÷ 20 = 2.5, which is 250 per 100, so the new height is 250% of the old one. A percentage above 100% means more than the starting whole: here two and a half times as tall.

Exit ticket

9. Amara got 18 out of 40 in a test and 45% in a quiz. Which statement is right?