Percentage means per hundred

What you will learn

• Read a percentage as a number of parts per hundred
• Convert between percentages, fractions and decimals
• Compare quantities fairly using percentages

Models used: hundred grids, fraction strips, number sentences, stories.

Before you start

• Tenths, hundredths and thousandths
• Equivalent fractions

Making the whole 100

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

Write 3/5 as a percentage.

1. We need an equivalent fraction with 100 parts.

   5 × ? = 100

   20

2. Multiply the top by the same number.

   3 × 20 = 60

   60/100 = 0.6 = 60%

3. So 3/5 = 60/100.

   3/5 = 60/100

4. Sixty hundredths is 60%.

   3/5 = 0.6 = 60%

Common mistakes to discuss

• Reading the digits of a decimal as the percentage. 0.4 is 4 tenths, which is 40 hundredths, so it is 40%.
• Comparing fractions with different wholes directly. 18/25 and 72/100 can only be compared once both are written over the same whole; percentages make that whole 100 every time.

Check your understanding

• say what 35% means on a hundred grid
• change 3/5 into 60%
• change 45% into 0.45 and 9/20
• explain why 0.4 is 40%, not 4%

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.