Find a percentage of a quantity

What you will learn

• Find a percentage of a quantity

Models used: number sentences, stories, tables.

Before you start

• Interpret percentages as parts out of 100

Percent is a share of one hundred

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.

   The same percentage can describe different quantities when the whole changes. In a change problem, identify the original whole.

   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: A new example, together

Find 10% of 280.

1. The share amount is unknown. Read each value with the heading above its column.

   Mark 100%, the percentage share and whether the question asks for that share or the final amount.

   A percentage part is that many hundredths of the whole.

   The share amount is unknown.

   Whole (100%)	Share required (%)
   280	10

2. The share amount is unknown. Read each value with the heading above its column.

   Identify the whole.

   The share amount is unknown.

   Whole (100%)	Share required (%)
   280	10

   Find 10% of 280.

   28

3. The share amount is unknown. Read each value with the heading above its column.

   Identify the whole.

   The share amount is unknown.

   Whole (100%)	Share required (%)
   280	10

4. The share amount is unknown. Read each value with the heading above its column.

   One percent is 280 ÷ 100.

   The share amount is unknown.

   Whole (100%)	Share required (%)
   280	10

5. The share amount is unknown. Read each value with the heading above its column.

   280 ÷ 100 × 10 = 28.

   The share amount is unknown.

   Whole (100%)	Share required (%)
   280	10

6. The share amount is unknown. Read each value with the heading above its column.

   Check the result against the question we started with.

   28 ÷ 280 = 10/100.

   We found 28. A percentage part is that many hundredths of the whole.

   The share amount is unknown.

   Whole (100%)	Share required (%)
   280	10

Common mistakes to discuss

• Treating the percentage as the answer. Find one part of a hundred first. 30% of 90 is 27, because one per cent is 0.9.

Check your understanding

• Find a percentage of a quantity
• connect a percentage, its reference whole and the requested quantity
• check the answer against the original quantities and units

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.