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Year 7 Maths | Understand, justify, check

Percentages depend on the whole

A percentage describes a proportion of a stated whole. Before calculating, identify what represents 100%. These examples connect familiar fractions with percentages, then distinguish the amount saved from the amount still payable.

What to notice

The percentage and the quantity have different roles. Twenty-five per cent means one quarter; it does not mean twenty-five objects unless the whole contains one hundred objects.

What to do

Rename the percentage as a fraction or decimal, apply it to the whole, and label the result. For a discount, take one further step: subtract the saving from the original price.

Why it works

Tracking the whole prevents a correct multiplication from answering the wrong question. A saving and a sale price are related quantities, but they are not interchangeable.

Work through an example

Find 15% of $80.

3/20 = 15% of the whole
Twenty equal parts represent $80, so each part is $4. Three parts are marked: 15% of the whole.
  1. 10% of $80 is $8; 5% is half of that, $4.
  2. Add the two parts: 15% of $80 is $12.
  3. This is the percentage amount, not a final price after a discount.

A common mistake

Multiplying by 15 rather than 0.15 makes the result one hundred times too large. Percent means out of one hundred.

A strategy to try

Estimate first. Fifteen per cent is less than one fifth, so the result should be below $16. Use that bound to challenge an implausible answer.

Try it now

Try three questions

No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.

1. What is 25% of 64?
Help: a starting point

Identify the quantity that represents 100%.

Help: the next step

Rename 25% as one quarter, then divide the whole into four equal parts.

2. Which decimal equals 3/5?
Help: a starting point

Think about how many tenths equal one fifth.

Help: the next step

Multiply both numerator and denominator by 2.

3. A $70 jacket is discounted by 20%. What is the sale price?
Help: a starting point

Calculate one fifth of the original price to find the saving.

Help: the next step

The amount payable is the original price minus the saving.

For parents and carers

Ask the learner to identify the whole and name the requested quantity. The printable percentage resource revisits these representations; the ratio lesson extends proportional thinking to comparisons between quantities.

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