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Year 6 · Mathematics · Number

Percentages

Connect percentages with fractions and decimals, and calculate common percentages of amounts, including discounts on prices in Australian dollars.

Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.

Learning goals

Learners will

  • Understand that a percentage is a number out of 100.
  • Convert between percentages, fractions and decimals.
  • Calculate 10%, 25% and 50% of an amount and use these to find discounts.

Success looks like

  • I can write a percentage as a fraction and a decimal.
  • I can find 10%, 25% and 50% of an amount of money.
  • I can work out a sale price after a percentage discount.

The big idea

Per cent means “out of 100”. If you shade 35 squares on a 100-square grid, you have shaded 35% of it. That is the same as 35100 or 0.35.

Some percentages are worth knowing by heart because they come up often:

  • 50% = 12 = 0.5
  • 25% = 14 = 0.25
  • 10% = 110 = 0.1
  • 75% = 34 = 0.75

To find 10% of an amount, divide it by 10. To find 50%, halve it. To find 25%, halve it and halve it again. Other percentages can be built from these. For example, 20% is double 10%, and 5% is half of 10%.

Shops often take a percentage off the price. To find the sale price, first work out the discount, then subtract it from the original price. For a $60 jacket with 10% off, the discount is $6, so the sale price is $60 − $6 = $54.

Worked examples

Converting a percentage

Write 35% as a fraction in simplest form and as a decimal.

  1. 35% means 35 out of 100, so it is 35100.
  2. 35 and 100 share a common factor of 5: 35 ÷ 5 = 7 and 100 ÷ 5 = 20, giving 720.
  3. 35 hundredths written as a decimal is 0.35.

Answer: 35% = 720 = 0.35

Finding 25% of an amount

What is 25% of $80?

  1. 25% is the same as one quarter.
  2. Halve $80 to get $40.
  3. Halve again to get $20.

Answer: 25% of $80 is $20.

Working out a sale price

A pair of shoes usually costs $90. They are on sale with 20% off. What is the sale price?

  1. 10% of $90 is $90 ÷ 10 = $9.
  2. 20% is double 10%, so the discount is $18.
  3. Sale price = $90 − $18 = $72.

Answer: The sale price is $72.

Practice check

Have a go, then check your answers. Each answer comes with an explanation.

  1. 1.Which fraction is equal to 50%?
  2. 2.What is 0.07 written as a percentage?
  3. 3.What is 10% of $350?
  4. 4.Which of these has the greatest value?
  5. 5.What is 25% of 48?
  6. 6.A scooter usually costs $120. It is on sale with 10% off. How many dollars is the sale price?
  7. 7.Write 34 as a percentage.
  8. 8.In a homeschool sports group of 30 children, 60% play netball. How many children play netball?
Answer guide for parents

  1. Which fraction is equal to 50%?

    1/2 — 50% is 50 out of 100, which simplifies to 12.

  2. What is 0.07 written as a percentage?

    7% — 0.07 is 7 hundredths, which is 7 out of 100, or 7%.

  3. What is 10% of $350?

    $35 — To find 10%, divide by 10: $350 ÷ 10 = $35.

  4. Which of these has the greatest value?

    70% — Convert each to a percentage: 70%, 0.6 = 60%, 12 = 50% and 35 = 60%. 70% is the greatest.

  5. What is 25% of 48?

    12 — 25% is one quarter. Half of 48 is 24 and half of 24 is 12.

  6. A scooter usually costs $120. It is on sale with 10% off. How many dollars is the sale price?

    $108 — 10% of $120 is $12. The sale price is $120 − $12 = $108.

  7. Write 34 as a percentage.

    75% — 34 = 75100, which is 75%.

  8. In a homeschool sports group of 30 children, 60% play netball. How many children play netball?

    18 — 10% of 30 is 3, so 60% is 6 × 3 = 18.

Watch out for

  • Thinking 0.07 is 70% because the digit 7 appears. Use a hundred square: 0.07 is only 7 small squares.
  • Subtracting the percentage number straight from the price, for example saying $90 with 20% off is $70. Always work out the dollar value of the discount first.
  • Believing that a percentage can never be more than 100%. In some situations, such as growth, it can be, though this lesson focuses on parts of a whole.

Tips for parents

  • Look at real sale signs when shopping or in catalogues and ask the learner to work out the sale price before you check.
  • Build up from 10%: once a learner is confident with 10%, they can find 20%, 30%, 5% and more by doubling, multiplying and halving.
  • Encourage the learner to estimate first: “Is the sale price going to be more or less than half the original?”

Go further

  • Plan a $200 shopping trip using a catalogue with discounted items. Calculate each sale price and keep a running total.
  • Survey family members about their favourite fruit, then show the results as percentages of the whole group.
  • Investigate: is taking 10% off and then another 10% off the same as taking 20% off? Try it with $100.