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Year 5 · Mathematics · Number

Fractions and decimals

Count by fractions, compare fractions with related denominators and connect tenths and hundredths to decimals, including in money.

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. How we review

These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.

Learning goals

Learners will

  • Count forwards by unit fractions such as halves, quarters, thirds and fifths, including past one whole.
  • Compare fractions whose denominators are related, such as quarters and eighths.
  • Connect tenths and hundredths to decimals, including amounts of money.

Success looks like

  • I can count by quarters and say where one whole comes in the count.
  • I can explain which of two fractions is larger when one denominator is double the other.
  • I can write tenths and hundredths as decimals, such as 710 = 0.7 and 35 cents = $0.35.

The big idea

We can count with fractions just as we count with whole numbers. Counting by quarters goes: 14, 24, 34, 44, 54, 64… When we reach 44, we have four quarters, which is one whole. So 44 = 1, and the count can carry on as 1 14, 1 24 and so on.

To compare fractions, they need to be parts of the same-sized whole. Fold one paper strip into quarters and an identical strip into eighths. You will see that each quarter is exactly the same size as two eighths. So 14 = 28, 24 = 48 and 34 = 68.

This helps us compare fractions with related denominators, where one denominator is double (or a multiple of) the other. Is 34 or 58 larger? Change the quarters into eighths: 34 = 68. Since 68 is more than 58, 34 is larger.

Remember that a larger denominator means smaller pieces. One eighth is smaller than one quarter, because the whole is cut into more pieces.

Tenths come from splitting a whole into 10 equal parts. We can write 710 as the decimal 0.7. The 0 shows there are no whole ones, the decimal point separates the wholes from the parts, and the 7 is in the tenths place.

Hundredths come from splitting a whole into 100 equal parts. On a 10 × 10 grid, each small square is 1100. Shading 35 squares shows 35100, which we write as 0.35: 3 tenths (3 full columns of 10) and 5 hundredths.

Money uses hundredths every day. One dollar is 100 cents, so each cent is one hundredth of a dollar. That is why 35 cents is written $0.35, and $2.50 means 2 dollars and 50 cents.

Worked examples

Counting by thirds

Count by thirds from 13 to 2.

  1. Start at 13, then add one third each time: 13, 23, 33.
  2. 33 is three thirds, which is one whole, so we can say 1.
  3. Keep going: 43, 53, 63. Six thirds is two wholes.

Answer: 13, 23, 1, 43, 53, 2

Comparing related fractions

Which is larger, 23 or 56?

  1. The denominators are 3 and 6. 6 is double 3, so each third is the same size as two sixths.
  2. Change 23 into sixths: 2 thirds = 4 sixths, so 23 = 46.
  3. Compare: 56 is more than 46.

Answer: 56 is larger than 23.

Hundredths, decimals and money

Write 48100 as a decimal, and write 48 cents in dollars.

  1. 48 hundredths is 4 tenths and 8 hundredths.
  2. Write 0 for no whole ones, then the decimal point, then 4 in the tenths place and 8 in the hundredths place: 0.48.
  3. A cent is one hundredth of a dollar, so 48 cents is 48100 of a dollar, which is $0.48.

Answer: 48100 = 0.48, and 48 cents = $0.48.

Practice check

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

  1. 1.Count by quarters: 14, 24, 34, … What comes next?
  2. 2.Which is larger, 34 or 58?
  3. 3.Which decimal shows seven tenths?
  4. 4.Which decimal shows 35 hundredths?
  5. 5.Write 910 as a decimal.
  6. 6.Write 42100 as a decimal.
  7. 7.A pencil costs 65 cents. Write this amount in dollars using a decimal point.
  8. 8.Which is smaller, 23 or 56? (Type your answer like 1/2.)
Answer guide for parents

  1. Count by quarters: 14, 24, 34, … What comes next?

    4/4 — Add one more quarter to 34 to get 44, which is one whole.

  2. Which is larger, 34 or 58?

    3/4 — 34 = 68, and 68 is more than 58, so 34 is larger.

  3. Which decimal shows seven tenths?

    0.7 — Seven tenths has no whole ones and 7 in the tenths place: 0.7.

  4. Which decimal shows 35 hundredths?

    0.35 — 35 hundredths is 3 tenths and 5 hundredths, which is written 0.35.

  5. Write 910 as a decimal.

    0.9 — Nine tenths has no whole ones and 9 in the tenths place: 0.9.

  6. Write 42100 as a decimal.

    0.42 — 42 hundredths is 4 tenths and 2 hundredths: 0.42.

  7. A pencil costs 65 cents. Write this amount in dollars using a decimal point.

    $0.65 — There are 100 cents in a dollar, so 65 cents is 65100 of a dollar, which is $0.65.

  8. Which is smaller, 23 or 56? (Type your answer like 1/2.)

    2/3 — 23 = 46, and 46 is less than 56, so 23 is smaller.

Watch out for

  • Thinking a bigger denominator means a bigger fraction, for example that 18 is more than 14. Compare paper strips folded into quarters and eighths to show that more pieces means smaller pieces.
  • Writing 5 hundredths as 0.5 instead of 0.05. Use the 10 × 10 grid: 0.5 is five whole columns (50 squares), but 0.05 is only five small squares.
  • Stopping a fraction count at the whole, as if fractions cannot go past 1. Count paper quarters aloud and keep going to 54, 64 and beyond.

Tips for parents

  • Use food to count by fractions: cut sandwiches or oranges into quarters and count the pieces as you put them on a plate.
  • Read prices aloud together and talk about what each digit means: in $3.45, the 4 means 4 tenths of a dollar (40 cents).
  • Always compare fractions using wholes that are the same size. Two halves of a large pizza and a small pizza are not the same amount.

Go further

  • Make a fraction wall with strips for halves, quarters and eighths, then another with thirds and sixths. List all the equal pairs you can find.
  • Shade amounts on 10 × 10 grids, such as 0.3, 0.30 and 0.03, and explain which are the same and which are different.
  • Set up a pretend shop with prices under $1 written as decimals, and buy items using coins.

About 45 minutes

Make a lesson planAssign to my child

You'll need

  • Paper strips of the same length
  • Coloured pencils and a ruler
  • A 10 × 10 grid drawn on paper (100 small squares)
  • Some coins (optional)

Key words

Fraction
A number that describes equal parts of a whole, such as 34.
Denominator
The bottom number in a fraction. It tells how many equal parts the whole is split into.
Numerator
The top number in a fraction. It tells how many of the equal parts we have.
Tenth
One of 10 equal parts of a whole. One tenth is written 110 or 0.1.
Hundredth
One of 100 equal parts of a whole. One hundredth is written 1100 or 0.01.
Decimal point
The dot that separates whole numbers from parts of a whole, as in 2.5.
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