Completing a whole | Year 3

01 / LEARN

The idea, step by step

Rebuild the whole

A whole contains all its equal parts: 2 halves, 3 thirds, 4 quarters, 5 fifths or 10 tenths. To find what is missing, count how many parts are already there.

If 3 fifths are coloured, 2 fifths are not coloured. Five fifths make the whole, so the chosen and missing parts must total 5 fifths.

Think about parts, not just numbers

Ask “How many more of this size part fill the whole?” If you have one quarter, three more quarters are needed.

Keep the same whole and the same part size. You do not need to change the denominator when finding the missing fifths or tenths. Count the missing pieces, then write their fraction.

A common trap

If three fifths are shown, the missing fraction is two thirds.

Instead: There are still 5 equal parts in the whole. Two parts are missing, so the missing fraction is two fifths.

02 / WORKED EXAMPLES

See the thinking

Example 1

Finish a strip

A strip is divided into 10 equal parts. Seven are blue. What fraction is not blue?

Ten tenths make the whole strip.
There are $10 - 7 = 3$ parts not blue. Each part is one tenth.

\frac{3}{10}

is not blue.

Example 2

Make one whole

What fraction joins one third to make one whole?

One whole has 3 thirds.
One third is already present, so $3 - 1 = 2$ thirds are needed.

Two thirds,

\frac{2}{3}

Check your understanding

Three quarters of a rectangle are coloured. What fraction is left?

Show answer

One quarter.

Four quarters make a whole, and $4 - 3 = 1$ quarter is missing.

03 / WORKSHEET

Your turn

6 questions · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

One half is shown. What fraction is needed for one whole?
Two thirds are shown. What fraction is missing?
One quarter is shown. What fraction is missing?
Four fifths are coloured. What fraction is not coloured?
Six tenths are used. What fraction remains?
A child says 3 quarters and 2 quarters make one whole. Explain the mistake.

Read the worked solutions

One half is shown. What fraction is needed for one whole?
Two halves make one whole. One is missing.
One half.
Two thirds are shown. What fraction is missing?
Three thirds make a whole; $3 - 2 = 1$ .
One third.
One quarter is shown. What fraction is missing?
Four quarters make a whole; $4 - 1 = 3$ .
Three quarters.
Four fifths are coloured. What fraction is not coloured?
Five fifths make a whole; $5 - 4 = 1$ .
One fifth.
Six tenths are used. What fraction remains?
Ten tenths make a whole; $10 - 6 = 4$ .
Four tenths.
A child says 3 quarters and 2 quarters make one whole. Explain the mistake.
$3 + 2 = 5$ quarters, which is more than the 4 quarters in one whole.
One whole is 4 quarters. Three quarters need only 1 more quarter.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Unit fractions; halves/thirds/quarters/fifths/tenths; multiples; completing a whole.

Official curriculum source ↗

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