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YEAR 3 · FRACTIONS · 12 MIN

Completing a whole

Find the fraction parts needed to rebuild one whole.

In this lesson

Before you start
  • Counting multiples of unit fractions
01 / LEARN

Understand the idea.

Rebuild the whole

A whole contains all its equal parts: two halves, three thirds, four quarters, five fifths or ten tenths. To complete a partly filled whole, find how many of that same kind of part are still missing.

If three fifths are coloured, count up to five fifths. Two more fifths complete the strip. The coloured and uncoloured fractions together must cover the whole once, without a gap or overlap.

Think about parts, not just numbers

Ask how many more pieces of the current size you need. If one quarter is present, the whole needs four quarters, so three more quarters are missing. Count the pieces before writing the fraction.

Keep the denominator unchanged because the whole is still divided into the same-sized parts. Subtract the chosen part count from the total part count. The result becomes the numerator of the missing fraction.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Finish a strip

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

Worked solution

  1. 1

    Identify the total number of equal parts.

    1010=1

    Ten tenths make the complete strip.

  2. 2

    Count the parts that are not blue.

    10−7=3

    Remove the seven blue parts from the ten parts altogether.

  3. 3

    Write the uncoloured fraction.

    310

    Three parts remain and each is still one tenth of the strip.

Answer

310 is not blue.

EXAMPLE 02

Make one whole

What fraction joins one third to make one whole?

Worked solution

  1. 1

    Express the whole in thirds.

    1=33

    Three one-third pieces make one whole.

  2. 2

    Count how many thirds are missing.

    3−1=2

    One of the three required pieces is already present.

  3. 3

    Check the completing fraction.

    13+23=33=1

    Two more thirds join the existing third to fill the whole.

Answer

Two thirds, 23.

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

One quarter.

A whole rectangle has four quarters. With three coloured, 4−3=1 quarter remains, so the uncoloured fraction is 14.

Keep practising

6 worksheet questions

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

    Two halves make one whole. One is missing.

    One half.
  2. Two thirds are shown. What fraction is missing?

    Three thirds make a whole; 3−2=1.

    One third.
  3. One quarter is shown. What fraction is missing?

    Four quarters make a whole; 4−1=3.

    Three quarters.
  4. Four fifths are coloured. What fraction is not coloured?

    Five fifths make a whole; 5−4=1.

    One fifth.
  5. Six tenths are used. What fraction remains?

    Ten tenths make a whole; 10−6=4.

    Four tenths.
  6. 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.
Checking saved progress…
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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