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The unit and equivalent fractions

Key idea: A fraction names equal parts of a chosen whole. Equivalent fractions keep the amount while changing the part size.

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  • MOE teaching syllabus · Primary 5 Mathematics (taught from 2025)
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Name the whole before the fraction

A fraction names parts of a chosen whole. In 3/4, the denominator, 4, says the whole is cut into quarters. The numerator, 3, counts three of those quarters.

Check your understanding 1

Half of which ribbon?

Ribbon A is 12 cm long. Ribbon B is 20 cm long.

Is half of every ribbon the same length? Find out.

Why are the two halves different lengths?
Show answerHide answer

Half of A is 6 cm; half of B is 10 cm. Both are one half, but the wholes are different. Always ask: a fraction of what?

Rename an amount without changing it

Both strips are the same whole. The second strip cuts each half into three equal pieces.

The shaded amount stays fixed

Each full strip is one equal-sized whole.

Both full strips are the same whole. Only the part size changes.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Halvesmarked; empty
Sixthsmarked; marked; marked; empty; empty; empty

Point to the shaded part in both strips. Is it the same amount?

Why both numbers changeHide answer
1/2 = 3/6.

Each half became 3 sixths, so both numbers were multiplied by 3. The shaded amount did not grow.

Group pieces the other way

Now join pieces. Every two eighths make one quarter.

Two eighths make one quarter

Each full strip is one equal-sized whole.

Both strips are the same whole.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Eighthsmarked; marked; marked; marked; marked; marked; empty; empty
Quartersmarked; marked; marked; empty

Pair up the shaded eighths. How many quarters do the pairs make?

Division can give a fraction

3 loaves are shared equally among 4 people.

Watch how one person's share is made.

Each loaf cut into quarters

Each full strip is one equal-sized whole.

Three loaves, each in 4 equal pieces.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Loaf 1empty; empty; empty; empty
Loaf 2empty; empty; empty; empty
Loaf 3empty; empty; empty; empty

One person's pieces

Each full strip is one equal-sized whole.

The shaded quarters go to one person.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Loaf 1marked; empty; empty; empty
Loaf 2marked; empty; empty; empty
Loaf 3marked; empty; empty; empty

One share, put together

Each full strip is one equal-sized whole.

Three quarters of one loaf.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
One person's sharemarked; marked; marked; empty
  1. Cut every loaf into 4 equal pieces. One piece for each person.
  2. One person takes one quarter from each of the 3 loaves.
  3. Join the 3 quarters: three quarters of a loaf. 3 ÷ 4 = three quarters.
3÷4 = (3/4) of a loaf.

The whole is one loaf, not all three loaves. Four shares of 3/4 loaf make the 3 loaves again.

Write the same share as a decimal.

Check your understanding 2

Sharing five pizzas

5 pizzas are shared equally among 4 people. Each person gets more than one pizza.

Each person gets one whole pizza. What happens to the last pizza?

Which check accounts for all five pizzas?
Show answerHide answer

5÷4 = 5/4 = 1 1/4 = 1.25 pizzas each. Four shares of 1 1/4 use all five pizzas. Each share is more than one pizza, so its fraction is more than 1.

Count parts across more than one whole

2 3/5 means 2 whole strips and 3 fifths of another strip of the same size.

Two and three fifths

Each full strip is one equal-sized whole.

Every strip is the same whole, cut into fifths.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Whole 1marked; marked; marked; marked; marked
Whole 2marked; marked; marked; marked; marked
Part of whole 3marked; marked; marked; empty; empty

Each whole has 5 fifths. Count every shaded fifth.

Before you move on

Show that 9/6 = 1 1/2 = 1.5. Name the whole, the unit (sixths) and how many units there are.

Six sixths make one whole. What is left over?

Show answerHide answer

Six sixths make one whole. Three sixths are left, and 3/6 = 1/2. So 9/6 = 1 1/2 = 1.5.

For a grown-up

Pip’s synthetic voice uses the University of Edinburgh’s Alba speech dataset, via Piper’s Alba voice, under CC BY 4.0. Audio is optional.

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