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Equal parts and fraction size

Key idea: Compare fractions of the same-sized whole. More equal parts make each part smaller.

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Enlarged diagram

Do the pieces match?

Let’s check the pieces. Each strip has two pieces. Which has matching pieces?

Two pieces: do their sizes match?

Compare the two pieces within each strip.

Both wholes are the same size. Both have two pieces.
Figure data

This table is included in print while it is open.

The visible pieces
StripPiecesLengths
A2The two lengths match
B2One shorter length and one longer length
Which strip is cut into halves?
Show answerHide answer

A. Two equal parts make halves. B has two unequal pieces. Neither piece is one half.

Name the whole, then its parts

Four equal parts make one whole. Three are marked: three quarters.

Point to the marked parts

Each full strip is one equal-sized whole.

The full strip is one whole. Shaded parts are selected.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
One wholemarked; marked; marked; empty

4 equal parts make the whole. 3 are marked: 3/4, three quarters.

Bottom: 4 equal parts in the whole. Top: 3 marked parts.

The fraction names

Find four at the bottom: the denominator. It counts the whole’s equal parts.

3/4
  1. Find four at the bottom: the denominator. It counts the whole’s equal parts.
  2. Point to three at the top: the numerator. It counts the marked parts.
Try with paper

Fold paper into four matching parts. Mark three. Ask someone to check your folds.

Build three quarters

Practise: Primary 2 Mathematics Equal parts, unit and like fractions practice · Primary 2 MathematicsPractise: Primary 5 Foundation Mathematics Fraction representations, mixed amounts and products practice · Primary 5 Foundation Mathematics

Check your understanding 1

Build three quarters

Make three quarters of one whole. Keep the pieces the same size.

Each piece is one quarter of the whole.

What this checks

Keep each piece the same size.

Show solutionHide answer

Three quarters

Each full strip is one equal-sized whole.

Three of the four equal parts are marked. One part is empty.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
One wholemarked; marked; marked; empty

Cut more pieces

Let’s compare parts. Compare matching wholes. Point to the larger marked part. What happens with more equal parts?

Compare one part

Each full strip is one equal-sized whole.

Both whole strips are the same size. Point to the larger marked part.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
One halfmarked; empty
One quartermarked; empty; empty; empty

A half is bigger than a quarter: 1/2 > 1/4. Use the same whole. More equal parts make each part smaller.

The numerator, or top number, is 1. These are unit fractions.

Compare two new pieces

Which is more: one third or one sixth? Compare matching wholes.

One third or one sixth?

Each full strip is one equal-sized whole.

Equal-sized wholes. Compare the marked parts.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
One thirdmarked; empty; empty
One sixthmarked; empty; empty; empty; empty; empty

Which marked part is larger?

Larger marked part
Show answerHide answer

1/3 > 1/6. The whole stayed the same size.

Same-sized parts: count how many

Let’s compare parts. The pieces and wholes match. Which strip has more eighths marked?

Compare eighths

Each full strip is one equal-sized whole.

Both wholes match in size. Both use eighths.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Two eighthsmarked; marked; empty; empty; empty; empty; empty; empty
Five eighthsmarked; marked; marked; marked; marked; empty; empty; empty

Each piece is the same size. Five eighths cover more than two eighths.

Make the fractions fit

Check your understanding 2

Make the fractions fit

Choose a fraction for each square. More than one way works. Keep the same whole.

1/(square) > 1/6

square/8 < 5/8

Show all the choicesHide answer

Bottom number: 2, 3, 4, 5. Fewer equal parts make each piece bigger. Your piece is bigger than a sixth.

Top number: 1, 2, 3, 4. Fewer eighth-pieces cover less than five eighths.

Look at the empty part

Which strip has more empty space?

Compare the unmarked parts

Each full strip is one equal-sized whole.

The wholes are the same size. Shaded parts are marked.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Amarked; marked; marked; empty
Bmarked; marked; marked; marked; marked; marked; marked; empty
Show answerHide answer

Greater than. A has 1/4 unmarked. B has 1/8 unmarked. Both wholes match. A quarter is bigger than an eighth.

Compare the gaps

Compare the unmarked parts

Each full strip is one equal-sized whole.

The wholes are the same size. Shaded parts are marked.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
Amarked; marked; marked; marked; marked; marked; marked; empty; empty
Bmarked; marked; marked; empty; empty; empty; empty; empty; empty
Show answerHide answer

Less than. 2/9 < 6/9. Both wholes use ninths. Count the empty pieces.

Check the pieces, then the sign

Do the pieces match the sign?

Check your understanding 3

Fix one comparison

Compare both cards

Each full strip is one equal-sized whole.

Same-sized wholes.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
A · 1/5marked; empty; empty; empty; empty
A · 1/3marked; empty; empty
B · 1/2marked; empty
B · 1/7marked; empty; empty; empty; empty; empty; empty

A · 1/5 > 1/3

B · 1/2 > 1/7

Show answerHide answer

A needs less than: 1/5 < 1/3. Each fifth is smaller than each third.

B already works: 1/2 > 1/7.

Check a new pair of cards

Check your understanding 4

Fix one comparison

Compare both cards

Each full strip is one equal-sized whole.

Same-sized wholes.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
A · 3/8marked; marked; marked; empty; empty; empty; empty; empty
A · 6/8marked; marked; marked; marked; marked; marked; empty; empty
B · 5/9marked; marked; marked; marked; marked; empty; empty; empty; empty
B · 2/9marked; marked; empty; empty; empty; empty; empty; empty; empty

A · 3/8 < 6/8

B · 5/9 < 2/9

Show answerHide answer

B needs greater than: 5/9 > 2/9. The pieces are the same size. Five pieces cover more than two.

A already works: 3/8 < 6/8.

Order fractions with one marked piece

Check your understanding 5

Order the unit fractions

Let’s put them in order. Point to marked amounts in order. Start with the smallest.

Put the fractions in order, smallest first.

What this checks

Keep all three cards. Compare the marked amounts.

Compare one part of each whole

Each full strip is one equal-sized whole.

All three wholes are the same size. Each has one marked part.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
A · 1/5marked; empty; empty; empty; empty
B · 1/2marked; empty
C · 1/8marked; empty; empty; empty; empty; empty; empty; empty

Show solutionHide answer

C, A, B: 1/8, 1/5, 1/2. More equal parts make one part smaller.

Order the eighths

Check your understanding 6

Order the eighths

Order the marked eighths. Point to the smallest first.

Put the fractions in order, smallest first.

What this checks

Keep all three cards. Compare the marked amounts.

Count same-sized pieces

Each full strip is one equal-sized whole.

The wholes are the same size. Every piece is an eighth.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
A · 3/8marked; marked; marked; empty; empty; empty; empty; empty
B · 1/8marked; empty; empty; empty; empty; empty; empty; empty
C · 7/8marked; marked; marked; marked; marked; marked; marked; empty

Show solutionHide answer

B, A, C: 1/8, 3/8, 7/8. The pieces are the same size. Count how many you marked.

Where does D fit?

A new fraction card

Each full strip is one equal-sized whole.

Same-sized wholes. A, B and C: smallest first.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
A · 1/10marked; empty; empty; empty; empty; empty; empty; empty; empty; empty
B · 1/6marked; empty; empty; empty; empty; empty
C · 1/3marked; empty; empty
D · 1/4marked; empty; empty; empty
Show answerHide answer

3rd. The wholes match in size. 1/6 < 1/4 < 1/3. D fits between B and C.

Place another card

A new same-sized-parts card

Each full strip is one equal-sized whole.

Same-sized wholes. A, B and C: smallest first.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
A · 2/9marked; marked; empty; empty; empty; empty; empty; empty; empty
B · 5/9marked; marked; marked; marked; marked; empty; empty; empty; empty
C · 7/9marked; marked; marked; marked; marked; marked; marked; empty; empty
D · 4/9marked; marked; marked; marked; empty; empty; empty; empty; empty
Show answerHide answer

2nd. The parts have the same size. 2/9 < 4/9 < 5/9. D fits between A and B.

Can you fix this order?

Check both rows

A: 1/2; 1/4; 1/8. B: 1/9; 1/6; 1/3.

Smallest first. Same-sized wholes. Fix one row.
Figure data

This table is included in print while it is open.

Values shown on the cards
SetValues
A1/2; 1/4; 1/8
B1/9; 1/6; 1/3
Show the repaired rowHide answer

A: swap 1st and 3rd. 1/8 < 1/4 < 1/2. The bottom numbers get smaller. The pieces get bigger.

B already works: 1/9 < 1/6 < 1/3.

Largest first this time

Check both rows

A: 6/7; 4/7; 2/7. B: 7/8; 3/8; 5/8.

Largest first. Same-sized wholes. Fix one row.
Figure data

This table is included in print while it is open.

Values shown on the cards
SetValues
A6/7; 4/7; 2/7
B7/8; 3/8; 5/8
Show the repaired rowHide answer

B: swap 2nd and 3rd. 7/8 > 5/8 > 3/8. Fewer eighths cover less of the whole.

A already works: 6/7 > 4/7 > 2/7.

Make your own unit fractions

Check your understanding 7

Make your own unit fractions

Choose three different unit fractions. Order them, smallest first.

Make three different unit fractions, smallest first. Use bottom numbers from 2 to 12. Keep the same whole.

What this checks

Compare the marked amounts.

Show solutionHide answer

One possible order

Each full strip is one equal-sized whole.

Same-sized wholes. Follow the marked amounts from smallest to largest.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
1/9marked; empty; empty; empty; empty; empty; empty; empty; empty
1/6marked; empty; empty; empty; empty; empty
1/3marked; empty; empty

1/9 < 1/6 < 1/3. The bottom numbers get smaller. The parts get bigger.

Your fractions may differ. Compare each pair: do the amounts get bigger?

Make your own eighths

Check your understanding 8

Make your own eighths

Make three different fractions in eighths. Order them, biggest first.

Make three different fractions with bottom number 8, largest first. Use top numbers from 1 to 7. Keep the same whole.

What this checks

Compare the marked amounts.

Show solutionHide answer

One possible order

Each full strip is one equal-sized whole.

Same-sized wholes and same-sized parts. Follow the marked amounts from largest to smallest.
Figure data

This table is included in print while it is open.

Equal parts in the picture
WholeParts in order
6/8marked; marked; marked; marked; marked; marked; empty; empty
4/8marked; marked; marked; marked; empty; empty; empty; empty
1/8marked; empty; empty; empty; empty; empty; empty; empty

6/8 > 4/8 > 1/8. The pieces stay the same size. Fewer pieces cover less.

Your fractions may differ. Compare each pair: do the amounts get smaller?

Keep the whole the same

Let’s check the whole. Could a quarter cover more than a half? Compare the wholes, then their shaded pieces.

What if the whole changes?

Both strips have the same height. Their whole lengths differ.

Different-sized wholes. Compare the striped pieces.
Figure data

This table is included in print while it is open.

Different wholes in this example
WholeEqual partsMarked amount
Small strip2One half
Larger strip: more than twice as long4One quarter, longer than the marked half

Draw one small whole and one large whole. Mark half the small one. Mark a quarter of the large one. Can the quarter be bigger?

Show answerHide answer

Yes. The marked quarter comes from a longer whole. Compare the wholes’ sizes first. Then compare the marked amounts.

Name a new fraction

Split a whole into six equal parts. Mark five and name your fraction. Mark one sixth on a matching whole.

Show answerHide answer

5/6 and 1/6. Both use sixths. Five sixths cover more than one sixth.

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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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