The idea, step by step
Useful fraction names
Two equal parts are halves. Three are thirds, four are quarters, five are fifths and ten are tenths. Each name tells how many equal pieces rebuild the whole.
Fold a paper strip in half, then fold each half in half again. There are now 4 equal parts, so each is one quarter. Keep the folds the same size.
| Equal parts in one whole | Name of one part |
|---|---|
| 2 | One half |
| 3 | One third |
| 4 | One quarter |
| 5 | One fifth |
| 10 | One tenth |
More parts means smaller pieces
Compare fractions using wholes of the same size. If the same strip is divided among 2 people, each share is larger than when it is divided among 5 people.
For unit fractions of the same whole, the larger denominator gives the smaller part. A tenth is smaller than a fifth, because ten equal pieces must fit in the same space.
A common trap
A tenth is bigger than a half because 10 is bigger than 2.
Instead: The denominator counts how many equal pieces share the same whole. More pieces means each piece is smaller.
See the thinking
Compare two shares
Two equal-sized pizzas are used. Ana gets one half of one pizza. Bo gets one quarter of the other. Who gets more?
- The pizzas have the same size, so the fractions can be compared fairly.
- Two quarters make one half. One quarter is only half of that share.
Name a fold
A strip is folded into 5 equal panels. Name one panel.
- Count all 5 equal panels in the whole.
- One of 5 equal panels is one fifth.
Check your understanding
Which is larger: one third or one fifth of the same strip?
Show answer
One third.
Dividing the same strip into 3 equal parts gives larger pieces than dividing it into 5.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Name one of 4 equal parts.
- Write one half as a fraction.
- Put these fractions from smallest to largest: .
- A strip has 3 equal panels. What fraction is one panel?
- How many tenths make one whole?
- Can you compare a half of a tiny biscuit and a quarter of a very large cake using only the fraction names? Explain.
Read the worked solutions
- Name one of 4 equal parts.
Four equal parts make a whole.
One quarter. - Write one half as a fraction.
One of 2 equal parts is chosen.
. - Put these fractions from smallest to largest: .
For the same whole, more equal parts means each unit fraction is smaller.
. - A strip has 3 equal panels. What fraction is one panel?
Three equal panels make the whole.
. - How many tenths make one whole?
Ten parts, each one tenth, rebuild the whole.
10 tenths. - Can you compare a half of a tiny biscuit and a quarter of a very large cake using only the fraction names? Explain.
The rule about unit fractions compares equal-sized wholes. The actual sizes must be known here.
No. The wholes have different sizes.
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 ↗