Understand the idea.
Useful fraction names
A fraction's name tells how many equal parts make the whole: halves need two, thirds need three, quarters need four, fifths need five and tenths need ten. One chosen part is a unit fraction, such as .
Folding a strip in half and then halving both halves creates four equal panels. Each panel is one quarter. Count all the equal parts in the original whole, rather than only the number of folds.
| 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
Use equal-sized wholes when comparing shares. Half of a small pizza and a quarter of a much larger pizza cannot be compared from the fraction names alone. First check that the original amounts are the same size.
For the same whole, more equal parts means smaller individual pieces. One fifth is larger than one tenth: dividing the whole into ten requires each piece to be smaller than when it is divided into five.
See the method in action.
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?
Worked solution
- 1
Check that the wholes are equal.
Both pizzas have the same size, so their fractions describe comparable amounts.
- 2
Express a half using quarters.
Two quarter-sized pieces exactly fill one half of the same whole.
- 3
Compare the shares.
Ana has two quarter-sized pieces while Bo has one, so Ana gets more.
Ana gets more.
Name a fold
A strip is folded into 5 equal panels. Name one panel.
Worked solution
- 1
Count the equal parts in the whole.
The five panels together make the complete strip.
- 2
Name one of those parts.
The denominator counts all five equal panels and the numerator counts the one panel chosen.
.
Try it yourself.
Check your understanding
Which is larger: one third or one fifth of the same strip?
Show answer & reasoning
One third.
Both fractions use the same strip. Dividing it into three equal pieces gives larger pieces than dividing it into five, so .
Keep practising
6 worksheet questions
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 ↗