To compare two fractions with drawings, both figures must show the same whole and be split into equal parts. If you shade half of an 8 cm bar and half of a 20 cm bar, the shaded parts measure 4 cm and 10 cm. The fraction is the same and the amount is not, and with different wholes a drawing can show the opposite order.
Before deciding, check how big each whole is. To draw a specific fraction, use the visual fraction models and the guide on how to draw fractions. To compare with numbers only, go to compare fractions.
| Question | Must be equal | How to check |
|---|---|---|
| Which fraction is greater? | The whole of both figures | Bars of the same length or a common denominator |
| Which shaded part is bigger? | The unit of measure | Compute fraction × whole in the same unit |
| Do two collections have the same proportion? | Nothing, because each collection is its own whole | Simplify each fraction |
The table separates two questions that a drawing easily mixes up: which fraction is greater and which shaded part is larger. The two answers agree only when the whole is the same.
Same fraction, different amount
In the 8 cm and 20 cm bars above, the fractions are equal and the lengths are not. A fraction says how many equal parts of the whole are taken, not how long the whole is. To turn it into an amount, multiply the fraction by the whole, which the fraction of a number tool does for you.
Worked example: half of 8 cm versus a third of 15 cm
An 8 cm bar has half shaded and a 15 cm bar has a third shaded. Which fraction is greater, and which shaded part is longer?
- Name each whole. The first is 8 cm and the second is 15 cm. They are different wholes.
- Compare the fractions as if the whole were the same. With denominator 6, 1/2 = 3/6 and 1/3 = 2/6, so 1/2 is greater.
- Compute each length. 8 ÷ 2 = 4 cm and 15 ÷ 3 = 5 cm.
- Compare the lengths. 4 cm is less than 5 cm.
Result: the greater fraction is 1/2, but the longer shaded part is the third.
Check: 4 × 2 = 8 and 5 × 3 = 15, so each part is computed correctly.
With different wholes, the greater fraction can give the smaller part. That is why a drawing with bars of different lengths cannot order fractions, even though it can measure.
When the whole is the same, the drawing decides
For 2/3 and 3/4, draw two bars of the same length and split them into twelve equal parts. That leaves 8 shaded parts in the first and 9 in the second, because 2/3 = 8/12 and 3/4 = 9/12. The second fraction is greater.
If the wholes change, the shaded parts change
Now change the wholes: the 2/3 bar is 12 cm and the 3/4 bar is 8 cm. The shaded parts measure 8 cm and 6 cm, so the smaller fraction gives the longer part. It is the same mistake as in the worked example with other numbers. For a drawing to compare fractions, fix the length before shading.
Different fractions can also give the same part. A third of a 9 cm strip and a quarter of a 12 cm strip both measure 3 cm, even though the fractions are different.
Parts that are not equal
A drawing represents a fraction only if the parts are equal in the quantity being compared. In a rectangle, the parts can have different shapes as long as they have the same area. On a strip, they must have the same length, and in a collection each object counts as one unit.
Collections of objects
In a collection, the whole is the total number of objects. If 6 of 15 counters are red and 4 of 10 counters are blue, the two collections have the same proportion: 6/15 = 2/5 and 4/10 = 2/5. There are more red counters than blue ones, and yet the fraction is the same.
The collections do not need to be the same size to compare proportions, because each fraction already compares a part with its own total. They do need to match if you want to compare quantities: then count the objects, not the fraction.
Practice
- A 10 cm bar has 3/5 shaded and an 8 cm bar has 3/4 shaded. Which fraction is greater, and which shaded part is longer?
- With the same whole, which is greater, 2/5 or 3/8?
- There are 8 green counters out of 10 and 12 yellow counters out of 15. Do they have the same proportion?
Show the answers
- Fourths are bigger than fifths, so the second fraction wins. Both shaded parts measure 6 cm: 10 ÷ 5 × 3 = 6 and 8 ÷ 4 × 3 = 6.
- 2/5 = 16/40 and 3/8 = 15/40, so 2/5 is greater.
- Yes: 8/10 = 4/5 and 12/15 = 4/5.
To go further, the fraction wall guide stacks rows of the same length one under another, and equivalent fractions shows how to move to a common denominator. If you want to bring it into the classroom, see teaching fractions.
Sources
The definition of a fraction as a way to represent parts of a whole, with the denominator as the number of equal parts that make up the whole, appears in the English Wikipedia article Fraction, in the introduction (accessed October 17, 2026). That source does not cover the effect of changing the whole; the comparisons in this guide are demonstrated by the examples above.