Fair shares
Imagine sharing a pizza with a friend. To be fair, you cut it so both pieces are the same size. Those are equal parts.
If the pieces are different sizes, they are not equal parts, and they can’t be named with a fraction.
Naming the parts
| Number of equal parts | Each part is called | Written |
|---|---|---|
| 2 | one half | ½ |
| 3 | one third | ⅓ |
| 4 | one quarter (fourth) | ¼ |
| 6 | one sixth | ⅙ |
| 8 | one eighth | ⅛ |
Each of these is a unit fraction: it names one of the equal parts. A fraction is a number that names part of a whole.
More parts, smaller pieces
The more equal parts you cut, the smaller each piece is.
- A pizza cut in 2 gives big halves.
- A pizza cut in 8 gives small eighths.
So one half is bigger than one quarter, even though 4 is bigger than 2. This surprises many people!
Checking for equal parts
Ask: if I cut these out and put one on top of another, would they match exactly?
- A rectangle cut down the middle → 2 equal parts ✓
- A circle cut off-centre → 2 unequal parts ✗
- A square cut corner to corner → 2 equal triangles ✓
Equal parts don’t have to look the same shape, but they must be the same size.
Counting the parts
Once a shape is split into equal parts, we count them:
- 2 halves make a whole.
- 3 thirds make a whole.
- 4 quarters make a whole.
If 3 out of 4 equal parts are shaded, we say "three quarters" are shaded.
Worked examples
Example 1: A sandwich is cut into 2 equal parts. What is each part called?
One half.
Example 2: A pie has 4 equal slices. You eat 1. What fraction did you eat?
One quarter (one fourth).
Example 3: Which is bigger: one third or one sixth of the same cake?
Fewer pieces means bigger pieces. One third is bigger.
Common mistakes
- Calling unequal pieces "halves". Halves must be the same size.
- Thinking a bigger number at the bottom means a bigger piece. One eighth is smaller than one half.
- Comparing fractions of different wholes. Half a small cookie is not the same amount as half a big cookie.
Try it yourself
- A shape is cut into 3 equal parts. What is one part called?
- How many quarters make a whole?
- Which is smaller: one half or one quarter?
- A rectangle is cut into two pieces of different sizes. Are they halves?
Answers: 1) one third 2) 4 3) one quarter 4) No, the parts are not equal.
Quick recap
- Equal parts are pieces that are all the same size.
- Half, third, quarter name 1 of 2, 3 or 4 equal parts.
- More parts means smaller pieces.