You have cut shapes into halves, thirds and fourths. Fractions start from one rule that is easy to forget: the parts must be the same size.
Why it works
A fraction tells how much of a whole you have. If the parts were different sizes, "one part" could be a big piece or a tiny one, so the name would not tell you how much. When all the parts are equal, every part is the same amount, and the number of parts names it: 3 equal parts are thirds, 4 equal parts are fourths.
| Equal parts | Each part is called | Written |
|---|---|---|
| 2 | a half | $\frac{1}{2}$ |
| 3 | a third | $\frac{1}{3}$ |
| 4 | a fourth (a quarter) | $\frac{1}{4}$ |
| 6 | a sixth | $\frac{1}{6}$ |
| 8 | an eighth | $\frac{1}{8}$ |
Key idea
A fraction needs a whole cut into equal parts. The number of equal parts gives the parts their name.
Worked example: Name the parts
A rectangle is cut into 6 equal parts. What is each part called?
- There are 6 equal parts.
- Each part is one sixth, $\frac{1}{6}$.
Answer: sixths
Worked example: Is it a fourth?
A sandwich is cut into 4 pieces, and one piece is bigger than the rest. Is each piece a fourth?
- The pieces are not the same size.
- So they are not fourths. Fourths must be 4 equal parts.
Answer: No
Common mistake
Calling any split a fraction. Cutting a cake into 3 pieces does not make thirds unless the pieces are the same size. Quick check: if each piece went to a different friend, would it be fair? If not, the parts are not equal.