A unit fraction is one piece. Now we put pieces together. $\frac{3}{4}$ means 3 pieces, each of size $\frac{1}{4}$.
Why it works
The bottom number (the denominator) tells the size of each piece: fourths. The top number (the numerator) counts how many of those pieces you have. So $\frac{3}{4}$ is one amount, "three fourths," just as "3 apples" is one amount: the 3 counts and the fourths say what is being counted.
| Fraction | Say | Pieces |
|---|---|---|
| $\frac{3}{4}$ | three fourths | 3 pieces of $\frac{1}{4}$ |
| $\frac{5}{6}$ | five sixths | 5 pieces of $\frac{1}{6}$ |
| $\frac{2}{8}$ | two eighths | 2 pieces of $\frac{1}{8}$ |
Key idea
$\frac{a}{b}$ is $a$ pieces, each of size $\frac{1}{b}$.
Worked example: Shaded parts
A circle is cut into 8 equal parts and 5 are shaded. What fraction is shaded?
- Each part is $\frac{1}{8}$.
- 5 parts are shaded: 5 pieces of $\frac{1}{8}$.
Answer: $\frac{5}{8}$
Worked example: Count the pieces
How many pieces of size $\frac{1}{6}$ make $\frac{4}{6}$?
- The numerator, 4, counts the pieces.
Answer: $4$
Worked example: What is left?
3 of 5 equal parts are shaded. What fraction is not shaded?
- $5 - 3 = 2$ parts are not shaded.
- Each part is $\frac{1}{5}$, so 2 parts make $\frac{2}{5}$.
Answer: $\frac{2}{5}$
Common mistake
Reading the two numbers separately. $\frac{3}{4}$ is not "3 and 4" and it is not bigger than 3. It is one number, less than 1: three of the four equal parts. Say it aloud as "three fourths" to keep it together.