Understanding Fractions: Practice

The denominator is the bottom number, the one that tells how many equal parts the whole is cut into.

$\frac{5}{9} \;\to\; \text{denominator} = 9$

The top number, $5$, is the numerator.

The numerator is the top number, and it counts how many of the equal parts you take.

$\frac{2}{7} \;\to\; \text{take } 2 \text{ of the } 7 \text{ equal parts}$

The denominator $7$ is what tells you the whole was cut into $7$ parts.

"Fifths" names the denominator (the whole is cut into $5$ equal parts), and "three" is the numerator (you take $3$ of them).

$\text{three fifths} = \frac{3}{5}$

The bar between the numerator and denominator is a division sign.

$\frac{a}{b} = a \div b$

So $\frac{3}{4}$ is another way of writing $3 \div 4$.

The bar is divided into $5$ equal parts, and $2$ are shaded.

$\frac{\text{shaded}}{\text{equal parts}} = \frac{2}{5}$

A unit fraction has a numerator of $1$: a single equal part of the whole.

$\frac{1}{8} \;\to\; \text{numerator } 1$

The others have numerators $3$, $2$, and $5$, so they are not unit fractions.

Both are unit fractions, so compare the sizes of one part. A bigger denominator cuts the whole into more, and therefore smaller, pieces.

$\frac{1}{4} > \frac{1}{8}$

Cutting a whole into $4$ parts gives bigger pieces than cutting it into $8$.

The numerator is read as a plain count and the denominator names the kind of part.

$\frac{4}{9} = \text{four ninths}$

The denominator $9$ gives "ninths," and the numerator $4$ gives "four."

A fraction whose numerator equals its denominator means you took every part of the whole, so it equals one whole.

$\frac{6}{6} = 1$

In contrast, $\frac{6}{1} = 6$, $\frac{1}{6}$ is less than $1$, and $\frac{0}{6} = 0$.

The fraction bar means divide, with the number being divided on top.

$9 \div 2 = \frac{9}{2}$

A fraction with denominator $0$ would mean dividing into $0$ equal parts, the same as dividing by $0$, which has no answer.

$\frac{5}{0} = 5 \div 0 \;\to\; \text{undefined}$

So a denominator of $0$ is never allowed.

The bar is divided into $3$ equal parts, and $1$ is shaded.

$\frac{\text{shaded}}{\text{equal parts}} = \frac{1}{3}$