Numerator: Definition, Method, and Examples

What is a numerator?

In any fraction, the upper number of a fraction is called the numerator. It sits directly above the fraction bar and represents the active count of the pieces you are focusing on.

The top number determines the value you hold, while the bottom number determines the size of the pieces. If you have the fraction $\dfrac{5}{8}$, the numerator is $5$.

Find the numerator in a fraction

You can find the numerator in any written fraction simply by looking at its position. The layout of a standard fraction always follows the same structure.

1. Locate the horizontal fraction bar that divides the numbers.
2. Identify the number written on top of that bar.

For example, in the fraction $\dfrac{7}{12}$, the number $7$ is written above the bar, so $7$ is the numerator.
In the fraction $\dfrac{15}{4}$, the number $15$ is written on top, so $15$ is the numerator.

What the numerator means

The numerator represents the count of the equal parts you are focusing on. If a cake is sliced into $10$ equal pieces and you serve $4$ of them, you are counting $4$ pieces. The numerator of the fraction served is $4$.

The numerator can be any whole number. When a fraction has a numerator of $1$, such as $\dfrac{1}{6}$, it is known as a unit fraction. If no pieces are selected, the numerator is $0$.

When the number of pieces you have equals the number of pieces in one whole, the numerator equals the denominator, such as $\dfrac{8}{8}$, which equals $1$. The numerator can also be larger than the denominator, representing a value greater than one whole.

Numerator and denominator compared

The numerator and the denominator work together to give a fraction its total value, but they represent entirely different concepts.

The numerator counts the parts you have, while the denominator defines the size of the parts.

Numerator in models and number lines

When working with visual models, you can find the numerator by counting the specific items or intervals that match the description you need.

• In an area model: Count the number of shaded shapes.
• In a set model: Count the number of individual objects in the group that share the specified trait.
• On a number line: Count the number of equal-sized jumps starting from zero to reach your point.

In the number line above, the space between $0$ and $1$ is divided into $6$ equal parts. The point plotted is $5$ jumps away from $0$, meaning $5$ parts are being counted. Therefore, the numerator is $5$.

Worked examples

You can apply these rules to find the numerator in different contexts, whether you are examining a shape, reading a word problem, or plotting a value.

Example 1: Identifying the numerator from an area model

Question: A circular pie is cut into $8$ equal slices. If $5$ slices are eaten, what is the numerator of the fraction that represents the eaten slices?

Method:

1. Identify the specific items being counted. The question asks for the eaten slices.
2. Count the eaten slices. There are $5$ eaten slices.
3. The count becomes the numerator.

Answer: The numerator is $5$.

Check: The fraction of eaten slices is $\dfrac{5}{8}$, and $5$ is the top number.

Example 2: Finding a numerator from a set

Question: A box contains $12$ markers. There are $3$ red markers, $4$ blue markers, and $5$ green markers. What is the numerator for the fraction of markers that are blue?

Method:

1. Determine the trait being counted. The question asks for blue markers.
2. Count the number of markers that match the trait. There are $4$ blue markers.
3. Write this count as the top number of the fraction.

Answer: The numerator is $4$.

Check: The total number of markers is $12$, which is the denominator. The fraction is $\dfrac{4}{12}$. The numerator is correct.

Example 3: Numerator in an improper fraction

Question: What is the numerator of the fraction $\dfrac{11}{4}$?

Method:

1. Locate the fraction bar.
2. Identify the number written directly above the fraction bar.

Answer: The numerator is $11$.

Check: The number on top is $11$, representing $11$ quarter-sized pieces.

Common mistakes

Thinking the numerator must be the smaller number

It is a common misunderstanding to assume the top number must always be smaller than the bottom number. While this is true for proper fractions, the numerator can be larger than the denominator in improper fractions, indicating a value greater than one whole.

Counting the wrong attribute

When answering a question based on a visual model, carefully read whether the question asks for the shaded parts or the unshaded parts. If a shape has $3$ shaded parts and $1$ unshaded part, the numerator for the shaded fraction is $3$, but the numerator for the unshaded fraction is $1$.

Frequently asked questions

Can a numerator be zero?

Yes. A numerator of $0$ means that zero parts are being counted or selected. For example, $\dfrac{0}{5}$ means zero fifths, which equals $0$.

Can a numerator and a denominator be the same number?

Yes. When the numerator equals the denominator, it means you have all the parts that make up exactly one whole. For example, $\dfrac{6}{6} = 1$.

Does the numerator tell you the size of the pieces?

No. The denominator tells you the size of the pieces. The numerator only tells you how many of those pieces you have.