Last modified on August 5th, 2022

chapter outline

 

Numerator and Denominator

Numerators and denominators are the parts of any fraction. We will learn about the two and their role in a fraction.

What are Numerator and Denominator in a Fraction

The numerator is the top number in a fraction. It represents the number of equal parts we consider from a certain quantity. In contrast, the denominator is the bottom number in a fraction. It represents the number of equal parts a whole quantity is divided into.

We write a numerator above and denominator below the fraction bar. The fraction bar represents the division operation. We often write it as ‘/’.

For the fraction ${\dfrac{4}{5}}$, 4 is the numerator, and 5 is the denominator. Therefore, 4 is the dividend, and 5 is the divisor.

Numerator and Denominator

Let us understand the concept with a real-life example.

Suppose, Robert bought an 8-sliced pizza, he gave one slice to his friend. Now, what fraction of the pizza is he left with? Write the numerator and the denominator of the fraction.

Numerator Denominator Example

In the figure above, the pizza is sliced into 8 equal parts (slices). After Robert gave one slice to his friend, he is left with 7 slices.

∴ Numerator = 7, Denominator = 8, and the fraction of the pizza remaining is ${\dfrac{7}{8}}$.

If Anthony has an 8-sliced pizza and ate 3 slices, find the numerator and denominator of the fraction and write what portion of the pizza he ate.

Solution:

As we know,
The numerator is the number of equal parts we have, and the denominator is the equal parts a whole quantity is divided into,
∴ Numerator = 3, and, Denominator = 8
And, the fraction of pizza Anthony ate = ${ \dfrac{3}{8}}$

What happens if the numerator is greater than the denominator?

When a numerator is greater than the denominator in a fraction, it is an improper fraction. Some examples of improper fractions are ${\dfrac{8}{5},\dfrac{7}{4},\dfrac{21}{10}}$.

Let us now summarize the differences between numerator and denominator.

Numerator vs Denominator

BasisNumeratorDenominators
MeaningThe numerator represents the number of equal parts from a whole quantity.The denominator represents the number of equal parts a whole quantity is divided into.
Position in a fractionIt is the value above the fraction bar.It is the value below the fraction bar.
Importance in a fractionIf its value is zero, then the fraction becomes zero. When it is greater than the denominator, the fraction is an improper fraction. For example, ${\dfrac{4}{3}}$ is an improper fraction. If it equals the denominator, the fraction value becomes 1. For example ${\dfrac{4}{4}}$= 1.Its value can never be zero because we cannot divide a whole quantity into zero. The fraction is a proper fraction when it is greater than the numerator. For example, ${\dfrac{3}{4}}$ is a proper fraction.
Role in divisionIt is the dividend.It is the divisor.

Besides numbers, we also use variables to express fractions.

For example, in ${\dfrac{x+a}{y+b}}$, the numerator is x + a, and the denominator is y + b.

Write the numerator and denominator for the fraction ${\dfrac{p+2q}{q^{2}+2q+7}}$

Solution:

As we know,
The top number is the numerator
∴ Numerator = p + 2q
And, denominator = q2 + 2q + 7

Last modified on August 5th, 2022

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