Continued Fraction Rectangle Diagrams Where Numerator is Smaller Than the Denominator

Numerator and Denominator

The numerator and denominator are the parts of fractions that are separated by a horizontal bar known as a vinculum. The numerator is an upper part of the fraction and the denominator is a lower part of the fraction. When we represent the numerator and denominator in the division operation, we treat the numerator as a dividend and the denominator as the divisor. Let us read about various parameters associated with numerator and denominator in detail.

1.	What are Numerator and Denominator?
2.	Difference Between Numerator and Denominator
3.	Numerator and Denominator of a Fraction
4.	Numerator and Denominator in Division
5.	FAQs on Numerator and Denominator

What are Numerator and Denominator?

The numerator indicates the total number of selected equal parts. Whereas, the denominator indicates the total number of equal parts. Let us consider the example given below. A circular wheel is divided into 6 equal sections. This situation can be represented as fraction 5/6, the numerator 5 represents the number of the equal shaded portion taken out from the set of 6 equal portions, and the denominator 6 represents that the 6 equal parts that make up a whole unit.

Difference Between Numerator and Denominator

The difference between numerator and denominator is shown below in the table.

Numerator	Denominator
The term above the vinculum in a fraction is called the numerator. It shows the number of parts we have out of a whole.	The term below the vinculum in a fraction is called the denominator. It shows the total number of parts we have as a whole.
If the value of the numerator is zero, then the complete fraction value is equal to zero.	A denominator can never be zero because zero parts can never make up a whole.
If the numerator is greater than or equal to the denominator, the fraction is called an improper fraction.	When denominator > numerator, a fraction is a proper fraction.
The numerator acts as a dividend.	The denominator acts as a divisor.
For example, 13/3, here 13 is the numerator.	For example, 13/3, here 3 is the denominator

Numerator and Denominator of a Fraction

As we know the numerator and denominator are two separate parts of a fraction. A fraction is usually represented in the form of 'X/Y', where 'X' is the numerator and 'Y' is the denominator.

Let us understand this better by looking at a solved example.

Example: Identify the numerator and denominator in the following fractions.

a) 7/9 b) 10/23 c) 15/4

Solution:

a) In the given fraction 7/9, 7 is the numerator and 9 is the denominator.
b) In the given fraction 10/23, 10 is the numerator and 23 is the denominator.
c) In the given fraction 15/4, 15 is the numerator and 4 is the denominator.

Numerator and Denominator in Division

When we write any fraction term in the form of x/y it is basically represented as x ÷ y. In simple terms it means, we need to divide the numerator (x) by the denominator (y) to simplify it.

For example, represent 3 ÷ 6 in terms of fraction and identify the numerator and denominator after simplification. 3 ÷ 6 can be represented as 3/6. On further simplification, it gives 1/2. In the fraction 1/2, 1 is the numerator and 2 is the numerator.

☛Topics Related to Numerator and Denominator

Check out the few more interesting articles which are closely related to the numerator and denominator.

• Arranging fractions in order
• Rationalizing denominator
• Fractions-formula
• Like fractions Calculator
• Numerator and Denominator Calculator

Examples on Numerator and Denominator

1. Example 1: Peter ordered garlic bread at a restaurant. Each piece of bread represents a part of a whole. The bread is divided into 7 equal slices. He ate two slices. Represent the situation in form of a fraction and identify the numerator and denominator of the fraction.

   Solution:

   Total number of slices of bread = 7
   Total number of the slices he ate = 2
   The fraction of bread he ate 2/7
   Here, 7 is the number that denotes the total number of slices of bread, and 2 is the numerator that represents the portion he ate.

2. Example 2: What is the sum of the numerators and sum of denominators of the first fraction and the second fraction: 1/3, 7/5.

   Solution:

   To find the sum of the fractions, let us first identify the numerator and denominator in both the fractions.
   The numerator of the first fraction 1/3 is 1 and the denominator is 3.
   The numerator of the second fraction 7/5 is 7 and the denominator is 5.
   The sum of numerators = 1 + 7 = 8.
   The sum of denominators = 3 + 5 = 8

   Therefore, the sum of numerators and the sum of the denominators of both the fractions are 8, 8 respectively.

3. Example 3: There are 27 students in a class and 13 of them are girls. Represent the number of boys and number of girls in terms of numerator and denominator.

   Solution:

   The number of girls in the class is given as 13.
   The number of boys in the class is (27 - 13 = 14)
   Fraction representing the number of boys in the class = 14/27
   Fraction representing the number of girls in the class = 13/27

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Practice Problems on Numerator and Denominator

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FAQs on Numerator and Denominator

What is the Meaning of Numerator and Denominator?

The numerator and denominator are two parts that form fractions. In other words, they are part of fractions. The top number in a fraction is always considered a numerator. It shows the number of parts we have. The bottom number in a fraction is considered a denominator. It shows the total number of parts into which anything is divided. For example, in the fraction 8/7, 8 is the numerator and 7 is the denominator.

How do you Differentiate Between the Numerator and Denominator of a Fraction?

A fraction is represented in the form of 'x/y', where 'x' is the numerator and 'y' is the denominator. The numerator represents the total number of parts taken into account. Whereas, the denominator represents the total number of equal parts in a fraction. The top number in a fraction is always considered a numerator. The bottom number in a fraction is considered a denominator.

How to Remember Numerator and Denominator?

There are various ways and tricks to remember the numerators and denominators. The simplest way to remember this is by understanding the placement of numbers in the fractions. We need to remember that the numerator will always place at the top part of the fraction and the denominator numeric value placed always at the bottom.

How to Divide Numerator and Denominator?

When numerator and denominator are represented in the form of p/q it means p ÷ q. Here 'p' acts as the numerator and 'q' acts as the denominator. For example, 7/2 means 7 ÷ 2, here numerator 7 is divided by denominator 2. While performing division, we will read 7 (numerator as a dividend) and 2 (denominator as a divisor).

What is the Line Between the Numerator and Denominator Called?

A line between the numerator and denominator is called Vinculum or a fraction bar. For example, 7/6 here numerator 7 and 6 denominator is separated by using a bar.

Identify the Numerator and Denominator in the Fraction 18/7?

In the given fraction 18/7, 28 is the numerator is 18 and 7 is the denominator.

What is the Numerator and Denominator of the Following Fractions? 7/3 and 9/7

In the fraction 7/3, 7 is the numerator and 3 is the denominator. In the fraction 9/7, 9 is the numerator and 7 is the denominator.

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Source: https://www.cuemath.com/numbers/numerator-and-denominator/

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