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Denominator

The definition of the denominator states that it is the number below the horizontal line of the fraction that acts as the divisor of the numerator. It is the bottom number in a fraction that shows the total number of equal parts an object is divided into.

1. What is Denominator?
2. Numerator and Denominator
3. Examples of Denominator
4. Common Denominator
5. Solved Examples on Denominator
6. Practice Questions on Denominator
7. FAQs on Denominator

What is Denominator?

Denominator is the part of a fraction that comes below the fractional bar. For any fraction a/b, a is the numerator and b is the denominator. Fractions represent a part of a whole or, more generally, any number of equal parts. Mathematically, it is shown by the division of two numbers. For example, 1/4 is one part out of the four equal parts created from that one whole thing. Here, 1 is the numerator and 4 is the denominator. The denominator shows the total amount of parts that make up a whole. Apart from numbers, variables are also expressed in the same form such as x/y, a/b, p/q, etc., where y, b and q are the denominators respectively.

The fraction is shown using the symbol "/" This symbol is known as the "fractional bar." The number on the top is known as the "numerator", and the number below is known as the "denominator".

definition of denominator

Numerator and Denominator

The denominator indicates how many of those parts make up a unit or a whole. The numerator indicates the number of parts that we have selected out of the total number of equal parts. For example, in the fraction 3/5, the numerator 3 represents 3 equal parts taken by us, and the denominator 5 represents the 5 equal parts created initially. 5 equal parts make up a whole. Look at the fraction model below. The shaded portion represents the fraction 3/5. Three portions are shaded(Numerator) out of the total 5 portions created in the circle (denominator).

identifying the denominator in the fraction model

Examples of Denominator

x/y means that x parts of the whole object that is divided into y equal parts. The bottom number y shows the number of equal parts that the object is divided into, forms the denominator. The denominator can also be variables. The numerator or the denominator can be algebraic variables or expressions. Some examples of denominators are given in the table below:

Fractions

Denominator

1/3

  3

    11/20

   20

 6/(x-2y)

 x-2y

  3x/8y

 8y

 (i × j) /5

 5

 (p+3)/(q+9) 

q+9

Common Denominator

When the denominators of two or more fractions are the same, they are known as the common denominators. The least common denominator (LCD) is the smallest number that can be a common denominator for a given set of fractions. Addition and subtraction of fractions and comparing two or more fractions are possible only if the fractions have common denominators. For Example: consider 3/8 + 1/8. Since the denominators are same, they are the like fractions and can be instantly added up.

common denominator

Like fractions are the fractions that have the same denominators. Example: 5/15, 3/15, 17/15, and 31/15. Unlike fractions are the fractions which have different denominators. Example: 2/7, 9/11, 3/13, and 39/46. Let us see some examples here to add and subtract fractions with common denominators.

  • 2/2 + 3/2 = (2+3)/2 = 5/2
  • 6/7 -2/7 = (6-2)/7 = 4/7

If you have different denominators, we have two methods to find the sum or difference of two or more fractional numbers:

  • Cross multiply the numerator and the denominator of both the fractions and get the numerator of the resultant fraction. Multiply both the denominators and get the denominator of the resultant fraction. Then finally simplify if needed. 1/2 + 1/3 =\(\dfrac{((1×3)+(1×2))}{2×3}\) =(3+2)/6 = 5/6
  • Convert the fractions to equivalent fractions having the same denominator. It is usually the most convenient to consider the Least Common Multiple (LCM) of the denominators, which is known as LCD( least common denominator) 1/2 + 1/4
  • Here, the LCM of denominators 2 and 4 is 4. Therefore convert the first fraction into an equivalent fraction having 4. Thus 1/2 becomes 2/4

2/4 + 1/4  = (2+1)/4 = 3/4

Topics Related to Denominator

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

Important Notes

  • A denominator must be an integer.
  • A denominator can never be zero because zero parts can never make up a whole.
  • The term denominator is widely used in the concepts of rational numbers, ratios and proportions, and division concepts.
Important Topics
 
Reduce Fractions
Simplifying Fractions
 
 
 

Solved Examples on Denominator

 

  1. Example 1: Rita ordered a pizza at a restaurant. Each piece of pizza represents a part of a whole. The pizza is divided into 6 equal slices. If she ate one slice, then what is the denominator of the fraction representing the amount she ate?

    Solution:

    Total number of slices of pizza = 6

    Total number of the piece she ate = 1

    The fraction of pizza she ate 1/6

    Here, 6 is the number that denotes the total number of slices of pizza. Therefore, the denominator is 6.

  2. Example 2: A grandmother bought an apple for her grandchild. She cut it into 4 pieces. If she gives one piece of an apple to the child, what is the denominator of the fraction of the remaining apple?

    Solution:

    Total number of pieces of apple in a whole = 4. If 1 piece of an apple is cut then, total number of pieces of an apple left = 3

    The fraction of the remaining apple = 3/4

    So, the denominator is 4 the number that denotes the total number of pieces of apple.

  3. Example 3: There are two boys and three girls playing together. Determine the fraction of boys and girls. What is the denominator of the fraction?

    Solution:

     Total number of kids = 5

    The fraction of boys who are playing = 2/5

    The fraction of girls who are playing = 3/5

    Here, 5 is the number that denotes the total number of kids and that is the denominator.

  4. Example 4: Harry James wants to find the fraction that shows vowels to the total letters in his name. What is the denominator of the fraction representing the names?
    Solution:

    Total number of letters in the first and last name = 10

    The total number of vowels in the name = 3 ( Vowels are A, A, E)

    The fraction of vowels to total letters =  3/10
    The denominator is 10 which represents the total number of letters in his name.

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Practice Questions on Denominator

 

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Frequently Asked Questions(FAQs)

What is a Denominator?

The bottom number in a fraction is called the denominator. Denominator indicates the number of equal parts into which the whole object is divided into.

What is an Example of a Denominator?

The fraction 4/7 has a top number 4 and a bottom number 7. Therefore, the denominator is 7.

Is Denominator on Top or Bottom?

The number below the fractional bar in a fraction is called the denominator. For example, in the fraction 3/4, 4 is the denominator.

Can a Denominator Have a Value of 0?

A fraction becomes undefined if the denominator has the value 0. No object can be divided into 0 equal parts. 

What is the Difference Between Numerator and Denominator?

Numerator is the number of equal parts we use in an object, whereas the denominator is the total number of equal parts we divide an object into. If we divide a cake into 5 equal parts and eat 2, 5 becomes the denominator and 2 becomes the numerator. This is represented as 2/5.

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