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. The denominator shows the total amount of parts that make up a whole.
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".
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.
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 (denominator).
Examples of Denominator
x/y means that x parts of the whole object that is divided into y equal parts. y forms the denominator. 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. 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.
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
- 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.
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.