Definition, How To Find Common Denominator, Examples, FAQs

Common Denominator

A common denominator is helpful to perform numerous mathematical operations on numbers. An important concept in Mathematics is the addition and subtraction of fractions. Fractions include a numerator (the number on top) and a denominator (the number below). The fractions which have the same denominators, such denominators are called common denominators. Consider the following examples: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 In both cases, the denominators in the fractions are common, hence, it is easy to calculate the answer.

However, if you are given a problem with different denominators, how would you solve it. A calculation of 2/5 + 3/4 is difficult to perform because of different denominators. Since the denominators in the fractions are not the same, we have to solve them using a different method. Let us explore this topic to learn more about the common denominators.

1.	What is a Common Denominator?
2.	How to find a Common Denominator?
3.	Common Denominator Examples
4.	Common Denominator Methods
5.	FAQs on Common Denominator

What is a Common Denominator?

Two or more fractions having the same denominator are referred to as a common denominator. The common denominator helps to easily perform numeric calculations. The number shown in the lower part of a fraction is called the denominator. The denominator shows you how many equal parts an item is divided into.

In the above figure, there are 4 slices in the first pizza. Thus, it is represented as 1, that is, a whole. When we take away one slice, we have 3 out of 4 slices, remaining. Thus, the fraction of the remaining slices is given as 3/4. This also means that 1/4 slice has been taken away. If we are to add these two, we get: 1/4 + 3/4 = 4/4 = 1. Further, depending on the size of the pizza, you can divide it into as many parts as you want.

How to find a Common Denominator?

While the example of the pizza shows you how simple it is to find the common denominator, you may not always be presented with such a situation. There may be times where you are asked to add fractions with different denominators like 3/7 + 12/13. In such cases, we need to find the common denominator and then solve the fractions. Let's look at a simpler example 1/3 + 1/6. Given below are the two common denominator methods to find the answer:

• By finding the least common multiple
• By cross multiplication

When you solve for the common denominator using the LCM method, you find the least common multiple of the given numbers. In this equation, the least common multiple is 6. Hence, the equation becomes 1/3 + 1/6 = (1 x 2 + 1)/6 = (2 + 1)/6 = 3/6 = 1/2. If you cross multiply, you will find the solution as: 1/3 + 1/6 = 2/6 + 1/6 = (2 + 1)/6 = 3/6 = 1/2

Common Denominator Examples

Examples of common denominators in our everyday lives include pizza slices, money, cooking and baking, and so on. The pizza as an example can be sliced into four slices and the possible parts of the pizza can be 1/4. 2/4, 3/4 respectively. Further, we can find the common denominators in instances we are sharing equal amounts of a quantity. In such a situation, the common denominators would be equal to 1/2 and 1/2 or 1/4 and 1/4 respectively.

Practically much of the daily life examples where quantities have been divided can be expressed as a common denominator. Another good example of a common denominator can be found in cooking and baking - you need fractions and denominators to measure the ingredients to make a cake.

Common Denominator Method

The common denominator methods, as explained above, include calculating the least common multiple or cross-multiplying. Common denominators are the products of the denominators of the given fractions. However, you need to remember that besides this, common denominators are also the factors that the fractions have in common and the factors that make each fraction different. A common denominator includes all factors from each fraction.

Related Topics

Listed below are a few topics related to common denominator, take a look. 

• Least Common Multiple
• HCF - Highest Common Factor
• Greatest Common Factor
• Divisor