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.

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.

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

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.

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

What Is a Common Denominator?

A common denominator is that in which the denominator i.e. the number below the fraction is the same throughout, thereby making your calculation process simpler. In case the two fractions do not have a common denominator, then you need to calculate the common denominator to get your answer.

How to Find the Common Denominator?

For a sum like 3/4 + 1/4 = 1, the common denominator is 4. However, when you are given a calculation such as 3/4 + 1/2, then you will need to find the common denominator for both 3/4 + 1/2. You can do this by either finding the least common multiple or cross-multiplying the above equation.

What is the Common Denominator of 3 and 4?

Unlike the previous example, in this case, neither 3 nor 4 are factors of each other. In this case, you can calculate the value of the common denominator by multiplying both numbers to get 12.

What is the Another Name for Common Denominator?

Another possible name for common denominator is the common divisor. Further, based on the denominators, the common denominator can be the lcm of the two denominators. Also, if one denominator is the factor of another denominator, then we can take the larger number as the least common denominator.

How to Find the Least Common Denominator?

The least common denominator depends on the kind of denominator. For denominators with co-prime numbers, the least common denominator is the product of the two denominators. Also, the least common denominator is the lcm of the two given denominators. Let us consider two denominator values: 4, 6. The least common denominator is the lcm of 4, 6, which is the number 12.

What is the Greatest Common Denominator?

The Greatest Common Denominator of two or more fractions, which are not zero, is the largest positive integer that divides each of the given denominators.

Can a Common Denominator be Equal to Zero or 1?

For a fraction with the common denominator of zero, it becomes undefined. And for fractions with only whole numbers as numerators and 1 as a denominator, the common denominator is 1. In the case of whole numbers being considered as fractions, the common denominator is 1.