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How To Add Fractions With Different Denominators: Adding And Subtracting Fractions With Different Denominators

How To Add Fractions With Different Denominators - Unlike Fractions, have always been a nightmare for kids and how to add fractions with different denominators is something that all kids would like to know.  We have explained in simple terms how to add fractions with different denominators and how to subtract fractions with different denominators

by Maria Thomas | Updated Sep 13, 2021 12:11 PM

How To Add Fractions With Different Denominators: Adding And Subtracting Fractions With Different Denominators
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Adding And Subtracting Fractions With Different Denominators

Fractions is one of the most unnerving chapters that children might face in school days especially when it is for the first time. Fraction as the English term might mean - a part of a whole is also representable in the form of numbers. For instance, you have a cake that is divided into 8 small pieces. One piece from that cake can be represented as either one - eighth of the cake or 1 by 8 or 1/8 . This would symbolise that we have taken 1 slice from the whole cake that is made up of 8 slices. One of the hardest functions in Fraction would be the task of Adding And Subtracting Fractions With Different Denominators. With like Denominators the process of how to add fractions with the same denominator is made easy but unlike denominators, the process of how to add fractions with different denominators and how to subtract fractions with different denominators. We have given here how to add fractions with different denominators, how to subtract fractions with different denominators and how to add fractions with the same denominator.

How To Add Fractions With Different Denominators?

Fraction is a term that is borrowed from Latin meaning to break. Only when a whole is broken do we get the pieces which are considered the fraction.

A Fraction is generally represented numerically in the form of a number by a number which as seen in the case of the previous Cake example can be noted as 1 by 8 or 1/8.  

You will notice that there are two parts to a fraction

The Upper part - 1 - Numerator 

The Lower part - 6 - Denominator

In the process of how to add fractions with different denominators we will need both the numerators and the denominators. Thus, it is imperative that we know what the numerator and the denominator mean.

Numerator is the part of the whole, and represents the sections of the whole 

Denominator is the whole that has been broken into parts from which the numerator is derived.

Now that all the terms regarding fractions have been cleared out of the way let us find out how to add fractions with unlike denominators. The process for how to add fractions with different denominatorsis as easy as can be, but only by following the steps required for the process for how to add fractions with different denominators

Generally in the process of how to add fractions with different denominators the first step would be finding out the common denominators. To find the common denominator we will need to find the least common multiple - LCM. 

Example : If you are given the task of Adding Fractions With Unlike Denominators for the following fractions - 2/5 and 6/7

We will notice here that the denominators of 2/5 and 6/7 are different making these unlike fractions

The LCM of 5 and 7 are 35.

The next step in Adding Fractions With Unlike Denominators would be to arrive at this common denominator 

Multiply 2/5 into 7 = 14/35 

Multiply  6/7 into 5 = 30/35

Now we will need to add these two fractions 

14/35 + 30/35 = 44/35

How To Subtract Fractions With Different Denominators?

The process for adding and subtracting fractions with unlike denominators are the same. But we have given an example to elucidate the same

Example - 2/3 and 3/7

The LCM of 7 and 3 are 21.

The next step in Adding Fractions With Unlike Denominators would be to arrive at this common denominator 

Multiply  2/3 into 7 = 14/21

Multiply 3/7 into 3 = 9/21

Now we will need to subtract these two fractions 

14/21 - 9/21 = 5/21

How To Add Fractions With The Same Denominator?

With the processes for how to add fractions with different denominators and how to subtract fractions with different denominators out of the way, let us find out how to add fractions with the same denominator. Fractions come in different types one of which is the unlike fractions whose processes of adding and subtracting fractions with different denominators we saw. Yet another type is the Lie fractions that has same denominator whose process of how to add fractions with the same denominator we have given below. 

Let us take the example 3/8 and 7/8

In this example since the denominator is the same we will not need to take the LCM or the common denominator as these two fractions already possess a common denominator. Thus all we need to do is add these two fractions

3/8 + 7/8 = 10/8

  • how to add fractions with the same denominator, 

  • how to subtract fractions with different denominators,

  • adding and subtracting fractions with different denominators

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How To Add Fractions With Different Denominators - FAQs

1. What are fractions?

Fractions are a topic in Mathematics wherein we are taught about portions and whol

2. What is the etymology of Fraction?

Fraction is a word coined from the Latin word Fracto which means to break

3. What are the two parts in Fraction?

Numerator and denominator are the two parts in fractions

4. What is Numerator?

Numerator is the part of the whole, and represents the sections of the whole

5. What is Denominator?

Denominator is the whole that has been broken into parts from which the numerator is derived.

6. What is Cross multiplying in fraction?

Cross multiply in fraction is whe you multiply the denominator of one fraction with another and vice versa

7. What are the types of Fractions?
  • Proper Fraction
  • Improper Fraction
  • Unit Fraction
  • Unlike Fraction
  • Like Fraction