Addition of Fractions


 
 
Concept Explanation
 

Addition of Fractions

Addition of Fractions:

Adding Fractions with the Same Denominator:

For example: Let us add large frac{3}{4};and;frac{2}{4}

The only thing we need to do is add the numerators and leave the denominator alone. The answer is:

large frac{3}{4};+;frac{2}{4}=frac{5}{4}

Adding Numbers and a Fraction

For example:

Adding Fractions

The first thing that we need to do in this case is to convert the 2 into a fraction. As you already know, we can simply put a 1 in the denominator of any number without changing its value:

Adding Fractions

When we have two fractions, we can start looking for the common denominator. In this example, it’s quite simple because the least common multiple of 1 and any number is that number. So:

Adding Fractions

Now, we only need to multiply 2 x 4 and we get:

adding

…and now we put it into our addition problem:

Adding Fractions

Adding Fractions with Co-Prime Denominators : Two numbers are co-prime if their greatest common divisor is 1. For example, in the problem: large frac{2}{3};and;frac{3}{4}

The denominators are co-prime because 3 and 4 have common factor as 1. These kinds of problems are simple to solve because the only thing that we need to do to find the new numerators is to multiply each numerator by the denominator of the other fraction.

Here, we first have to find the LCM of 3 and 4, which is 12. Then, use equivalent fractions by making the denominators of the fractions same. Finally add the two numerators as shown:

large frac{2}{3};+;frac{3}{4}=frac{2times 4+3times 3}{12}=frac{8+9}{12}=frac{17}{12}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

large frac{4}{11}+frac{7}{11}=__________________________

Right Option : B
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Question : 2

Add:   large large frac{2}{3}+frac{3}{4}

 

Right Option : A
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Question : 3

Which number should come in place of x?  large frac{4}{9}+frac{7}{9}+frac{x}{9}=2frac{1}{9}

Right Option : C
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