[Maths Class Notes] on Addition of Fractions Pdf for Exam

One day Alaina gave a chocolate bar to Cristopher. John saw this and started shouting “give me one, give me one.” Alaina did not have another one. So she asked them to share the chocolate bar equally. John ran to the kitchen and brought a knife and cut the bar into two equal pieces. He took one and gave the other to his brother Cristopher. As both the pieces were of equal size, they did not quarrel over the size of the piece they received.

The next day, John was given some sums of division by his maths teacher in the school. He solved all of them except the following: 

i) 1 ÷ 2            ii) 1 ÷ 3          iii) 2 ÷ 5

He was confused and did not know how to divide 1 by 2, 1 by 3 or 2 by 5. Can we divide 1 by 2? Yes, we can! I divided by 2 is [frac{1}{2}]. It means that one part out of the two equal parts. In the same way, 1 divided by 3 will be written as [frac{1}{3}] and it means that one part out of the three equal parts. 2 divided by 5 means two parts out of the five equal parts and can be written as [frac{2}{5}].

The numbers such as [frac{1}{2}, frac{1}{3}, frac{2}{5}] are called fractions. In a faction [frac{5}{12}], 12 is called the denominator and it means the total number of equal into which the whole number has been divided. 5 is called a numerator and it is a number of equal parts which have been taken.

Therefore, 5/12 represents five-twelfth of the whole. Hence, we can define function as:

Types of Fractions

Addition of Fractions 

Now you must be wondering how to solve fractions addition? By the end of this section, we would know how to add fractions with unlike denominators and addition of like fractions. First we will start with addition of like fractions. Addition of fractions examples are also given to properly guide you.

Addition of Like Fractions

For the addition of like fractions we just need to add the numerators of the fractions as the denominations of all the fractions would be the same. Here is an example of addition of like fractions.

Adding fractions examples:

Example 1) Add [frac{2}{18}] and [frac{12}{18}]

Solution 1) The addition of like fractions is done in the following ways:

[frac{2}{18}] + [frac{12}{18}]

= [frac{2 + 12}{18}]

= [frac{14}{18}]

Example 2) Add [frac{3}{21}] and [frac{7}{21}]

Solution 2) The addition of like fractions is done in the following ways:

[frac{3}{21}] and [frac{7}{21}]

= [frac{3 + 7}{21}]

= [frac{10}{21}]

Now, I’m sure that you know how to solve fractions addition or rather I should say the addition of like fractions. Now that we know how the addition of like fractions is done, we can move onto and learn how to add fractions with unlike denominators.

How to Add Fractions With Unlike Denominators?

Adding fractions with unlike denominators examples are a little different from the addition of like fractions. Let us see how?

Adding fractions examples:

Example 1) Add [frac{11}{4}, frac{35}{6}, frac{3}{8}]

Solution 1) Since the denominator of the fractions are different from each other, we first have to make them equal and we can do that by finding the L.C.M.  of 4, 6 and 8. The L.C.M. would be 24. Therefore,

[frac{11 + 35 + 3}{24} = frac{49}{24}]

Example 2) Add [frac{5}{8}] and [frac{9}{12}]

Solution 2) Again, first we have to find out the L.C.M. of 8 and 12 which will be 24. Therefore, 

[frac{5 + 9}{24} = frac{14}{24}]

Addition of Mixed Fractions

Addition of mixed fractions includes a bit more of process than addition of like fractions or addition of fractions with unlike denominator. 

Adding fractions examples:

Example 1) Add [5frac{4}{2}] and [2frac{3}{3}]

Solution 1) For the addition of mixed fraction we need to follow few steps, these are:

Step 1: Multiply the denominator with the whole number then add the result with the numerator.

2 x 5 = 10 + 4 = 14                                      3 x 2 = 6 + 3 = 9

Step 2; The final outcome will become the numerator and the denominator will remain the same.

[frac{14}{2}]                                              [frac{9}{3}]

                      

Step 3: Find the L.C.M. if the denominators are different. So the L.C.M. of 2 and 3 will be 6, therefore, 

[frac{14 + 9}{6} = frac{23}{6}]