Adding Mixed Numbers – Definition with Examples

Adding Mixed Numbers

A fraction consisting of a whole number as well as a fractional part is called a mixed number.

Improper fractions, fractions greater than one, written in the form of a whole number, and proper fractions are called mixed numbers.

Adding Mixed Numbers with Like Denominators

Let us see an example of the addition of mixed numbers with like denominators. There is 2 ⁴⁄₅ kg of apples in one basket and 3 ³⁄₅ kg of apples in another basket. How many apples are there altogether in both the baskets? 

Here, to find the number of apples in both the baskets, we add the mixed numbers 2 4⁄5 and 3 3⁄5. The denominators of both the fractional parts are the same. So, to add mixed numbers with like denominators we add the whole parts together and the fractional parts together and then combine the sum of the two as shown below:

Add the whole part with the whole part and the fractional part with the fractional part.

If the sum of the fractional parts is an improper number, convert it to a mixed number.

Combine the sum of the wholes and fractions.

Therefore, there is 6 ²⁄₅ kg of apples. 

What we did:

2 ⁴⁄₅ + 3 ³⁄₅ = 2 + 3 + ⁴⁄₅ + ³⁄₅

                   = 5 + ⁷⁄₅

                   = 5 + 1 ²⁄₅

                   = 6 ²⁄₅

Adding Mixed Numbers with Unlike Denominators

Now, let us look at an example to understand the addition of mixed numbers with unlike denominators.

Susan has 1 4⁄7 liters of orange juice. Keith has 2 2⁄5 liters of orange juice. How much orange juice do they have? Here, to find the answer, we need to add mixed numbers 1 4⁄7 and 2 2⁄5. Here, the denominators of both the fractional parts are different. 

To add mixed numbers use any of the following methods:

Method 1:  

• Add the whole numbers separately and add unlike fractions separately.

Add   1 4⁄7  + 2 2⁄5
Adding whole numbers	Adding Unlike fractions
1 + 2 = 3	4⁄7 + 2⁄5 LCM of 7 and 5 is 35. Therefore  4⁄7 = 4⁄7  x  5⁄5 =  20⁄35      and 2⁄5  =  2⁄5  x  7⁄7 =  14⁄35 so, 4⁄7 + 2⁄5  =  20⁄35 +  14⁄35 = 34⁄35

• Combine the sum of the whole numbers and the fractional parts.

        3 + ³⁴⁄₃₅  = 3 ³⁴⁄₃₅

Method 2:

• Convert the mixed numbers to improper fractions.

       1 ⁴⁄₇  = ¹¹⁄₇ and 2 ²⁄₅ = ¹²⁄₅

• Add, unlike fractions.

       1 ⁴⁄₇ + 2 ²⁄₅ = ¹¹⁄₇ + ¹²⁄₅

Therefore, 

        LCM of 7 and 5 = 35

So,

    ¹¹⁄₇ = ¹¹⁄₇ x ⁵⁄₅ = ⁵⁵⁄₃₅

and 

   ¹²⁄₅ = ¹²⁄₅ x ⁷⁄₇ = ⁸⁴⁄₃₅

Therefore,

  ¹¹⁄₇ + ¹²⁄₅ = ⁵⁵⁄₃₅ + ⁸⁴⁄₃₅

                   = ¹³⁹⁄₃₅

• Convert the improper fraction to a mixed number.

        ¹³⁹⁄₃₅ = 3 ³⁴⁄₃₅