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 fraction are called mixed numbers.
Adding mixed numbers with like denominators
Here, to find the quantity 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.
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.
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}
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