# ADDING AND SUBTRACTING MIXED FRACTIONS

Adding and subtracting mixed fractions :

To add and subtract mixed fractions, first we have to convert the mixed fractions into improper fraction.

After converting the mixed fraction into improper fraction we have to consider the denominators.

• If the denominators are same then we can put one denominator commonly and combine the numerators.
• If the denominators are not same, then we have to take L.C.M in order to make the denominators same.After making the denominators same, we can combine the numerators.

Let us see some example problems based on the concept.

Example 1 :

Find the value of the following expression in lowest terms Solution :

First we have to convert the mixed fractions into improper fraction. Since the denominators are not same, we have to take L.C.M

L.C.M (5, 4) = 20

To make the denominator as 20, we have to multiply both numerator and denominator of the first fraction by 4 and multiply the numerator and denominator of the second fraction by 5.

(11/5) x (4/4)  =  44/20

(7/4) x (5/5)  =  35/20

(44/20) + (35/20)  =  79/20 Example 2 :

Find the value of the following expression in lowest terms Solution :

Improper form of first fraction

(11 + 10)/11  =  21/11

Improper form of second fraction

(3 + 1)/3  =  4/3

Now we have to subtract 4/3 from 21/11. By considering the denominator, they are not same so take L.C.M

L.C.M (11, 3) = 33

In order to make the denominator of the first fraction as 33, we have to multiply both numerator and denominator by 3.

(21/11) x (3/3)  =  63/33

In order to make the denominator of the second fraction as 33, we have to multiply both numerator and denominator by 11.

(4/3) x (11/11)  =  44/33

(63/33) + (44/33)  =  107/33 Example 3 :

Find the value of the following expression in lowest terms Solution :

Improper form of first fraction

(8 + 3)/4  =  11/4

Improper form of second fraction

(5 + 1)/5  =  6/5

L.C.M (4, 5) = 20

Multiply both numerator and denominator of the first fraction by 5.

Multiply both numerator and denominator of the first fraction by 4.

(11/4) x (5/5)  =  55/20

(6/5) x (4/4)  =  24/20

=  (55+24)/20

=  79/20 After having gone through the stuff given above, we hope that the students would have understood "Adding and subtracting mixed fractions".