Adding and Subtracting Mixed Numbers with Different Denominators

We have previously shown that, when we add (or subtract) fractions with different denominators, we must first change the unlike fractions to equivalent like fractions. The same applies to adding (or subtracting) mixed numbers that have different denominators.

EXAMPLE 1

Find the sum of .

Solution

The denominators have no common factor other than 1. Therefore the least common denominator is the product of 5 and 3, or 15.

Now we use the rule for adding mixed numbers that have the same denominator.

The sum of is .

Subtracting mixed numbers that have different denominators is similar to adding them.

EXAMPLE 2

Subtract .

Solution

As usual, we use the LCD (which is 100) to find equivalent fractions. Then we subtract the equivalent mixed numbers with the same denominator. Again, let’s set up the problem vertically.

Therefore the answer is .

EXAMPLE 3

Find the sum of .

Solution

Set up the problem vertically and use the LCD, which is 60.

Since .

EXAMPLE 4

Find the missing dimension.

Solution

The total length of the figure is feet. To find the missing dimension, we need to add feet and feet and then subtract this sum from .

The missing dimension is feet. We can check this answer by adding , , and , getting .