Adding and Subtracting Mixed Numbers with the Same
Denominator
Now let’s consider how to add and subtract mixed
numbers with the same denominator. We start with
addition.
Suppose, for instance, that we want to add  . Let’s draw a diagram to represent this sum.
We can rearrange the elements of the diagram by combining the
whole numbers and the fractions separately.
This diagram shows that the sum is  .
Note that we can also write and solve this problem vertically.
Similarly, we can subtract mixed numbers that have the same
denominator.
Can you explain how the preceding diagrams confirm this
answer?
To Add (or Subtract) Mixed Numbers That Have the Same
Denominator
- add (or subtract) the fractions, ¦ add (or subtract) the
whole numbers, and
- write the answer in simplest form.
EXAMPLE 1
Add:  .
Solution
Because 
Our answer is  .
EXAMPLE 2
Find the sum of  .
Solution
EXAMPLE 3
Subtract:  .
Solution
We set up the problem vertically.
Because  . Therefore the difference is  .
EXAMPLE 4
The value of stock shares is normally expressed in dollars as
a mixed number or fraction. Suppose that one morning the stock of
a certain company opened at a price of  per share. By the end of the day, the
price had risen by  . What was the price of the stock per
share by the end of the day?
Solution
The price of the stock rose by so we must add and .
At closing, then, the price of the stock was  per share.
EXAMPLE 5
A movie lasts  hours. After an hour-and-a-quarter has
passed, how much longer will the movie run?
Solution
This question asks us to subtract  from
So there is still an hour-and-a-half of the movie to see.
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