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.