Multiplying Mixed Numbers

Some situations require us to multiply mixed numbers. For instance, suppose that your regular hourly wage is and that you make time-and-a-half for working overtime. To find your overtime hourly wage, you need to multiply by . The key here is to first rewrite each mixed number as an improper fraction.

So you make per hour overtime.

To Multiply Mixed Numbers

• change each mixed number to its equivalent improper fraction,
• follow the steps for multiplying fractions, and
• write the answer in simplest form.

EXAMPLE 1

Multiply by .

Solution

EXAMPLE 2

Multiply:

Solution

Note in this problem that, although there are several ways to cancel, the answer always comes out the same.

EXAMPLE 3

A nurse gave a patient tablets of the medication atropine sulfate. If each tablet contains grain (gr) of this medication, how much atropine sulfate did the patient receive?

Solution

To find the total amount of atropine sulfate administered, we need to multiply by .

Therefore the nurse gave the patient gr of atropine sulfate.

EXAMPLE 4

A lawn surrounding a garden is to be installed, as depicted in the following drawing.

How many square yards of turf will we need to cover the lawn?

Solution

Let’s break this problem into three steps. First, we find the area of the rectangle with dimensions yards and yards. Then, we find the area of the small rectangle whose length and width are yards and 2 yards, respectively. Finally, we subtract the area of the small rectangle from the area of the large rectangle.

We will need sq yd of turf for the lawn.