Multiplying Fractions
Many situations require us to multiply fractions. For
instance, suppose that a mixture in a chemistry class calls for g of sodium chloride. If we make only of that mixture, we need of , that is, g of sodium chloride.
To illustrate how to find this product, we diagram these two
fractions.
![](./articles_imgs/714/pic3.gif)
In the following diagram, we are taking of the .
![](./articles_imgs/714/pic4.gif)
Note that we divided the whole into 15 parts and that our
product, containing 8 of the 15 small squares, represents the
double-shaded region. The answer is therefore of the original whole, which we can compute as
follows.
![](./articles_imgs/714/pic6.gif)
The numerator and denominator of the answer are the products
of the original numerators and denominators.
To Multiply Fractions
- first multiply the numerators,
- then multiply the denominators, and
- finally write the answer in simplest form.
EXAMPLE 1
Multiply: .
Solution
![](./articles_imgs/714/pic8.gif)
EXAMPLE 2
What is of 10?
Solution
Finding of 10 means multiplying by 10.
![](./articles_imgs/714/pic10.gif)
In Example 2, we multiplied the two fractions first and then
simplified the answer. It is preferable, however, to reverse
these steps: Simplify first and then multiply. By first
simplifying, which is called canceling, we divide any numerator
and any denominator by a common factor. Canceling before
multiplying allows us to work with smaller numbers and still
gives us the same answer.
EXAMPLE 3
Find the product of .
Solution
![](./articles_imgs/714/pic12.gif)
EXAMPLE 4
Multiply: .
Solution
We cancel and then multiply.
![](./articles_imgs/714/pic14.gif)
EXAMPLE 5
At a college, of the students take a math course. Of these
students, take elementary algebra. What fraction of
the students in the college take elementary algebra?
Solution
We must find of .
![](./articles_imgs/714/pic17.gif)
One-tenth of the students in the college take elementary
algebra.
EXAMPLE 6
Suppose that you spend of your monthly salary on rent. If your salary is
$960, how much do you have left after paying the rent?
Solution
Apply the strategy of breaking the question into two parts.
- First, find
of $960.
- Then, subtract that result from $960.
Thus you can solve this problem by computing .
![](./articles_imgs/714/pic20.gif)
You have $600 left after paying the rent.
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