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Multiplying FractionsMany situations require us to multiply fractions. For
instance, suppose that a mixture in a chemistry class calls for To illustrate how to find this product, we diagram these two fractions.
In the following diagram, we are taking
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
The numerator and denominator of the answer are the products of the original numerators and denominators. To Multiply Fractions
EXAMPLE 1 Multiply: Solution
EXAMPLE 2 What is Solution Finding
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
EXAMPLE 4 Multiply: Solution We cancel and then multiply.
EXAMPLE 5 At a college, Solution We must find
One-tenth of the students in the college take elementary algebra. EXAMPLE 6 Suppose that you spend Solution Apply the strategy of breaking the question into two parts.
Thus you can solve this problem by computing
You have $600 left after paying the rent.
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g of sodium chloride. If we make only 
of that mixture, we need 
g of sodium chloride. 
of the original whole, which we can compute as
follows. 
.
of 10? 
.
.
of the students take a math course. Of these
students, 
take elementary algebra. What fraction of
the students in the college take elementary algebra? 
of your monthly salary on rent. If your salary is
$960, how much do you have left after paying the rent? 
. 
