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Expanding and
Reducing Fractions | Multiplication of
Fractions | Reciprocals | Division
of Fractions | Summary
Multiplication of Fractions
CAGR5 NS 2.4 & 2.5
CA GR7 NS 1.2
Now you are ready to multiply fractions.
Here's how it's done:
So...
...and that's all there is to it.
Usually you will want to reduce your result
to its lowest terms. In other words, check to see if any number
will go into both top and bottom of the fraction evenly. If this
is possible, you can reduce the fraction.
Let's take the above examples to see if the
results are in the lowest terms:
and
Look at the results. Is there any number
that will go evenly into 8 and 15 above? No. So the result
is
in the lowest terms.
Is there any number that will go evenly into
3 and 105 above? Yes. The number 3 goes into both of them. So...
...or, the way that it's
generally shown:
which is the result in lowest
terms.
If
possible, do all of the
reducing of fractions before you multiply, so that
the result will automatically be in the lowest terms. Remember
when we considered what a term
is? A term is considered to be one
number. And when two numbers are divided or multiplied together,
they are considered to be one term. So...
....is one term, so if there is
any number that goes into top and bottom of either fraction, we
can reduce:
Three will go into the top of
one fraction and the bottom of the other. The result:
The product is produced automatically in lowest
terms.
CAUTION: Do you remember what separates one
term from another? Plus (+) and minus (-) signs separate terms. So
you cannot
reduce a fraction if plus and minus signs separate the
terms:
Here you CANNOT cancel (reduce)
the three and the nine. The plus sign (+) is in the way.
actually
means 
Remember? So, if you did cancel the 3 and 9
above, you would change the denominator for the 2. This you cannot
do. Here:
You could
cancel the 3 and the 9...
...because no plus or minus sign is in the
way.
Now you know how to multiply fractions, but
how about:
multiplying a fraction by a whole
number...
...or multiplying a fraction
by a mixed number...
...or multiplying a mixed
number by a mixed number?
Well, you change whole numbers
and mixed numbers to improper fractions, then multiply.
becomes
 which is also 
- Any mixed number can be changed to an
improper fraction by multiplying the whole number by the
denominator and adding the result to the numerator of the
fraction (remember?). So...
becomes 
which is
also 
...and...
becomes 
and remember to cancel...
which is the
same as 
Let's stop and do
Practice Exercise 5-1.
Next Page:
Reciprocals
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