Multiplying Fractions
There are three ways to arrive at an answer when multiplying numbers where
fractions are present. The traditional method is to leave the terms in fraction
form. Here is the discussion about this method.
Method One
Multiplying Fractions
When we multiply integers, the answer is always a larger value than the two
numbers being multipled. Something different about multiplying proper fractions
is that the answer will always be smaller than both of the fractions being
multiplied. You could say that when you multiply two fractions you are getting a
portion of a portion of a whole. For example, let's multiply 1/8 x 1/4. If you
start with a whole pizza and take 1/8 of the pizza, you have one slice. Now if
you take 1/4 of that slice of pizza you end up with a very small portion of the
whole pizza. One fourth of one eigth of the pizza is one thirtysecondth of the
whole pizza. Mathematically, this can be written as:
1/8 x 1/4 = 1/32
When you multiply fractions you multiply the numerators to get
the numerator for the answer and you multiply the denominators to get the
denominator for the answer.
1 x 1 = 1
8 x 4 = 32
therefore 1/8 x 1/4 = 1/32
Let's look at an example using the integer bars. In this next example we
multiply 1/2 x 1/4. We start with a size 8 bar as one unit, then split it in two
halves (two size 4 bars). Next the size 4 bar is split into four quarters (four
size 1 bars). The answer is one of the size 1 bars or 1/8 of the unit bar. Here
is the picture that shows the process:
Mathematically, this is written as:
1/2 x 1/4 = 1/8
Our next example multiplies a proper fraction and an improper
fraction:
1/2 x 4/3
We start with a size 6 bar because it is the multiple of the two
denominators, 2 x 3 = 6. First we divide it into two halves because the first
fraction is 1/2. Then we divide one half into thirds and take four of them
because the second fraction is 4/3. The result is 4/6 which can be simplified to
2/3.
Mathematically, this is written as:
1/2 x 4/3 = (1 x 4) / (2 x 3) = 4/6 = 2/3
Now let's multiply a fraction and an integer. We will solve the
equation 2/3 x 9. First we convert the value of 9 to the equivalent fraction
9/1. We then multiply the numerators to get 18 and the denominators to get 3.
The fraction 18/3 is then simplified to 6.
2/3 x 9 = 2/3 x 9/1 =(2 x 9) / (3 x 1) = 18/3 = 6
Therefore, 2/3 of 9 is 6.
For our last example we will multiply four fractions. The
process is the same as for multiplying only two fractions. We multiply all of
the numerators to get the numerator for the answer and multiply all of the
denominators to get the denominator for the answer. Another way to solve an
equation which multiplies four fractions is to multiply two fractions then
multiply the remaining two fractions, then multiply the two results. Let's solve
the following equation using both of these methods. First we will multiply all
the fractions together:
2/3 x 9/2 x 3/8 x 4
(2 x 9 x 3 x 4) / (3 x 2 x 8 x 1)
216 / 48 = 108/24 = 54/12 = 27/6 = 9/2 = 4 1/2
Now we will solve the same equation by multiplying 2/3 x 9/2
then 3/8 x 4 then multiplying those two results to get the final answer:
2/3 x 9/2 x 3/8 x 4
(2/3 x 9/2) x (3/8 x 4)
18/6 x 12/8
which can be simplified to:
3/1 x 3/2 = 9/2 = 4 1/2
The answer is 4 1/2 with either method that is used.
Method Two
My favorite method is to convert each fraction to a decimal with the aid of a
calculator, then proceed with the multiplication. Here is a discussion of that
method.
When you encounter a mixed number, whole number with a fraction, convert the
expression to a decimal number. For example, a 4 11/16 inch box is actually a 11
divided by 16 plus 4 box. This will produce a decimal equivalent to the 4 11/16
which would be difficult to work with.
So 4 11/16 is actually 4.6875
Method Three
The calculator has a key a b/c which can be used to enter fractions into a
calculator without the need for conversion before the multiplication is begun.
Here is a discussion of this method.
The Fraction Key Perhaps one of the nicest
features of this particular calculator is its ability to work fraction
arithmetic. When properly entered, the calculator will use fractions correctly
in any calculation. First, you need to know how to enter a fraction.
Single fraction: Enter the numerator (top number), press the fraction
key  , then enter the denominator (bottom
number). So the fraction  is entered as  .
The calculator displays the fraction something like  .
Mixed numbers: Use the fraction key twice. The mixed number  is
entered as  . In short,
simply press the fraction key between each number in a fraction or mixed number.
Your calculator knows the difference. The mixed number is displayed as  .
Now you are ready to use fractions in other calculations. Simply enter the
fraction wherever it appears as you continue typing the entire calculation. For
example, try computing  by entering the
following sequence:
The answer will be displayed as a fraction or a mixed number (if more than
1). In this case, you should get  , which means
 .
Find a practice worksheet HERE.
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Listen to an audio file on this topic HERE.
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