GRE Arithmetic: Fractions (Part 3 of 5) | Multiplication


Arithmetic Review: Fractions (Part 3)
In this third part we are going to review
multiplication of fractions.
There is really nothing tricky about multiplying
fractions. Say we wanted to multiply the following
two fractions, 8/3 times 7/3. When multiplying
fractions all you need to do is multiply across
each fractions numerator and each fractions
denominator, in this case we multiply the
numerators 8 and 7 which is equal to 56, and
we multiply the denominators 3 times 3 obtaining 9.
In essence you pretty much place the
product of the numerator
over the product of the denominator.
When dealing with fractions always remember to simplify and reduce the fraction whenever possible.
In this example the answer 56/9 is already
reduced in simplist form
since there are no common factors
that can be canceled out from both the numerator
and denominator. Let’s go over another example,
Say I want to multiply the following fractions: 10/7 times negative 1/3, once again multiplying
multiplying fractions is fairly straight forward all we
need to do is to multiply the numerators together
in this case 10 times negative 1, and multiply
the denominators together in this case 7 times 3.
Then it’s just a matter of individually
simplifying the numerator and denominator,
simplifying the numerical expressions we obtain
the final answer equal to negative 10 over 21,
recall that we can also move the negative
sign in front of the fraction as follows
yielding the following equivalent fraction: -10/21. Notice that in this example the fraction is in simplest form
there is no need to reduce the fraction.
Now let’s try an example were we need to
reduce the fraction, say we want to multiply
the following fractions: 4/5 times 10/12
we first multiply each fractions numerator and
denominator across, doing that we obtain the fraction
40/60, notice that we can simplify this fraction
since both 40 and 60 have a common factor,
both 40 and 60 end with zero so we can
divide both of these numbers by ten,
dividing numerator and denominator by 10 yields the fraction 4/6,
this fraction can
be further reduced since both 4 and 6 are even,
meaning that they have 2 as a common
factor, so we go ahead and divide both numerator
and denominator by 2 doing that yields the
final answer equal to 2/3.
Always reduce a fraction whenever possible,
we can also reduce
the fraction first before proceeding with
the multiplication step, for example we can
first start by reducing the fractions, across
the multiplication sign, in other words, we
can reduce the numerator of one fraction and
the denominator of the other fraction.
In this example
the numerator 4 can be simplified with the
denominator 12, since both of these numbers
have a common factor in this case they are
both divisible by 4, so the numerator 4 simplifies
to 1 and the denominator 12 reduces to 3.
In the same manner, the numerator 10, can be simplified with the denominator 5,
since both of these numbers have 5 as a common factor,
so the
numerator 10 simplifies to 2, and denominator
and the denominator 5 simplifies to 1,
by reducing first we will
now be multiplying smaller numbers,
in this case we now have 1 over 1 times 2/3 which
simplifies to 2/3. Keep in mind that this
method of reducing fractions across the multiplication operator only works when multiplying fractions,
do not try to simplify fractions when you are adding or subtracting them!
Recall that you need to find the common denominator before you add or subtract fractions.
The final type of multiplication problems
that you might encounter is when you are multiplying
an integer by a fraction for example say we
want to multiply the following numerical expressions:
2 times 4/5, recall that another way of
writing the integer 2 as a fraction is by
thinking about the number as having a denominator
of 1, so we can rewrite the integer 2 as 2
over 1, now we can go ahead and multiply across,
carrying out the product we obtain the final answer equal to 8/5.
Alright let’s end the video with the
final example lets multiply the following
numerical expressions: 3/36 times 3, we can
write 3 as a fraction by including the integer one in
the denominator as follows, next we can take
the numerator of either fraction and simplify
it with the denominator of the left fraction,
since both 3 and 36 have a common factor of 3,
so we go ahead and divide the numerator of
either fractions and 36 by three, I am going
to simplify the numerator of the right fraction,
doing that we obtain the following.
Next we go ahead and multiply the fractions, any number multiplied by 1 is equal to itself.
In this case we obtain 3/12, this fraction can be
further simplified by dividing both numerator and
denominator by 3. Reducing the fraction we obtain the final answer equal to 1/4.
Alright in our next video we are going to continue reviewing operations with fractions.
This time around we will review division of fractions and review how to convert mix numbers into fractions.

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