# 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.

Very good