MULTIPLYING AND DIVIDING FRACTIONS

Case 2

MULTIPLICATION

Multiplying fractions is actually very easy!

You begin by placing the two fractions you wish to

multiply next to each other.• Example: 1/3 x 5/8

Next you multiply the two numerators• Example- the two numerators are 1 and 5 so the

numerator of the answer will be 1 x 5 which is 5

MULTIPLICATION

Next multiply the two denominators together• The two denominators are 3 and 8 so the

denominator in the answer will be 3 x 8 which equals 24

Combine the final numerator and denominator

together to get a final fraction• Example- the final numerator was 5 and the final

denominator was 24 so the final fraction will be 5/24.

MULTIPLICATION

The final step in multiplying fractions is to check

if your final answer can be reduced• Reducing means checking to see if the numerator and

denominator can be divided by a common number• In our case the fraction is 5/24. There is no number that you

could divide 5 and 24 by. Therefore, 5/24 is the final answer.• An example of a fraction that can be reduced would be

5/30. The common number that you can divide by is 5. You can divide 5 by 5 to get 1 and you can divide 30 by 5 to get 6. So the new numerator will be 1 and the new denominator will be 6. The final fraction is 1/6.

DIVISION

Dividing fractions is actually very similar to

multiplying.

Before we begin you will need to know what

the term reciprocal means.• The reciprocal of a fraction is simply switching the

numerator and the denominator. • For example, the reciprocal of 5/8 is 8/5

DIVISION

Now that you know what the reciprocal of a

fraction is we can learn to divide.

We will begin with the equation 5/8 ÷ 3/4.• To divide a fraction, what you really want to do is

multiply by the reciprocal.• So we want to do 5/8 x the reciprocal of 3/4• As we mentioned earlier, the reciprocal is simply

switching the numerator and denominator of a fraction. Therefore the reciprocal of 3/4 would be 4/3

DIVISION

So, if dividing fractions really means multiply

by the reciprocal we want to do 5/8 x the

reciprocal of 3/4. • We know that the reciprocal of 3/4 is 4/3 so the

equation we really want to solve is 5/8 x 4/3

From this point you simply solve the equation

the exact same way you solve a multiplication

problem.

DIVISION

First you multiply the numerators of 5 and 4 to

get 20 and then multiply the denominators to

get 24. The final fraction is 20/24.• Like any multiplication problem, you have to see if the

fraction can be reduced by a common number.• In this case, 20 and 24 can both be divided by 4 so the

new numerator will be 5 and the new denominator will be 6. The result is a final answer of 5/6

So, 5/8 ÷3/4 is 5/6.

SUMMARY

As you can see, multiplying and dividing

fractions is really not too difficult.

Some key things to remember are to always

make sure your fraction is reduced and also

make sure you take the reciprocal in a division

problem before solving the equation.