Working with Fractions

Multiplying fractions.

to multiply a fraction with another fraction multiply the tops together and the bottoms together a/b X c/d = ac / bd.

For example

a whole number could be written as n/1, for example 9 = 9/1 so multiplying by a whole number is the same

2/3 * 9 = 2/3 * 9/1 = 2*9 / 3*1 = 18/3 = 6

Dividing fractions

to divide a fraction by another fraction, you flip the divisor then multiply .

For example

Manipulating fractions

Sometimes we need to changes to numbers in a fraction to make it easier to understand without changing the value. We can multiply or divide the top and bottom of a fraction by any number we want, as long as we do the same thing to the top and bottom. In the first example, if we divide the top and bottom by 6 we get.

In the second example, if we want the answer expressed as 16ths instead of 4ths we can multiply the top and bottom by 4.

Notice that in both cases you can also look at it as multiplying by 1.

Over half of the math that we do in this class is just different ways of multiplying by 1!!

Canceling and simplifying

Sometimes when we have to multiply several fractions together we can make our work a lot easier and reduce risk of errors in on our calculator by doing canceling and simplifying. This is because when multiplying and dividing the order doesn’t matter.

so

So, if we find ourselves multiplying a string of fractions

If we see the same number on bottom and top we know that the result of that division will be one and we can “cancel” them