# Basic Algebra/Working with Numbers/Multiplying

## Vocabulary[edit | edit source]

## Lesson[edit | edit source]

Multiplication of rational fractions is perhaps easier than addition and subtraction (lessons 4 and 5). This is because the denominators do not have to be equal, so you do not need to find a common denominator before carrying out a calculation. Consider the following problem:

This may look like a difficult calculation but in reality it's rather easy. We simply multiply the two numerators together, then multiply the denominators. So, the answer to the above problem would be:

This fraction is irreducible as 35 and 36 share no common factors.

Notice that in the problem above there was a top heavy fraction (). When multiplying two fractions, if one is top heavy then leave it as it is until you have your final answer. Attempting to multiply a mixed number with a fraction will result in an incorrect answer.

Let us now consider a more complex problem. Say we had three large fractions which we had to multiply together:

The first thing you should notice is that can be simplified to . This should make this calculation a little easier. As above, we simply multiply the numerators together then multiply the denominators together.

Now this is a huge number so trying to find common factors in order to reduce it will be very difficult and time consuming. If you have a scientific calculator to hand, simply enter the above fraction and it should give you an irreducible fraction out. My calculator gives the following result:

## Practice Problems[edit | edit source]

Use `/`

as the fraction line!