# Basic Algebra/Working with Numbers/Multiplying

## Lesson

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:

${\displaystyle {\frac {5}{9}}\times {\frac {7}{4}}}$

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:

${\displaystyle {\frac {5}{9}}\times {\frac {7}{4}}={\frac {5\times 7}{9\times 4}}={\frac {35}{36}}}$

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

Notice that in the problem above there was a top heavy fraction (${\displaystyle {\frac {7}{4}}}$ ). 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:

${\displaystyle {\frac {100}{101}}\times {\frac {263}{325}}\times {\frac {150}{175}}}$

The first thing you should notice is that ${\displaystyle {\frac {150}{175}}}$  can be simplified to ${\displaystyle {\frac {6}{7}}}$ . This should make this calculation a little easier. As above, we simply multiply the numerators together then multiply the denominators together.

${\displaystyle {\frac {100}{101}}\times {\frac {263}{325}}\times {\frac {6}{7}}={\frac {100\times 263\times 6}{101\times 325\times 7}}={\frac {157800}{229775}}}$

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:

${\displaystyle {\frac {6312}{9191}}}$

## Practice Problems

Use / as the fraction line!

1

 ${\displaystyle {\frac {5}{7}}\times {\frac {10}{12}}=}$

2

 ${\displaystyle {\frac {3}{2}}\times {\frac {1}{2}}=}$

3

 ${\displaystyle {\frac {125}{2}}\times {\frac {32}{4}}=}$

4

 ${\displaystyle {\frac {25}{1000}}\times {\frac {50}{75}}=}$

5

 ${\displaystyle {\frac {120}{500}}\times {\frac {100}{170}}=}$

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