Basic Algebra/Working with Numbers/Multiplying

< Basic Algebra < Working with Numbers

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:

{\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:

{\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 ( ${\frac {7}{4}}$ ). 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:

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

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

{\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:

{\frac {6312}{9191}}

Practice Problems

Here are some problems for you to try yourself. Make sure you set out all working as above so you can see where you've went wrong if your answers don't match those given.

${\frac {5}{7}}\times {\frac {10}{12}}=({\frac {25}{42}})$
${\frac {3}{2}}\times {\frac {1}{2}}=({\frac {3}{4}})$
${\frac {125}{2}}\times {\frac {32}{4}}=(500)$
${\frac {25}{1000}}\times {\frac {50}{75}}=({\frac {1}{60}})$
${\frac {120}{500}}\times {\frac {100}{170}}=({\frac {12}{85}})$

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