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:

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

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

Use / as the fraction line! <quiz display=simple points="1/1"> { |type="{}"} $\frac{5}{7}\times \frac{10}{12}=${ 50/84|25/42_13 }

{ |type="{}"} $\frac{3}{2}\times \frac{1}{2}=${ 3/4_13 }

{ |type="{}"} $\frac{125}{2}\times \frac{32}{4}=${ 4000/8|4,000/8|1000/2|1,000/2|500/1|500_13 }

{ |type="{}"} $\frac{25}{1000}\times \frac{50}{75}=${ 1250/75000|1,250/75,000|2/120|1/60_13 }

{ |type="{}"} $\frac{120}{500}\times \frac{100}{170}=${ 12000/85000|12,000/85,000|60/425|12/85_13 } </quiz> Template:BookCat Template:Simple Page Navigation