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!  { $$\frac{5}{7} \times \frac{10}{12} = $${ 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 }
 * type="{}"}