Saturday, 18 April 2009

Multiplication of fractions

The next GCSE question is about multiplication of fractions.

First, a bit about the words we use. A fraction has a bit that you multiply with and bit that you divide by, which we call the numerator and the denominator. In 4/5, for instance, 4 is the numerator and 5 is the denominator.

Now, let's say you have 1/2 x 4/5. Do you know how to deal with this? You multiply the numerators together and then the denominators so you get 4/10. You can see how both the numerator and the denominator end up bigger than in either of the original fractions.. The request usually follows to put the fraction in its simplest form. Now I hope you can just see that 4/10 = 2/5. We look for whole numbers which can divide into both the numerator and denominator. 2 is a number which will do that in this case. Dividing both the numerator and the denominator by the same amount makes no difference to the value of a fraction, so we do this to 4/10 and get 2/5. We know we can't make the fraction simpler still because both 2 and 5 are prime numbers, so neither of them can be divided to make even smaller whole numbers.

What happens when you have to divide by a fraction? Division is the opposite of multiplication, so, for instance, dividing by 1/2 is the same as multiplying by 2/1.

Imagine a cake, divided into 4 pieces. You get one piece, so you have 1/4 of the cake. Multiplying that by 4 would give you a full cake. Dividing by 1/4 is the same as multiplying by 4/1, which is the same as just multiplying by 4. So starting with 1/4 and dividing that by 1/4 gives you a full cake again.

If that isn't obvious, then try to see that anything divided by itself is 1. Three divided by three is one. 99 divided by itself is 1, and so on. So 1/4 divided by 1/4 is 1. 1/4 of a cake, divided by 1/4, is 1 cake.

That sums it up.

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