Friday, 6 March 2009

More cake and a clock

Some people don't cut their cake into halves, quarters or eighths. They might cut it into three and each piece is a third of the cake. What happens if you add a third to a half? Well you first need to cut the cake in half. Think of a round cake and now think of it as a clock. So the first cut is from o'clock to half past.

You can now visualise the half (from o'clock to half past) and add the third (another twenty minutes) from half past to ten to the hour. You have 1/2 + 1/3 which looks like most of a cake minus 10 minutes. What is the sum of these two fractions? To add fractions you have to have pieces of cake that are the same size. 1/4 +1/4 = 1/2. That's easy but what about 1/2 + 1/3? You can still find the answer in the clock. Half and hour is 3 lots of 10 minutes and 20 minutes is two lots of ten minutes which makes five lots of 10 minutes.

The only thing left that you need to know is that six lots of 10 minutes makes a full hour. Each 10 minutes is 1/6 of an hour. Back to the cake. You add 3/6 to 2/6 to make 5/6. The posh words for adding different fractions is that you have to find the lowest common denominator. It sounds difficult but think of it as a clock. How many minutes will divide into both the numbers that you are given?

That sums it up

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