Transcript

INSTRUCTOR:

Here is a mathematical cake. Mathematical cakes are split into 10 equal slices. The whole cake is 100%. So each slice is 100% divided by 10, which is 10%. Here is a percentage question. Suppose the whole cake costs 3 pounds. How much would 70% of the cake cost? Well, 70% is seven slices of cake. If we work out how much one slice, or 10%, of the cake costs, then we can find the cost of 70% of the cake.

100% of the cake cost 3 pounds. So one slice costs 3 pounds divided by 10. That's 300 pennies divided by 10, or 30 pence. We can write this as naught pounds 30. One slice cost naught pounds 30, two slices cost naught pounds 60, three slices cost naught pounds 90, four slices costs 1 pound 20, and so on, all the way up the cake. Finally, 10 slices cost 3 pounds.

Now we can read off the answer to 70% of 3 pounds as 2 pounds 10. Work out these other percentages using the mathematical cake-- 40% of 3 pounds. Read across, and that's 1 pound 20. 80% of 3 pounds-- read across, and that's 2 pounds 40. 50% of 3 pounds-- read across, and that's 1 pound 50.

Suppose the cake weighs 500 grammes. We can use the mathematical cake method to work out multiples of 10% of 500 grammes. 10% of 500 grammes is the same as 1/10 of 500 grammes, or 50 grammes. We can label the right-hand side of the cake going up in 50 grammes. No slices weigh naught grammes.

One slice weighs 50 grammes, two slices weigh 100 grammes, and so on all the way up the cake. Finally, 10 slices weigh 500 grammes. Then we can read off the answer to the following questions-- 20% of 500 grammes, 90% of 500 grammes, 30% of 500 grammes. Do these questions for yourself and then click on reveal answers to check your answers.