You and your brother have your pocket money split in the ratio 2:7. If your brother receives £42, how much do you receive?

Ratios are best thought of as how to split up one total amount into different portions. People often like to think about a cake; in this particular scenario we are splitting a cake with 9 slices (7 + 2) into one portion of 2 slices, and another portion of 7 parts.
To answer this question we need to find out the value of one 'slice', in order to find out how much your 2 'slices' would be worth altogether. Because we know that your brother's portion of 7 slices is equal to £42, we can use that to work out what one slice is worth by diving £42 by 7. This gives us £6, meaning that one single slice of the cake is £6. All that is left to do is to go back to the initial ratio - 2:7 - and multiply the £6 we've got by the 2 on our side of the ratio in order to find out how much pocket money we receive. That gives us £12, and that is the answer to the question.