Multiplication and division structures

Contexts in the equal sharing structure - part 2

The context of money does, however, provide some of the more natural examples in real life for this structure of the division operation. For example, a group of people might share a prize in a lottery, or share a bill in a restaurant: in both cases it is likely that we would share equally between the people in the group. An important class of everyday situations is where items are sold in multiple packs: a familiar requirement is to want to know the price per item. So, for example, if a shop is selling a pack of 9 CDs for €7.92 cent, the cost per CD, in cents, is found by the division 792 divided by 9. We can think to ourselves that the 792 cent are being shared equally between the 9 CDs.

This then extends naturally to the idea of price per unit of measurement. For example, to find the cost per litre of a 6-litre flagon of milk costing 210 cent, we should recognise that the calculation to be entered on a calculator is the division, 210 divided by 6. It is as though the 210 cent are being shared out equally between the 6 litres, giving 35 cent for each litre. Once again the word ‘per’, meaning ‘for each’, plays an important part in our understanding of this kind of situation.

This idea of ‘per’ turns up in numerous other situations in everyday life. For example, when calculating for a purchase how many or how much we get per cent or per euro, when finding miles per litre, determining how much someone earns per hour, an average speed in miles per hour, the number of words typed per minute, and so on: all these situations would correspond to the operation of division using the equal-sharing structure.