Calculating amounts using proportions
Proportion calculations can be used to calculate values when one relationship is known.
Example
8 pens cost ÂŁ2.16. Calculate how much 7 pens cost.
To find out the cost of one item use the unitary method - divide the cost by how many items have been bought. Any amount can be calculated when the value of 1 is known.
8 pens cost ÂŁ2.16.
Dividing both numbers by 8:
\(\begin{array}{ccc} 8~\text{pens} & = & \pounds 2.16 \\ \div 8 && \div 8 \\ 1~\text{pen} & = & \pounds 0.27 \end{array}\)
Multiplying both numbers by 7:
\(\begin{array}{ccc} 1~\text{pen} & = & \pounds 0.27 \\ \times 7 && \times 7 \\ 7~\text{pens} & = & \pounds 1.89 \end{array}\)
So 7 pens cost ÂŁ1.89.
Best buys
proportionProportion is used to show how quantities and amounts are related to each other. The amount that one quantity changes in relation to another quantity is governed by proportion rules. calculations can be used to decide which items in a shop offer the best value. Many items sold in supermarkets have a price and a price per 100 g or per kg. This lets people compare products and get the best value for money.
Comparing best buys
Proportion calculations must be used to compare the cost of items. This makes either their cost or their size the same so comparisons can be made. It is generally easier to make the size of the items the same but how this is done can vary depending on the numbers that are used.
Example
If 2 kg of basmati rice costs ÂŁ2.68 and 500 g of long grain rice costs ÂŁ0.95 which one represents the best value for money?
There are many ways to approach this problem:
- calculate the cost of 500 g in the 2 kg bag
- calculate the cost of 2 kg worth of the 500 g bags
- calculate the cost of 1 kg for each of the bags
These are just a small number of ways in which this problem could be attempted.
For this solution, the cost of 1 kg for each of the bags will be calculated.
Price per kg for basmati rice:
\(2.68 \div 2 = \pounds1.34\)
Price per kg for long grain rice:
\(0.95 \div 0.5 = \pounds1.90\)
| Basmati rice | Long grain rice | |
| Price | 2 kg costs ÂŁ2.68 | 0.5 kg costs ÂŁ0.95 |
| Price per kg | ÂŁ1.34 | ÂŁ1.90 |
| Price | |
|---|---|
| Basmati rice | 2 kg costs ÂŁ2.68 |
| Long grain rice | 0.5 kg costs ÂŁ0.95 |
| Price per kg | |
|---|---|
| Basmati rice | ÂŁ1.34 |
| Long grain rice | ÂŁ1.90 |
This shows that basmati rice is cheaper per kg and better value for money than the long grain rice.