By using the Unitary Method, it becomes easier to compare different proportions. The Unitary Method involves finding out the quantity of one item.
This involves setting one part of the proportion to a value of 1. It does not matter which part of the proportion is being set to 1, although it is necessary to understand what the method is indicating.
Three hundred grams of chocolates are being sold for £1.20, or 120p This can be written as either:
300 : 120, or 1 : 0.4 (1 gram will cost 0.4p), or
120 : 300, or 1 : 2.5 (1p will buy 2.5g).
Using the unitary method allows different comparisons to be made. Having found the proportion in terms of one unit, the proportion can be multiplied to find the amounts for other units.
1. A company has two production lines making bread. The first production line produced 4 faulty loaves out of 2600 in the last shift. The second produced 5 faulty loaves out of 3400. Which production line produces more faulty bread?
Answer: First production line
First production line: 4 faults per 2600, 4 : 2600 is a proportion of 1 : 650
Second production line: 5 faults per 3400, 5 : 3400 is a proportion of 1 : 680
The first production line produces a faulty loaf more frequently than the second.
2. In one year 1092 were offered a flu vaccination and 42 people accepted. In the following year, following a publicity campaign, 2455 people were offered a vaccination, and 90 people accepted. Was there an increase in the proportion of people being vaccinated in the second year?
Answer: No, there was a decrease
In the first year 42 people from 1092, or 42 : 1092 which is 1 : 26
Second year: 90 : 2455 which is 1 : 25.8