Percentages are useful measures because they tell us how much of the whole we currently have. If we have 50\% then we have half the amount. If we have 100\%, what we have is equal to the amount. And if we have 200\% then we have double that amount.
When looking at percentages, the 'whole' is our reference number that our percentage amount refers to.
For example: 14 is equal to half of 28, so 14 is 50\% of 28.
But also: 14 is equal to double of 7, so 14 is 200\% of 7.
In both cases our amount is 14. The numbers that change are the percentage value and our reference number - the whole.
20\% of a quantity is the same as:
When looking at percentages, the 'whole' is our reference number that our percentage amount refers to.
Let's consider the case where we don't know the whole, or reference number:
14 is 50\% of some number. What is this number?
To work out the whole, we can use the percentage value to figure out how much of the whole we
currently have. Since 50\% is equal to \dfrac{1}{2}\,when written as a fraction, we know that 14 is half of our
missing number. If we let x represent our missing number, we can express this information as the equation:14=x\times \frac{1}{2}
We can solve for x by multiplying both sides of the equation by 2, and find that x=28, so we know the 'whole' we are looking for is 28.
We can apply this same technique to any amount and percentage.
20\% is of number is equal to 7. What is this number?
If 39 is 30\% of some number, what is this number?
An approach to solving this would be to find 1\% of the number first. From there we can find the whole, or indeed any other percentage amount.
We know that 30\% of the number is 39, so if we divide 39 by 30, we now know 1\% of the number. Multiplying this amount by 100 will then tell us 100\% or the whole of the amount.x=\frac{39}{30}\times 100=1.3\times 100 = 130
This is known as the unitary method.
We can find the whole by:
Dividing the given amount by the percentage number. This finds 1\%of the whole.
Multiplying the result by 100. This will give us 100\% of the whole which is the number we are looking for.
Since the order of operations allows us to perform either multiplication and division in any order, we can do whichever operation is easier first.
9\% of a number is 72.
Complete the statement:
Because 9\% of the number is ⬚, we know that 1\% of the number is ⬚.
What is the number?
We can find the whole by using the unitary method:
Dividing the given amount by the percentage number. This finds 1\%of the whole.
Multiplying the result by 100. This will give us 100\% of the whole which is the number we are looking for.