Percentages are often found in proportional situations. Percentage notation is one way to express a proportional ratio.
A percentage, denoted |\%,| is a ratio with the denominator |100.|
||24\ \%=\dfrac{24}{100}||
To learn more about calculating percentages, consult the following.
The following examples illustrate the use of percentages in proportional situations.
A motorist travels from Montebello to Quebec City. The distance between the 2 cities is |350\ \text{km}.|
The following animation illustrates the ratio between the percentage of the trip completed and the distance traveled by the driver.
Move the black slider to control the animation.
Looking at the animation, we notice the following equalities.
||\begin{align}7\ \%\text{ of }350\ \text{km}&=24.5\ \text{km}\\\\52\ \%\text{ of }350\ \text{km}&=182\ \text{km}\\\\100\ \%\text{ of }350\ \text{km}&=350\ \text{km}\end{align}||
There is a mathematical way to calculate a percentage of a number.
A Secondary I class generally has a maximum of |28| students. The percentage of students in the class varies according to the school’s enrollment.
The following animation illustrates the ratio between the percentage of students actually enrolled in the class and the number of students it represents. Move the black slider to control the animation.
The number of students has been rounded up to the nearest whole number. For example, for a class filled to |30\ \%| capacity, we obtain the following equation.
||30\ \%\text{ of }28\text{ students}=8.4\text{ students}||
Since it is impossible for a group of students to be a decimal number, we round off to the nearest whole number. Therefore, a class filled to |30\ \%| capacity is a class with |8| students.
Note also that some classes may exceed the |28| student limit. In this case, the capacity would exceed |100\ \%.|
Like in the previous example, when solving proportional situations where one of the variables corresponds to the number of people or objects, we must round off the answer. Depending on the context, round up or down.