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To solve a directly proportional situation where percentages are involved, use one of the following strategies, depending on the context.
Calculating the percentage of a number consists of finding the number that corresponds to the desired percentage.
This calculation involves finding the missing term in an equation with fractions where one of the fractions has a denominator of |100|. Basically, the goal is to find the portion of a whole that corresponds to the given percentage. There are several methods for calculating the percentage of a number.
Method 1: Multiplication by Percentage
Method 2: Cross Multiplication
To perform this method successfully, it is important to know how to express a percentage in decimal notation.
Express the percentage in decimal notation.
Multiply the decimal by the number in order to find n percent of the number.
The results of a poll indicate that |30\ \%| of students of a high school with |1\ 500| students think that the cafeteria menu should be changed.
Express the percentage in decimal notation ||\displaystyle 30\ \%=\frac{30}{100}=0.3||
Multiply the decimal by the number in order to find n percent of the number ||0.3\times 1\ 500=450||
So, |450| students want the cafeteria menu changed.
This method is derived from the fundamental property of proportions. It should be noted that several methods can be used to solve a directly proportional situation when calculating the percentage of a number. However, the cross multiplication method is often preferred in situations involving percentages.
Convert the problem into an equation with two fractions where one of the fractions represents the percentage and the other fraction contains the term with a missing numerator.
Calculate the percentage of the number using cross multiplication or another method of choice.
In a class of |32| students, |75\ \%| are boys. How many boys are there in the class?
Convert the problem into an equation with two fractions where one of the fractions represents the percentage and the other fraction contains a term with a missing numerator ||\displaystyle \frac{?\ \text{students}}{32\ \text{students}}=\frac{75}{100}||
Calculate the percent of the number using cross multiplication ||\begin{align}?\times 100&=32\times 75\\ \\ ?&=\frac{32\times 75}{100}\\ \\ ?&=24\end{align}||
So there are |24| boys in the class of |32| students.