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Welcome to our Math lesson on Operations with Percentages, this is the fifth lesson of our suite of math lessons covering the topic of Definition of Percentages, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
We can complete operations with percentages in the same way as we do with fractions and decimals. Yet, with percentages, we can do more types of additions and subtractions than with fractions or decimals.
If the amounts expressed in percent are independent from each other, we can add or subtract the percentages as in addition or subtraction of real numbers. For example, if 45% of a Spanish crew staff speak English and 37% of the same crew staff speak French, the percentage of staff who speak at least one foreign language is 45% + 37% = 82% of the staff.
The same is true for subtraction as well. For example, if 35% of students in a class have scored 80 points or higher in an exam but only 12% of students have scored 90 points or higher, the percentage of students who scored 80 - 89 points is 35% - 12% = 23% of the class.
However, we must be careful to make the distinction between independent events such as the situations given above and dependent events where one percentage determines the other, i.e. there are situations where one percentage is calculated based on another percentage. Look at the example below.
85 percent of a company staff with 200 employees speak English and 70 percent of English speakers can speak French as well. What is the number of English speakers only?
We can calculate the percentages one by one, but the shortest method would be calculating all at once. We can write
This percentage is equal to
We can multiply or divide percentages in the same way as we multiply or divide fractions or decimals. Thus, if we have, for example, to multiply 30% and 40% the result is not 1200% as some may incorrectly think, we find the correct result by turning the two percentages into decimals or fractions first and then completing the operations using the known methods we have explained in the previous chapters. In this way, we obtain
We can use the same method with the division of percentages as well. Thus, if we have to divide 27% and 9%, the result is not 3% as somebody may think but
instead. This is because multiplication and division of percentages does not work in the same way as multiplication and division of integers.
Remark! As we have seen demonstrated within the examples in this tutorial and previous math tutorials when working with fractions and decimals, the term "of" means "multiplication". Thus, if we want to find 12% of 20% of 400, we write
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