Percentages

Many mathematical missteps in the public sphere involve percentages. It is a good habit to note explicitly the quantity to which a percentage is applied, as a common error is to add or subtract percentages applied to different quantities.

For example, suppose a woman earned a salary of $40,000 last year and got a raise of 10% this year, but expects a salary cut of 10% next year. This will not leave her where she started. The first 10% is applied to $40,000, so her earnings this year are $44,000. It is this amount to which the 10% reduction is applied, so that next year, the salary will be reduced by $4400 to the amount $39,600, for a net reduction of 1% from last year's salary.

Example 1

Mr. and Mrs. Buyer are visiting the ClothesLine Shop to get Mr. Buyer a coat. A suitable item has been found; the regular price is $160, but this is reduced by 25% because of the spring sale. However, a sales tax of 15% applies to the actual cost of the item.