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Percent Change - Problem 1
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
The percent change formula is: (new price - original price) / original price. A common mistake is to divide the numerator by the new price, instead of the original price. Since we are comparing what the change is compared to the original price, we must divide by that value.
Percent change is easy if you can remember the formula new price take away the original price divided by the original. Let's apply it to this problem. Bus fares went up from $1.50 to $2 this July. What percent increase does this represent? Well a lot of students will do the following in their head, they'll figure out okay 50cents is how much it changed and so they'll say 50 cents is 1/4 of $2 or 25%. It makes sense right? And a lot of students will get that answer. That answer is actually incorrect.
The way to find percent change is to do new take away old or original and divided by the old or original. So what we want to do is take a new price take away the old price $2 take away $1.50 is 50 cents so that was on the right track but then we need to divide by the old price. Students who got the answer 25% or 1/4 divided by the new price, that was the mistake. Down here in the denominator, we have to divide by the old price. Tiny little difference in the formula but it makes a big difference in your answer. So when you do 50 cents divided by $1.50 you end up getting 33.3 repeating percent or 0.33, either one of those is fine.
The important thing to remember though guys is this formula especially in multiple choice tests. They would have 25% as one answer, and 33% as the other and I know you guys are going to get these problems right.
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