Percent Increase and Decrease

Links and useful resources

Increase and decrease

When you have a problem that is talking about percent increase or decrease, the thing you have to keep in mind is simple: You always start with the current amount and the increase or decrease is the percentage of the original amount, that gets added or subtracted from the original.

$new amount = old amount + old amount \times percent change$

With that equation, you can always find any of the three quantities (new amount, old amount, or percent change). Which one you solve for depends on how the question is asked!

If the problem says it decreased by a percent, then the percent change is negative.

A shortcut that is handy sometimes

Notice that we can factor the right hand side of the equation:

\begin{aligned} new amount & = old amount + old amount \times percent change \\ = old amount \times (1 + percent change) \end{aligned}

That means that an increase will multiply by a number a bit bigger than one, and a decrease will multiply by one that's a bit smaller than one.

Decrease $x$ by 10% means the same thing as $(1 - 0.1) x = 0.9 x$
Increase x by 10% means the same thing as $(1 + 0.1) x = 1.1 x$

Media resources

Youtube search for "How to work with increase and decrease percentages"

Guided practice

In 2009, Heart & Sole Shoe Company sold 15 million pairs of shoes. In 2010, they increased advertising, and they sold 20% more shoes than in 2009. How many pairs of shoes did they sell in 2010?
Wendy’s stock in GloboSuperOmni Corp is worth $500 at the start of January. In each month, the stock goes up 10% in value. What is the stock worth at the end of March?
In 2005 the population of Cedar Falls was 16,000. In 2010, the population was 20,000. By what percent did the population increase from 2005 to 2010?

Homework

#hw (math) (gr7) 8.3 Percent Increase and Decrease (p. 337) 2025-02-17