# The basics of percent of change

The two videos below have to do with the **basics of percent of change,** (percent of increase or decrease). You are given the initial and final quantities, and you have to calculate the percentage change (percent change).

The main idea is simply to write the *fraction* PART/TOTAL, and then convert that into a percentage (you may possibly first need to write it as a decimal).

In the case of percentage change, the TOTAL is the *original* quantity, and the PART is the actual *change* (difference).

So, in the case of percent of change, the generic formula *part*/*total* becomes

DIFFERENCE ORIGINAL |
(= decimal) = percentage |

The "decimal" is in parenthesis, because sometimes you can convert this fraction directly into a percentage (such as if it happens to be 1/4 or 1/5 or some other easy fraction). But in most cases, you'd use a calculator and divide to get a decimal, then write the decimal as a percentage.

**Example.** Joe weighed 90 kg in March and 85 kg a month later. What percentage of his weight did he lose?

The original weight is 90 kg and the change (the difference) is 5 kg. We get the fraction 5 kg/90 kg. In it, the units "kg" cancel out and we're left with

5 90 |
≈ 0.055555556 ≈ 5.56% |

Joe lost 5.56% of his weight.

In the second video, I solve two word problems that involve percentage change. One hast to do with percentage increase in area. In the other, the price of a washer is discounted by 10%, then by another 10%, and we are asked the total discount percentage – yet the PRICE of the washer is NOT given!

Teachers - feel free to use these problems as lesson plans!

### See also

Percent – free lesson

How to calculate percentages – free lesson

How to calculate percentages of numbers – free lesson

Percentage of a number using mental math – free lesson

**Math Lessons menu**