Percent Change
In short: Percent change tells how much a quantity grew or shrank compared with its starting value, found by dividing the amount of change by the original amount and writing the result as a percent.
7th GradeRatios and Percents7.RP.A.3
What is Percent Change?
When a price, a population or a score moves from one value to another, percent change says how big that move is relative to where things began. A jump of 20 means little for a quantity near 30 but almost nothing for one near 5,000, and the percent makes that visible.
The formula is \(\text{percent change} = \frac{\text{new} – \text{original}}{\text{original}} \times 100\%\). A positive answer signals growth, a negative answer signals a drop, and the denominator is always the starting value, never the ending one.
How to spot it
- A problem gives a before value and an after value and asks how much something went up or down in percent.
- Words such as grew, dropped, rose, fell, shrank or changed appear next to two numbers from different times.
- You must compare two stores, years or seasons fairly even though their starting sizes are very different.
- A sale, a raise, a population report or a game score is described in percent rather than in plain units.
The method
- Subtract: take the new value minus the original value, keeping the sign of the result.
- Divide that difference by the original value, the one that came first in time.
- Multiply the quotient by \(100\) to turn it into a percent.
- Read the sign: a positive percent is an increase, a negative percent is a decrease.
Percent Change: solved example
Problem
The Maplewood public library lent 1,840 books in March of last year and 2,162 books in March of this year. Find the percent change.
Solution
Difference: \(2{,}162 – 1{,}840 = 322\) books.
Divide by the original: \(\frac{322}{1{,}840} = 0.175\). Multiply by \(100\%\): the lending rose by 17.5%.
Try it
Question 1
A winter coat costs \(\$64\) in October and \(\$52\) in January. What is the percent change?
Show the answer
\(\frac{52 – 64}{64} = \frac{-12}{64} = -0.1875\), so the price changed by -18.75%, a decrease.
Question 2
A town grows from 8,500 residents to 9,350 residents. Find the percent change.
Show the answer
\(\frac{9{,}350 – 8{,}500}{8{,}500} = \frac{850}{8{,}500} = 0.10\), an increase of 10%.
Percent Change vs. Percent Error
Percent change compares a new value with an earlier value of the same thing, and its sign tells the direction. Percent error compares a measurement or estimate with a true value and is reported without direction, as an absolute amount. Time separates the two ideas in one, accuracy separates them in the other.
Keep going
Lessons
Worksheets and quizzes
- Percent Problems: Tax, Tips, Discounts and Markups – Worksheet
- Percent Problems: Tax, Tips, Discounts and Markups – Quiz
- Percent as a Rate per 100 – Worksheet
- Percent as a Rate per 100 – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Ratios and Percents