Percent Increase

In short: Percent increase is the share of its old size that a value has gained, computed as the gain divided by the starting value and then written with a percent sign.
7th GradeRatios and Percents7.RP.A.3
What is Percent Increase?
A percent increase answers one question: by what fraction of its old size did something get bigger? Rent that climbs, a plant that grows taller, or a team that scores more points all fit.
If the original value is \(a\) and the new value is \(b\) with \(b > a\), then \(\text{percent increase} = \frac{b – a}{a} \times 100\%\). The result is always positive, and it can exceed \(100\%\) when the new value is more than double the original.
How to spot it
- A story says a number grew, rose, climbed, or was raised, and gives both the old and the new values.
- You are told a raise, a tip, or a growth rate in percent and must find the new amount.
- The question asks how many percent more one year has than the year before it.
- A final value is larger than the starting value and the comparison must be fair across different sizes.
The method
- Compute the growth: new value minus original value, which is positive here.
- Divide the growth by the original value, not by the new one.
- Multiply by \(100\) and attach the percent sign.
- Working backward from a known rate \(r\), the new amount is \(\text{original} \times (1 + r)\) with \(r\) as a decimal.
Percent Increase: solved example
Problem
A barista in Tucson earned \(\$15\) per hour and now earns \(\$18\) per hour. By what percent did the hourly wage increase?
Solution
Raise: \(18 – 15 = 3\) dollars.
Compare with the old wage: \(\frac{3}{15} = 0.2\). In percent, that is a 20% increase.
Try it
Question 1
A sunflower is 48 inches tall on Monday and 60 inches tall on Friday. Find the percent increase.
Show the answer
\(\frac{60 – 48}{48} = \frac{12}{48} = 0.25\), so the plant grew by 25%.
Question 2
A game app had 350 players and the number rose by 40%. How many players are there now?
Show the answer
\(350 \times 1.40 = 490\) players.
Percent Increase vs. Percent Decrease
Both follow one recipe, difference over original, but here the final value is larger so the change is a gain, while in a decrease it is smaller. Beware of reversing: a 50% gain then a 50% loss leaves you below the start, since the loss is figured on a bigger base.
Keep going
Lessons
Worksheets and quizzes
- Percent Problems: Tax, Tips, Discounts and Markups – Worksheet
- Percent Problems: Tax, Tips, Discounts and Markups – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Ratios and Percents