Percent Increase

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Percent Increase: meaning, method and solved example (7th Grade) – Maths PDF

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

  1. Compute the growth: new value minus original value, which is positive here.
  2. Divide the growth by the original value, not by the new one.
  3. Multiply by \(100\) and attach the percent sign.
  4. Working backward from a known rate \(r\), the new amount is \(\text{original} \times (1 + r)\) with \(r\) as a decimal.
0$4$12$18$24$15+$33 ÷ 15 = 0.20, so the raise is 20%
From $15 to $18 the wage gains $3, which is one fifth of the old wage.

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.

Percent Decrease

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