Percent Decrease

Sommaire

In short: Percent decrease expresses how much a quantity shrank as a percent of its original size, found by dividing the amount lost by the starting amount.

7th GradeRatios and Percents7.RP.A.3

What is Percent Decrease?

Whenever something gets smaller, percent decrease gives the size of the drop as a share of where it began. A reservoir losing water, a phone battery draining or a bus route losing riders are typical stories. The same idea works for temperatures, enrollment counts or the weight a hiker carries after unpacking a few items.

With original value $a$ and new value $b$ where $a > b$, the formula is $\frac{a – b}{a} \times 100\%$. Because a quantity cannot lose more than everything it had, an ordinary decrease never goes past $100\%$. The loss is divided by the larger, earlier number, which is why a drop from 50 to 40 is 20% but a climb from 40 back to 50 is 25%.

How to spot it

A report says something fell, shrank, dropped, declined or lost, with a before number and an after number.
A store marks an item down and the question asks what percent of the old price was removed.
The ending value is smaller than the starting value and you need a comparison that ignores the units.
You are asked how much was lost relative to the beginning, not how much remains.

The method

Find the loss: original value minus new value, giving a positive number.
Divide the loss by the original value, the larger number that came first.
Convert the decimal to a percent by multiplying by $100$.
Check by computing $\text{original} \times (1 – r)$; it must return the new value.

The dashed piece is 96 of 640 students, which is 15%.

Percent Decrease: solved example

Problem

Last season 640 students attended the Friday football game at Lincoln High. This season only 544 came. Find the percent decrease in attendance.

Solution

Loss: $640 – 544 = 96$ students.

Relative to last season: $\frac{96}{640} = 0.15$. The attendance fell by 15%.

Try it

Question 1

A kayak that cost $\$480$ is now priced at $\$396$. What is the percent decrease?

Show the answer

$\frac{480 – 396}{480} = \frac{84}{480} = 0.175$, so the price fell by 17.5%.

Question 2

A tank holds 250 gallons and its contents drop by 32%. How many gallons remain?

Show the answer

$250 \times (1 – 0.32) = 250 \times 0.68 = 170$ gallons.

Percent Decrease vs. Discount

A discount is a price reduction announced by a seller, usually stated up front as a percent off the tag price. A percent decrease is the broader calculation you can run on any pair of values, such as temperatures, enrollment or battery levels. A discount is one situation where the calculation applies.

Discount

Keep going

Lessons

Percent Problems: Tax, Tips, Discounts and Markups

Worksheets and quizzes

Related words

Whole dictionary: A–Z · 7th Grade · Ratios and Percents

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