Have you ever been at a store during a huge sale, and tried to mark down individual items in your head based on their regular price, and percentage off? Or maybe you had an additional 20% off coupon and wanted to be sure how that would apply to an item that’s already been marked down?
Knowing how to work with percentages is an extremely important and applicable math skill next to the basics, like addition and subtraction. In this guide, we’ll go over the percentage change equation, how to use it, and let you loose to practice with some example problems.
100% of people capable of computing simple mathematical formulas should know how to do this!
Introduction to Percentages
The actual term “percent” comes from the Latin word per centum, which means “by the hundred.” In mathematics, that’s exactly what a percent means: per 100.
If we say A is 50% of B, what we’re saying is there are 50 of A per 100 of B.
If a bag of candy contains 100 pieces, and exactly 25% of those pieces are blue, and exactly 75% are pink, that means there are 25 blue pieces of candy per 100 pieces, and 75 pink pieces of candy per 100 pieces.
You could also say 25 out of 100 pieces are blue, or 25/100, or reduce the fraction down to 1/4. 25%, 1/4, and a quarter all represent the same amount.
If there were 200 pieces of candy, and 50 of those were blue, the amount of blue candies would still be 25%, or 1/4, or a quarter. We know this because when we divide 50 by 200, our answer is 0.25, the decimal value representative of 25%.
To find a specific percentage of a number, you simply multiply the number by the percentage you want to find, in decimal form.
Say you’re at a restaurant, and the bill comes out to $23.18. You want to tip 20%, meaning you want to find 20% of $23.18 and add it to the total.
$23.18 × 0.20 = ?
For the sake of clarity, we’ve formatted the decimal as 0.20, but .2 means the same thing. You could have two hundred 0’s at the end of the .2 and it wouldn’t make a difference.
Want to know why? This foundations of math course, though aimed at kids, is a good source for learning basic math concepts.
Back to the equation! So after a quick calculation, we get the following answer:
$23.18 × 0.20 = 4.636
You can’t tip someone $4.636, but you can always round up or down as you see fit. $4.60 or even $5.00 would suffice! This isn’t a tutorial on etiquette, though. What’s important to note here is that the number 4.636 is 20% of 23.18 – depending on how much you round up or down, that’s the number you’ll want to add to your total.
That’s a mundane application for percentages that you’ll probably find yourself using quite a lot.
Percent Change Equation Example
Finding out how to measure percent change is just as easy.
Let’s say you’re doing a research report for a government class about rising food prices. At your local food market, loaves of bread were selling for $1.50 each two years ago. Now, they sell for $3.80 each.
You can tell that’s a huge leap just by looking at it, but to find out what percent the price was raised, we use a simple formula.
All we have to do here is plug in the numbers from our example.
$3.80 – $1.50 = $2.30
When we subtract the old value of $1.50 from the new value of $3.50, we get $2.30. That means the bread at your local store is $2.30 more expensive than it was two years ago. It doesn’t tell us what percent the price was raised, though, because we’re not done with the equation.
2.30 / 1.50 = 1.5333
When we multiply our result of $2.30 with our old value of $1.50, we get 1.5333. Next, we multiply that by 100.
1.5333 × 100 = 153.333
What we have is a 153% increase in the price of bread at your local food market!
Percent Change Equation Example 2
Let’s do a second example for something a bit more uplifting.
You’re working for $12 an hour at a local bookstore. You were recently promoted to assistant manager, and now you’re making $20 an hour. To find out what percentage your pay was raised, use the same formula as above.
$20 -$12 = $8
$8 / $12 = 0.66
0.66 × 100 = 66.6
If you round it up, your paycheck has been raised by nearly 67%! This means you’re making an additional 67% of your previous paycheck.
Percent Change Practice Quiz
Time to test your skills! First, remember the percent change formula:
Use this formula to work out the following scenarios. Answers will be at the bottom of the page.
1. The population of your town increased within the past 10 years, from approximately 82,000 people to 87,000. What was the percent increase in population?
2. Gas prices decreased in the past month from $4.32 a gallon to $3.89 a gallon. What was the percent decrease in gas prices?
3. Yesterday, you wrote the first 5 pages of your novel. Today, you were extra productive and wrote 18 pages. What is the percent increase in your productivity between today and yesterday?
4. The number of unemployed students at your local high school has decreased in the past year, from 2,867 to 2,053. What is the percent decrease in unemployed students at your school?
5. At least year’s company Christmas party, only 200 people participated in the Secret Santa gift give-away. This year, 350 people participated. What was the percent increase in participants?
6. The local cyber cafe used to charge $5 an hour to use their computers and video game equipment. Now they charge $7 an hour. What was the percent increase in hourly rate?
1. Approximately 6.1% increase in population.
2. Approximately 10% decrease in gas prices.
3. Approximately 260% increase in productivity.
4. Approximately 28% decrease in unemployed students.
5. Approximately 75% increase in participants.
6. Approximately 40% increase in hourly rate.
Calculating percent change is really easy! For more math help, consider taking a course on advanced math skills made easy. Getting ready for the SAT test, and worried about the math potion? Prepare with this SAT Math class.