Percent Equation

Common Questions

What is a percent?

Good question! Like decimals, a percent is another way of expressing a fraction. The “cent” in percent means 100100 (like how centipedes have 100\textbf{100} legs), so percent means “out of 100100.” For example, 39%39\% means 3939 out of 100100 and is equal to the fraction 39100\frac{39}{100}.

Read below to learn more.

Common Questions

What is a percent?

Like fractions and decimals, percents are a ratio between two numbers. The “cent” in percent means 100100 (like how centipedes have 100\textbf{100} legs), so “percent” means “per 100100” or “out of 100100.” A percent is always a ratio out of 100100.

Since percentages are just fractions out of 100100, we can use equivalent proportions to solve problems involving percentages. The equation below relates proportions and percents:

partwhole=percent100\frac{{\color{#b5179e}\text{part}}}{{\color{#3A86FF}\text{whole}}} = \frac{{\color{#4ac783}\text{percent}}}{100}

Click the button below if you need to review proportions!

Let’s rearrange our equation a bit. If we multiply both sides of the equation by “whole,” we can change this equation into a different form.

partwhole=percent100\frac{{\color{#b5179e}\text{part}}}{{\color{#3A86FF}\text{whole}}} = \frac{{\color{#4ac783}\text{percent}}}{100} part × wholewhole=percent×whole100\frac{{\color{#b5179e}\text{part }}\times{\sout\color{#3A86FF}\text{ whole}}}{{\sout\color{#3A86FF}\text{whole}}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}

This equation is called the percent equation. If we know two of the unknowns, we’ll always be able to solve for the third. As you’ll see later, writing the equation in this form makes it easier for us to solve problems involving percentages.

The Percent Equation

Let’s look at a few examples involving the percent equation.

Example 1: What is 60%60\% of 2525?

Here’s where the percent equation really comes in handy. It can help us transform word problems into equations. For this problem, our percent is 60%60\%, and our whole is 2525. We are looking for the part, so we can replace it with the variable xx:

What is 60% of 25?{\color{#b5179e}\text{What }} \text{is } {\color{#4ac783}\text{60}}\% \text{ of } {\color{#3A86FF}\text{25}}?part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}x=60×25100{\color{#b5179e}x} = \frac{{\color{#4ac783}\text{60}} \times {\color{#3A86FF}\text{25}}}{100}

Now that we've transformed the question into an equation, we can flex our algebra skills and solve for xx!

x=60×25100=15{\color{#b5179e}x} = \frac{{\color{#4ac783}60} \times {\color{#3A86FF}25}}{100} = {\textbf{\color{#b5179e}15}}

Great! We should get 1515 as our answer. At first, you might not know how to answer a percent problem by just looking at it, but as you can see from this example, the percent equation is like a pair of glasses. Using it can make things a whole lot clearer!

Man with stars in his glasses

Exchanging Values 💱

From Example 11, we know that 60%{\color{#4ac783}60}\% of 25{\color{#3A86FF}25} is 15{\color{#b5179e}15}. Now let’s look at a similar problem:

What is 25%25\% of 6060?

Using the percent equation, we’ll get:

What is 25% of 60?{\color{#b5179e}\text{What}} \text{ is } {\color{#4ac783}25}\% \text{ of } {\color{#3A86FF}60}?part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}x=25×60100{\color{#b5179e}x} = \frac{{\color{#4ac783}25}\times {\color{#3A86FF}60}}{100}x=15{\color{#b5179e}x} = {\textbf{\color{#b5179e}15}}

Hmmm. It looks like 60%60\% of 2525 and 25%25\% of 6060 are the same value! This is because in the percent equation, we multiply percent times whole. Since order doesn’t matter for multiplication, swapping the order of our percent and whole values won’t change the value of our part.

part=percent×whole100=whole×percent100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100} = \frac{{\color{#3A86FF}\text{whole}} \times {\color{#4ac783}\text{percent}}}{100}

Keep in mind that this exchanging trick only works for percent and whole! Knowing this trick can be useful, but to keep things consistent, we will use part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100} for the rest of this lesson.

Is and Of 🌈

Here are a few more tips to help you remember the percent equation! In addition to changing the part, percent, and whole, we can also change the following:

  • is → =
  • of → ×\times (multiplication)
  • % → /100100

“Is” means the same as “equals to,” so when we change our problem to equation form, we can replace “is” with the equals sign. Similarly, “of” becomes a multiplication sign. And last but not least, percent means “out of 100100,” so when we see percentage signs, we know we have to divide by 100100.

Here’s an example of how we could use these tips:

What is 60% of 90?\text{What} \text{ is } 60\% \text{ of } 90?What is 60% of 90?\text{What} {\color{#00bbff}\text{ is }} 60 {\color{#925cff}\%} {\color{#f92a82}\text{ of }} 90?part = percent100×whole\text{part} {\color{#00bbff}\text{ = }} \frac{\text{percent}} {\color{#925cff}100} {\color{#f92a82}\times} \text{whole}part = percent×whole100\text{part} {\color{#00bbff}\text{ = }} \frac{\text{percent} {\color{#f92a82}\times} \text{whole}}{{\color{#925cff}100}}x = 60×90100x {\color{#00bbff}\text{ = }} \frac{60 {\color{#f92a82}\times} 90}{{\color{#925cff}100}}x=54x = \textbf{54}

If you ever forget the percent equation, the “is” and “of” trick can help you remember where to multiply and divide.

Let’s look at another example.

Example 2: 2424 is what percent of 6464?

This time we know our part and whole, and we are looking for percent. Try rewriting the problem into the form of the percent equation:part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}

  =
  ×\times   
100

Awesome job! Let’s isolate x{\color{#4ac783}x} by first multiplying both sides by 100100:

24=x×64100{\color{#b5179e}24} = \frac{{\color{#4ac783}x}\times{\color{#3A86FF}64}}{100}24×100=x×64{\color{#b5179e}24} \times 100 = {\color{#4ac783}x}\times{\color{#3A86FF}64}

Then, we’ll divide both sides by 64{\color{#3A86FF}\text{64}}, so we have x{\color{#4ac783}x} alone on the right side

24×10064=x\frac{{\color{#b5179e}\text{24}}\times100}{{\color{#3A86FF}64}} = {\color{#4ac783}x}24×10064=37.5\frac{{\color{#b5179e}\text{24}}\times100}{{\color{#3A86FF}64}} = {\textbf{\color{#4ac783}37.5}}

We get that 24{\color{#b5179e}\text{24}} is 37.5%{\textbf{\color{#4ac783}\text{37.5}\%}} of 64{\color{#3A86FF}\text{64}}.

Let’s look at one more example together!

Example 3: 6060 is 20%20\% of what number?

This time we know our part and whole, and we are looking for percent. Try rewriting the problem into the form of the percent equation:part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}

  =
  ×\times   
100

Awesome job! Let’s isolate x{\color{#4ac783}x} by first multiplying both sides by 100100:

60=20×x100{\color{#b5179e}60} = \frac{{\color{#4ac783}20}\times{\color{#3A86FF}x}}{100}60×100=20×x{\color{#b5179e}60} \times 100 = {\color{#4ac783}20}\times{\color{#3A86FF}x}

Then, we’ll divide both sides by 20{\color{#4ac783}\text{20}}, so we have x{\color{#3A86FF}x} alone on the right side

60×10020=x\frac{{\color{#b5179e}\text{60}}\times100}{{\color{#4ac783}20}} = {\color{#3A86FF}x}60×10020=300\frac{{\color{#b5179e}\text{60}}\times100}{{\color{#4ac783}20}} = {\textbf{\color{#3A86FF}300}}

We get that 60{\color{#b5179e}\text{60}} is 20%{\color{#4ac783}\text{20}\%} of 300{\textbf{\color{#3A86FF}\text{300}}}.

If you want to see more examples of the percent equation in action, check out our Percent Equation Calculator. And when you’re ready, click the 🤩 button below to explore some fantasTik applications of percentages!

Percent Equation Calculator

What is your unknown variable?  

Next, let’s plug the values into the percent equation:

part=percent×whole100{\color{#b5179e}\text{part}}= \frac{{\color{#4ac783}\text{percent}}\times{\color{#3A86FF}\text{whole}}}{100}

To isolate xx, we’ll multiply both sides by 100100 and then divide both sides by {\text{ }}.

 =x×100{\color{#b5179e}\text{ }} = \frac{{\color{undefined}x} \times {\color{undefined}\text{}}}{100} ×100=x×{\color{#b5179e}\text{ }} \times 100 = {\color{undefined}x} \times {\color{undefined}\text{}}×100 =x\frac{{\color{#b5179e}\text{}} \times 100}{{\color{undefined}\text{ }}} = {\color{undefined}x}

Let’s Tok About It

You may not know it, but influencers frequently use percentages to see how their posts are doing. On many platforms like YouTube and TikTok, creators have a statistic known as the CTR or Click-Through Rate. The CTR is equal to the number of views on a video divided by the number of thumbnail impressions, or how many times the thumbnail is seen. Most CTRs are between 2%2\% and 10%10\%. They can tell creators how engaging their thumbnails are and help them estimate how much money they’ll make from a video.

Let’s look at some questions about the CTR and practice answering word problems using the percent equation.

Application: YouTuber Nyma Tang’s new makeup review has 536k\text{536k} (536536 thousand) views and a CTR of 6.7%6.7\%. Approximately how many people saw the thumbnail of Nyma’s video?

We want to change this word problem into number form. To start off, we want to connect our YouTube lingo to the percent equation

part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}

Match the number of views, number of impressions, and CTR with their counterparts in the percent equation:

Great work! Now that we’ve identified the components of our percent equation, we can plug our numbers in and solve:

part=number of views=536k{\color{#b5179e}\text{part}} = {\color{#b5179e}\text{number of views}} = {\color{#b5179e}\text{536k}}percent=CTR=6.7{\color{#4ac783}\text{percent}} = {\color{#4ac783}\text{CTR}} = {\color{#4ac783}6.7}whole=number of impressions=x{\color{#3A86FF}\text{whole}} = {\color{#3A86FF}\text{number of impressions}} = {\color{#3A86FF}x}part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}536k=6.7×x100{\color{#b5179e}\text{536k}} = \frac{{\color{#4ac783}6.7} \times {\color{#3A86FF}x}}{100}

We isolate xx by multiplying both sides by 100100 , then dividing both sides by 6.76.7:

536k×100=6.7×x{\color{#b5179e}\text{536k}} \times 100 = {\color{#4ac783}6.7} \times {\color{#3A86FF}x}536k×1006.7=x\frac{{\color{#b5179e}\text{536k}} \times 100}{{\color{#4ac783}6.7}} = {\color{#3A86FF}x}536k×1006.7=8000k=8M\frac{{\color{#b5179e}\text{536k}} \times 100}{{\color{#4ac783}6.7}} = {\color{#3A86FF}\text{8000k}} = {\textbf{\color{#3A86FF}\text{8M}}}

In total, about 8{\color{#3A86FF}8} million people saw the thumbnail of Nyma’s video.

Great work! Now it's time to try a few practice questions by yourself.

In the practice below, select the correct dropdown to rewrite these word problems in the following equation form:

part=percent×whole100{\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}

These numbers might look a little trickier but don’t worry, we’ll do the calculations for you!

Quick Practice 1 / 3

Tabitha Brown’s latest TikTok has a CTR of about 10%10\%. If the TikTok thumbnail is shown to 15M15\text{M} people, approximately how many views will the TikTok have

  =  
  ×\times   
100

Awesome! Let’s use algebra to solve for xx:

=×100{\color{#b5179e}\text{}}= \frac{{\color{#4ac783}\text{}}\times{\color{#3A86FF}\text{}}}{100}

Click the 🏆 when you’re ready to reveal the answer.

x=1.5Mx = \textbf{{\color{#b5179e}1.5\text{M}}}

If Tabitha Brown’s TikTok has a CTR of 10%{\color{#4ac783}10}\%, and it was shown to 15M{\color{#3A86FF}15\text{M}} people, it would get about 1.5M\textbf{{\color{#b5179e}1.5\text{M}}} views.

Nice work! You completed all the questions! 👏🏿👏🏽👏🏻

Great work! As you can see, percentages are useful in all sorts of situations. They can even help influencers on the route to clout!

Harvey falls facefirst onto the ground