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Introduction

QUICK LINKS


Introduction

INTRO
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The word percentage comes from the word percent, which means "per ." In other words, a percent tells us what amount out of we have.
Percentages are often used for grades. For example, if we get out of questions correct, our grade percentage would be .
The percentage tells us how much of the test we got correct if the test were split into questions.
If we got a on a question test, then we got out of questions right.
In general, percentage problems involve proportions (equivalent ratios) between a given percent and a given part of a whole.
So a percentage problem like is really asking us, "What amount out of is equal to out of ?"

What is a proportion?

A proportion is an equation that lets us know two ratios (or fractions) are equal.
For example:
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about percentages and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

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CALCULATOR
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Percentage Calculator

What is your unknown?
What is of?

Step 1. Change the percent into a fraction.

The percent tells us an amount out of . Remove the percent sign and place the number over .

Step 2. Set up the proportion.

The percent over is equal to the part over the whole. Use a variable like for the value you're solving for.

Step 3. Cross-multiply.

Step 4. Solve for the unknown.

These values result in an answer that our calculator rounds to 0. Let us know in the feedback if you need help with problems like this!
KEY STEPS
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How to Calculate Percentages

Step 1. Change the percent into a fraction.

The percent tells us an amount out of . Remove the percent sign and place the number over .

Step 2. Set up the proportion.

The percent over is equal to the part over the whole. Use a variable like for the value you're solving for.

Step 3. Cross-multiply.

Step 4. Solve for the unknown.

LESSON
β€” Calculating Percentages

Calculating Percentages

Since percentages are just fractions out of , we can use proportions to solve problems involving percentages:If we're solving for the , then our proportion looks like this:

The Percent Formula

If we multiply both sides by to get the percent by itself:We end up with the percent formula:
Let’s walk through some step-by-step examples of percentage problems!

EXAMPLE 1

Let's start with this problem: what is of ?

Step 1. Change the percent into a fraction.

The percent tells us an amount out of . Remove the percent sign and place the number over .

Step 2. Set up the proportion.

The percent over is equal to the part over the whole. Use a variable like for the value you're solving for.

Step 3. Cross-multiply.

Step 4. Solve for the unknown.

So our answer is
.

EXAMPLE 2

Nice work! Now, try this one: is what percent of ?

Step 1. Change the percent into a fraction.

The percent tells us an amount out of . Remove the percent sign and place the number over .
Since we don't know what the percent is, we'll place a variable over

Step 2. Set up the proportion.

The percent over is equal to the part over the whole. Use a variable like for the value you're solving for.

Step 3. Cross-multiply.

Step 4. Solve for the unknown.

So our answer is
.

EXAMPLE 3

Amazing! Last problem: is of what number?

Step 1. Change the percent into a fraction.

The percent tells us an amount out of . Remove the percent sign and place the number over .

Step 2. Set up the proportion.

The percent over is equal to the part over the whole. Use a variable like for the value you're solving for.

Step 3. Cross-multiply.

Step 4. Solve for the unknown.

So our answer is
.
Awesome! If you’d like to practice additional problems with percentages, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Calculating Percentages

Practice: Calculating Percentages

Question 1 of 10: What is of ?

Step 1. Change the percent into a fraction.

The percent tells us an amount out of . Remove the percent sign and place the number over .

Step 2. Set up the proportion.

Use x for the unknown value we're looking for.


Step 3. Cross-multiply.

Step 4. Solve for .

Great work! Our answer is .

CONCLUSION
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Incredible job, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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