Math: Basic Tutorials : Percents

Understanding Percents

A percent is a way of expressing a number as a fraction of 100, meaning "per hundred." The word percent comes from the Latin phrase "per centum," which translates to "by the hundred." The symbol '%' is used to represent the word percent, making it easier to write and recognize in calculations. For example, 50% means 50 out of 100, or $\frac{1}{2}$ . Percents are closely related to fractions and decimals, as they can be converted between these forms for easier calculations. For instance, 25% is the same as the fraction $\frac{25}{100}$ , which simplifies to $\frac{1}{4}$ , or the decimal 0.25. Understanding percents and their relationship to fractions and decimals is essential for solving various mathematical and real-world problems.

This section will explain how to compare and convert percentages to fractions and decimals, learn keywords, and how to solve percent-based problems. With a variety of examples, we’ll walk through solving real-world percent word problems, providing you with the tools to confidently handle percentage-based calculations in healthcare.

Understanding Percents Video transcript - RTF

Relationship and Conversions

Now that you understand what a percent is, let's take a look at how to convert a percent to a fraction or a decimal as well as a fraction or a decimal to a percent.

To change a percent to a fraction place it over 100 and simplify:
- $60 % = \frac{60}{100} = \frac{3}{5}$
To turn a fraction into a percent divide the numerator by the denominator and multiply by 100:
- $\frac{3}{4} = 0.75 = 75 %$

To convert a percent to a decimal divide by 100 or move the decimal left:
- $75 % = 0.75$
To convert a decimal to a percent move the decimal right and add %:
- $0.2 = 20 %$

These conversions make working with percentages much easier.

Here is a quick tip for conversions:

Percent to Decimal/Fraction conversion	Divide by 100
Fraction/Decimal to Percent conversion	Multiply by 100

Keywords in Percent Word Problems

There are keywords in percent word problems that relate to a specific mathematical operation.

"Of" translates to multiplication ×.
"Is" translates to equal =.
"What" translates to any letter or variable.
"%" translates to divide by 100 or multiply by $\frac{1}{100}$ or 0.01.

Click on the titles below to view each example of a percent-based word problem.

Example 1

Example 1:
23% of 5 is what?
We can translate each part of the question, based on the keywords above. Therefore 23% of 5 is what? translates to:	$(23 \times \frac{1}{100}) \times 5 = x$
Solution:	$x = 1.15$

Example 2

Example 2:
45% of what is 23?
Performing the translations we get:	$(45 \times \frac{1}{100}) \times x = 23$
To solve for $x$ , we need to multiply the fraction and divide it out to the other side:	$(0.45) \times x = 23$ $\frac{(0.45) \times x}{0.45} = \frac{23}{0.45}$
Solution:	$x = 5.11$

Example 3

Example 3:
374,000 is what percent of 561,000?
Performing the translations we get:	$374,000 = p \times 561,000$
To solve for our variable, $p$ , we need to use 561,000 as our divisor: Then to get the percentage, multiply by 100:	$\frac{374,000}{561,000} = \frac{p \times 561,000}{561,000}$ $0.666666 = p$ $0.666666 \times 100 % = p$
Solution:	$p = 66.6 %$ (nearest tenth percent)

Practice

Additional Resources

Learning Portal Basic Tutorials: Decimals & Percent

Last Updated: Jun 5, 2025 4:16 PM
URL: https://tlp-lpa.ca/math-tutorials
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Math: Basic Tutorials