01 / 20
%

Percent of a
Quantity

Master the skill of finding any percent of any number using multiplication: the essential building block for discounts, taxes, tips, and data analysis.

Pre-Algebra

What Is a Percent?

The word percent comes from the Latin per centum, meaning "per hundred." A percent is simply a ratio that compares a number to \(100\).

=
$$\frac{\color{#818cf8}75}{100}$$
=
\(75\%\)

Percent ↔ Decimal

Every percent can be written as a decimal by dividing by \(100\). This is equivalent to moving the decimal point two places left.

\(25\%\)
\(25 \div 100 = 0.25\)
\(8\%\)
\(8 \div 100 = 0.08\)
\(150\%\)
\(150 \div 100 = 1.50\)

Why Percents Matter

Percents appear everywhere in daily life. Any time you need to find a part of a whole, you are computing a percent of a quantity.

Shopping
"Save \(20\%\) on a \(\$60\) jacket" means you need to find \(20\%\) of \(60\).
Grades
"You scored \(85\%\) on a \(40\)-question test" means you got \(85\%\) of \(40\) correct.
Statistics
"\(60\%\) of \(500\) students prefer pizza" means you need to find \(60\%\) of \(500\).

The Core Rule

\(\text{Part} = \text{Percent} \times \text{Whole}\)

To find a percent of a quantity, convert the percent to a decimal (divide by \(100\)), then multiply by the whole amount.

Percent as a Multiplier

Instead of thinking "find \(30\%\) of \(200\)," think: "multiply \(200\) by \(0.30\)." The decimal form of the percent is the multiplier.

Whole = 200
\(30\% = 60\)
remaining 70%
\(200 \times 0.30 = 60\)

Percent of vs. Percent Change

These two ideas sound similar but ask different questions. Today we focus on percent of a quantity, but it helps to see the difference.

Percent of a Quantity Percent Change
Question What is \(p\%\) of \(W\)? By what \(\%\) did it grow/shrink?
Formula \(\frac{p}{100} \times W\) \(\frac{\text{new} - \text{old}}{\text{old}} \times 100\)
Example \(20\%\) of \(80 = 16\) \(80 \to 96\) is a \(20\%\) increase

How to Apply It

1
Identify the percent (\(p\)) and the whole quantity (\(W\)) in the problem.
2
Convert the percent to a decimal: divide \(p\) by \(100\), or move the decimal point two places left.
3
Multiply: \(\text{Part} = \text{decimal} \times W\).
4
Check your answer: Does it make sense? (e.g., \(50\%\) of a number should be half.)

Example 1: Basic

Find \(40\%\) of \(250\).

250
\(40\% = 100\)
\(60\% = 150\)
\(40\% \to 0.40 \quad \to \quad 0.40 \times 250 = 100\)

Example 2: Small Percent

A store charges \(7.5\%\) sales tax. How much tax is added to a \(\$84\) purchase?

$84.00
\(7.5\%\)
\(92.5\%\)
\(7.5\% \to 0.075 \quad \to \quad 0.075 \times 84 = \$6.30\)

Example 3: Over \(100\%\)

A population of deer is now at \(125\%\) of its original size of \(600\). What is the current population?

\(100\% = 600\)
\(125\% = 750\)
\(+25\%\)
original 100%
\(125\% \to 1.25 \quad \to \quad 1.25 \times 600 = 750\)

Example 4: Fraction Percent

Find \(\frac{1}{2}\%\) of \(1{,}200\).

1
\(p = 0.5\), \(W = 1{,}200\).
2
\(0.5 \div 100 = 0.005\).
3
\(0.005 \times 1{,}200 = \) \(6\).

Common Mistakes

✕ Forgetting to Divide by 100
Writing \(25\% \times 80 = 2{,}000\) instead of \(0.25 \times 80 = 20\). Always convert the percent to a decimal first.
✕ Moving the Decimal Wrong
\(6\% = 0.6\) is wrong. It should be \(0.06\). Move the decimal two places left, not one.
✕ Confusing \(\frac{1}{2}\%\) with \(50\%\)
\(\frac{1}{2}\% = 0.005\), but \(50\% = 0.50\). These differ by a factor of \(100\)!

Quick Reference Table

Percent Decimal Fraction Meaning
\(1\%\) \(0.01\) \(\frac{1}{100}\) One hundredth
\(10\%\) \(0.10\) \(\frac{1}{10}\) One tenth
\(25\%\) \(0.25\) \(\frac{1}{4}\) One quarter
\(50\%\) \(0.50\) \(\frac{1}{2}\) One half
\(75\%\) \(0.75\) \(\frac{3}{4}\) Three quarters
\(100\%\) \(1.00\) \(\frac{1}{1}\) The whole thing
\(200\%\) \(2.00\) \(\frac{2}{1}\) Double

Putting It All Together

1
Percent means "per hundred." It is a ratio comparing a number to \(100\).
2
Convert to a decimal by dividing by \(100\) (move decimal two places left).
3
Multiply the decimal by the whole quantity: \(\text{Part} = \frac{p}{100} \times W\).
4
Over \(100\%\) gives a result larger than the original. Under \(1\%\) gives a tiny fraction.
5
Always sanity-check: \(50\%\) should give half, \(10\%\) should give one-tenth, etc.

Question 1 of 5

What is \(15\%\) of \(80\)?

Question 2 of 5

A jacket costs \(\$120\). A \(35\%\) discount is applied. How much is the discount (in dollars)?

Question 3 of 5

Which expression correctly computes \(8\%\) of \(550\)?

Question 4 of 5

What is \(150\%\) of \(40\)?

Question 5 of 5

A school has \(800\) students. If \(0.5\%\) of students are absent today, how many are absent?