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Find Percent
of a Quantity

Master the skill of computing any percent of any number by treating percent as a rate per 100.

6th Grade Math

What Does Percent Mean?

The word percent comes from the Latin per centum, meaning "for every hundred." When we say \(30\%\), we mean 30 out of every 100.

30 shaded out of 100 = 30%

Percent as a Rate per 100

A percent tells you how many per hundred. This makes it easy to compare different quantities on the same scale.

\(25\%\)
\(\frac{25}{100} = 0.25\)
One quarter
\(50\%\)
\(\frac{50}{100} = 0.50\)
One half
\(75\%\)
\(\frac{75}{100} = 0.75\)
Three quarters

Why Percents Matter

Percents show up everywhere in daily life. Knowing how to find a percent of a quantity lets you handle real money, real data, and real decisions.

Shopping
"Save \(20\%\) on a \(\$45\) jacket" : how much do you actually save?
Statistics
"Rainfall increased by \(15\%\)" : what does the new amount look like?
Nutrition
"Contains \(8\%\) of daily iron" : how many milligrams is that?

The Core Formula

Finding a percent of a quantity Part = Percent × Whole where Percent is written as a fraction over 100

This single formula handles every "find percent of a quantity" problem you will ever see.

A Bar Model View

Picture the whole quantity as a full bar. The percent tells you what fraction of the bar to shade.

40% remaining 60% Whole = 200 40% of 200 = 80 0% 100%

Fraction, Decimal, and Percent

Every percent can be written three equivalent ways. Use whichever makes the arithmetic easiest.

Percent Fraction Decimal
\(10\%\) \(\frac{10}{100} = \frac{1}{10}\) \(0.10\)
\(25\%\) \(\frac{25}{100} = \frac{1}{4}\) \(0.25\)
\(50\%\) \(\frac{50}{100} = \frac{1}{2}\) \(0.50\)
\(75\%\) \(\frac{75}{100} = \frac{3}{4}\) \(0.75\)

Step-by-Step Method

1
Identify the percent \((p)\) and the whole quantity \((Q)\).
2
Convert the percent to a fraction: write \(\frac{p}{100}\).
3
Multiply: compute \(\frac{p}{100} \times Q\).
4
Check your answer: does it make sense? (It should be less than the whole if \(p < 100\).)

Example 1: \(30\%\) of \(150\)

30% 70% 0 150 = 45
1
Identify: \(p = 30\), \(Q = 150\).
2
Convert: \(\frac{30}{100} = 0.30\).
3
Multiply: \(0.30 \times 150 = \) \(45\).

Example 2: \(15\%\) of \(\$60\)

Problem: A store offers a \(15\%\) discount on a \(\$60\) backpack. How much money do you save?

1
Identify: \(p = 15\), \(Q = 60\).
2
Convert: \(\frac{15}{100} = 0.15\).
3
Multiply: \(0.15 \times 60 = \) \(9\).

Example 3: \(120\%\) of \(80\)

Percents can be greater than \(100\%\). This means the part is larger than the whole.

80 (100%) 120% 120% of 80 = 96 (the result is bigger than the original!)
1
Convert: \(\frac{120}{100} = 1.20\).
2
Multiply: \(1.20 \times 80 = \) \(96\).

Finding the Whole

Sometimes you know the part and the percent, and you need to find the whole. Just rearrange the formula:

Rearranged formula Whole = Part ÷ (Percent ÷ 100)

Example 4: Find the Whole

Problem: A student answered \(36\) questions correctly, which was \(60\%\) of the test. How many questions were on the test?

1
Identify: Part \(= 36\), Percent \(= 60\%\), Whole \(= \text{?}\)
2
Set up: \(36 = \frac{60}{100} \times Q\)
3
Solve: \(Q = 36 \div 0.60 = \) \(60\)

Finding Part vs. Finding Whole

Finding the Part Finding the Whole
You know Percent and Whole Percent and Part
You find The Part The Whole
Operation Multiply Divide
Formula \(\frac{p}{100} \times Q\) \(\text{Part} \div \frac{p}{100}\)
Example \(20\%\) of \(80 = 16\) \(16\) is \(20\%\) of \(80\)

Common Mistakes

✕ Forgetting to Divide by 100
Writing \(25\% \times 80 = 2000\) instead of \(\frac{25}{100} \times 80 = 20\). Always convert percent to a decimal or fraction first.
✕ Multiplying When You Should Divide
"15 is 25% of what?" requires division: \(15 \div 0.25 = 60\), not multiplication \(15 \times 0.25 = 3.75\).
✕ Moving the Decimal the Wrong Way
\(5\% \neq 0.5\). Move two places left: \(5\% = 0.05\). A misplaced decimal makes answers 10 times too big or too small.
✕ Not Checking Reasonableness
If your answer to "\(10\%\) of \(200\)" is \(200\), something went wrong. The part should be smaller than the whole for percents under \(100\%\).

Summary Reference

Scenario Formula Example
Find the Part \(\frac{p}{100} \times Q\) \(20\%\) of \(90 = 18\)
Find the Whole \(\text{Part} \div \frac{p}{100}\) \(18\) is \(20\%\) of \(90\)
Percent > 100% \(\frac{p}{100} \times Q\) (result > Q) \(150\%\) of \(40 = 60\)
Quick Decimal Move decimal 2 left \(8\% = 0.08\)

Question 1 of 5

What is \(40\%\) of \(250\)?

Question 2 of 5

A jacket costs \(\$80\). It is on sale for \(25\%\) off. How much do you save?

Question 3 of 5

\(45\) is \(75\%\) of what number?

Question 4 of 5

What is \(5\%\) of \(300\)?

Question 5 of 5

A town's population is \(4{,}000\). It grows by \(110\%\). What is the new population?