Percent Problems

Solving problems involving percentages

Percent Problems

Converting Between Forms

Percent to Decimal: Divide by 100

$25\% = \frac{25}{100} = 0.25$

Decimal to Percent: Multiply by 100

$0.4 = 0.4 \times 100 = 40\%$

Percent to Fraction: Write over 100 and simplify

$30\% = \frac{30}{100} = \frac{3}{10}$

The Percent Equation

$\text{part} = \text{percent} \times \text{whole}$

Or: "is" = "percent" × "of"

Three Types of Percent Problems

Find the part: What is 20% of 50? $x = 0.20 \times 50 = 10$
Find the percent: 15 is what percent of 60? $15 = x \times 60$ → $x = 0.25 = 25\%$
Find the whole: 12 is 30% of what number? $12 = 0.30 \times x$ → $x = 40$

Percent Change

$\text{Percent Change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$

Increase: positive change Decrease: negative change

📚 Practice Problems

1Problem 1easy

❓ Question:

What is 15% of 80?

💡 Show Solution

Convert the percent to a decimal and multiply:

$15\% = 0.15$

$0.15 \times 80 = 12$

Answer: 12

2Problem 2medium

❓ Question:

18 is what percent of 72?

💡 Show Solution

Set up the equation: part = percent × whole

$18 = x \times 72$

Solve for $x$ : $x = \frac{18}{72} = \frac{1}{4} = 0.25$

Convert to percent: $0.25 = 25\%$

Answer: 25%

3Problem 3hard

❓ Question:

A shirt originally costs $40. After a sale, it costs $32. What is the percent decrease?

💡 Show Solution

Use the percent change formula:

$\text{Percent Change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$

$= \frac{32 - 40}{40} \times 100\%$

$= \frac{-8}{40} \times 100\%$

$= -0.2 \times 100\%$

$= -20\%$

The negative indicates a decrease.

Answer: 20% decrease

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