Learn Percents: Interactive Problems and Worked Examples
Use the question set below to practice percents and percentages: percent of a number, percent increase and decrease, and "what percent is it?" questions. If you want a refresher, click Start lesson to open a clear, step-by-step percent guide.
Jawab rangkaian soal dan tinjau kesalahanmu di akhir.
How this percents practice works
1. Take the practice set: answer the percent questions below.
2. Open the lesson (optional): review the method with examples and quick checks (percent, fraction, decimal conversions and more).
3. Retry: return to the question set and apply what you reviewed right away.
What you will learn in the percents lesson
Meaning & vocabulary
Percent means "per 100"
The whole, the part, and the percent rate
Benchmarks: 100%, 50%, 25%, 10%, 1%
Percent, decimal, fraction
Convert percent to decimal: \(\,p\%=\frac{p}{100}\)
Convert decimal to percent: multiply by 100
Recognize common fractions (like \(\frac14\), \(\frac12\), \(\frac34\)) as percents
Percent of a number
Find \(p\%\) of a number using \(\frac{p}{100}\times \text{whole}\)
Mental strategies: 10%, 5%, 20%, 25%, 12.5%
Estimate quickly using friendly percents (like 20% or 30%)
Percent change & real-life problems
Find what percent one number is of another
Percent increase and percent decrease using multipliers
Discounts, tax, tips, data, and everyday percentage word problems
Purpose: Build a clear understanding of percents and learn reliable methods for percent of a number, percent change, and percent word problems.
Success criteria
Explain percent as "per 100" and interpret \(100\%\) as the whole.
Convert between percent, decimal, and fraction (for example, \(25\% = 0.25 = \frac14\)).
Find percent of a number using \(\frac{p}{100}\times \text{whole}\) and mental benchmarks (10%, 5%, 25%, 50%).
Find what percent one number is of another using \(\frac{\text{part}}{\text{whole}}\times 100\%\).
Solve percent increase and percent decrease problems using multipliers.
Estimate percents quickly using friendly percents (like 20% or 30%).
Apply percents to real life: discounts, tax, tips, data, and everyday situations.
Key vocabulary
Percent: "per 100" (out of 100).
Whole (base): the total amount you start with.
Part: the amount you are comparing to the whole.
Percent rate: the percent you are taking or comparing.
Percent change: how much something increases or decreases as a percent of the original.
Quick pre-check
Pre-check 1: What does "percent" mean?
Hint: "Percent" literally means "per 100".
Pre-check 2: Ten percent of 80 is what number?
Hint: Ten percent means one tenth of the whole.
Percent • Decimal • Fraction
Convert percent, decimal, and fraction
Learning goal: Convert between percent, decimal, and fraction so you can choose the easiest form for a problem.
Key idea
A percent is a number out of 100. That is why: \[ p\% = \frac{p}{100}. \] To switch forms:
Percent → decimal: divide by 100 (move the decimal point 2 places left).
Decimal → percent: multiply by 100 (move the decimal point 2 places right).
Fraction → percent: make the denominator 100 or convert to a decimal, then to a percent.
Worked examples
Example 1: Convert \(45\%\) to a decimal and fraction
Percent to decimal: \(45\% = \frac{45}{100} = 0.45\). Percent to fraction: \(\frac{45}{100}\) simplifies to \(\frac{9}{20}\).
Example 2: Convert \(0.6\) to a percent
\(0.6 \times 100\% = 60\%\).
Example 3: Convert \(\frac{3}{4}\) to a percent
\(\frac{3}{4} = 0.75\). So \(0.75 = 75\%\).
Try it
Try it 1: Convert \(0.32\) to a percent.
Hint: Multiply by 100 to convert a decimal to a percent.
Try it 2: Which decimal is equal to \(25\%\)?
Hint: Divide by 100 to convert a percent to a decimal.
Summary
\(p\% = \frac{p}{100}\) because percent means "per 100".
Percent ↔ decimal uses ÷100 or ×100.
Fractions become percents by converting to a decimal or a denominator of 100.
Percent of a Number
Find a percent of a number
Learning goal: Find \(p\%\) of a quantity using a reliable method and quick mental benchmarks.
Key idea
To find a percent of a number, convert the percent to a decimal or fraction and multiply: \[ p\%\text{ of }N=\frac{p}{100}\times N. \] Mental math is often easiest with benchmark percents like \(10\%\), \(5\%\), \(20\%\), \(25\%\), \(50\%\), and \(12.5\%\).
Worked example
Example: Find \(15\%\) of \(200\)
Method 1 (benchmarks): \(10\%\) of 200 is 20, and \(5\%\) of 200 is 10. Add: \(20+10=30\). So \(15\%\) of 200 is \(30\).
Hint: \(12.5\%\) is one eighth. One eighth of 80 is 10.
Summary
Use \(\frac{p}{100}\times N\) to find \(p\%\) of \(N\).
Benchmarks (10%, 5%, 25%, 50%, 12.5%) make mental math fast.
What Percent Is It?
Find what percent one number is of another
Learning goal: Use part ÷ whole to find the percent.
Key idea
When you see "What percent of the whole is the part?", use: \[ \text{percent}=\frac{\text{part}}{\text{whole}}\times 100\%. \] A quick check: the answer should make sense — the percent should be less than \(100\%\) when the part is smaller than the whole.
Worked example
Example: What percent of 60 is 15?
Part ÷ whole: \(\frac{15}{60} = \frac{1}{4} = 0.25\). Convert to percent: \(0.25\times 100\% = 25\%\). Answer: 15 is \(25\%\) of 60.
Try it
Try it 1: What percent of 80 is 20?
Hint: Compute part ÷ whole: \(20/80 = 1/4\).
Try it 2: A class has 30 students and 12 are left-handed. What percent are left-handed?
Hint: \(12/30 = 0.4\). Convert \(0.4\) to a percent.
Summary
To find the percent, use part ÷ whole, then multiply by \(100\%\).
Always check if your answer makes sense (is the part smaller or larger than the whole?).
Percent Change
Percent increase and percent decrease
Learning goal: Solve percent change problems using a clear step-by-step method and multipliers.
Key idea
Percent change compares the change to the original value: \[ \text{percent change}=\frac{\text{change}}{\text{original}}\times 100\%. \] For "increase by \(p\%\)" or "decrease by \(p\%\)", it is often fastest to use a multiplier:
Increase by \(p\%\): new \(=\) original \(\times (1+\frac{p}{100})\).
Decrease by \(p\%\): new \(=\) original \(\times (1-\frac{p}{100})\).
Worked example
Example: Increase 45 by \(20\%\)
Method 1 (find the percent, then add): \(20\%\) of 45 is \(0.20\times 45 = 9\). New value: \(45+9=54\).
Method 2 (multiplier): New value \(= 45\times 1.20 = 54\).
Try it
Try it 1: Increase 45 by 20 percent. What is the new number?
Hint: Find twenty percent of 45, then add it to 45.
Try it 2: If \(n = 50\), what is \(n + 10\%\) of \(n\)?
Hint: Ten percent of 50 is 5, so add 5.
Summary
Percent change compares the change to the original amount.
For increase/decrease, multipliers are fast: \(1+\frac{p}{100}\) or \(1-\frac{p}{100}\).
Estimation
Estimate percents quickly
Learning goal: Use friendly benchmark percents to estimate without a calculator.
Key idea
Estimation helps you check reasonableness and work quickly. Use benchmarks like \(10\%\), \(20\%\), \(25\%\), \(50\%\), and \(30\%\). You can estimate by using a nearby percent and adjusting a little.
Worked examples
Example 1: Estimate \(18\%\) of \(75\) using \(20\%\)
\(20\%\) of 75 is 15 (because \(10\%\) is 7.5, and double is 15). \(18\%\) is a bit less than \(20\%\), so the estimate is a bit less than 15. A quick estimate is about 14.
Example 2: Estimate \(33\%\) of \(120\) using \(30\%\)
\(30\%\) of 120 is 36. \(33\%\) is a little more than \(30\%\), so the estimate is a little more than 36. A quick estimate is about 40.
Try it
Try it 1: Estimate eighteen percent of seventy-five using twenty percent, then adjust down slightly. Type your estimate.
Hint: Twenty percent of seventy-five is 15, and eighteen percent is a little less.
Try it 2: Estimate \(33\%\) of \(120\) using \(30\%\), then adjust up slightly.
Hint: Thirty percent of 120 is 36. Thirty-three percent is a bit more, so about 40.
Summary
Estimate with friendly percents like 10%, 20%, 25%, 30%, and 50%.
Use "a bit more" or "a bit less" adjustments to stay quick and accurate.
Above 100%
Percents greater than 100%
Learning goal: Understand percents above 100% and compute them using multipliers.
Key idea
Percents can be greater than \(100\%\). That means more than the whole. A fast way to compute is to convert to a multiplier:
\(100\% = 1.00\)
\(125\% = 1.25\)
\(200\% = 2.00\)
\(112.5\% = 1.125\)
Worked examples
Example 1: \(200\%\) of \(30\)
\(200\% = 2\). So \(200\%\) of \(30\) is \(2\times 30 = 60\).
Example 2: \(125\%\) of \(40\)
\(125\% = 1.25\). So \(125\%\) of \(40\) is \(1.25\times 40 = 50\). (You can also think: \(100\%\) of 40 is 40 and \(25\%\) of 40 is 10, total 50.)
Try it
Try it 1: What is two hundred percent of 30?
Hint: Two hundred percent means double.
Try it 2: What is \(112.5\%\) of \(64\)?
Hint: \(112.5\% = 100\% + 12.5\%\). Find \(12.5\%\) (one eighth) of 64 and add it to 64.
Summary
Percents above \(100\%\) mean more than the whole.
Convert to a multiplier (like \(125\% = 1.25\)) to compute quickly.
Applications & History
Why percents matter
Learning goal: Connect percents to real life (discounts, tax, tips, data) and build "percent sense".
Where you use percents
Discounts and sales: find the discount and the sale price.
Tax and tips: add a percent to a total.
Grades and data: interpret charts, surveys, and statistics.
Science and probability: compare parts of a whole.
Worked example: discount
Example: A jacket costs \$50 and is \(20\%\) off.
Discount amount: \(20\%\) of 50 is \(0.20\times 50 = 10\). Sale price: \(50 - 10 = 40\). Answer: The jacket is \$40 after the discount.
Try it
Try it 1: A 50 dollar item has a 20 percent discount. What is the discount amount?
Hint: Find twenty percent of fifty.
Try it 2: If sales tax is \(8\%\), which calculation finds the total price for a \$25 item?
Hint: Tax is added to the price, so compute tax and add it to 25.
Fun fact (a little history)
The percent sign: The symbol \( \% \) is widely used today to mean "per 100", and you will also see percents in finance, statistics, and science.
Percent sense: Skilled percent thinking is about choosing a simple method: benchmarks (10%, 25%, 50%), a fraction, or a decimal multiplier.
Final recap
Percent means "per 100" and \(p\%=\frac{p}{100}\).
Convert percent ↔ decimal by ÷100 or ×100, and connect common fractions to percents.
To find \(p\%\) of a number, use \(\frac{p}{100}\times \text{whole}\).
To find "what percent", use \(\frac{\text{part}}{\text{whole}}\times 100\%\).
Percent increase/decrease can be solved with multipliers.
Percents appear everywhere: discounts, tax, tips, grades, and data.
Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the skill.
