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Increase $45$ by $20\%$.

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Explanation: $20\%$ of $45$ = $9$; $45 + 9 = 54$.

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Percents

Percents Practice Quiz with a Step-by-Step Interactive Lesson

Use the quiz at the top of the page 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.

How this percents practice works

1. Take the quiz: answer the percent questions at the top of the page.
2. Open the lesson (optional): review the method with examples and quick checks (percent, fraction, decimal conversions and more).
3. Retry: return to the quiz and apply what you reviewed right away.

What you’ll 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

Back to the quiz

When you’re ready, return to the quiz at the top of the page and continue practicing percents.

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Percents
Lesson

Step-by-step guide

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Percents Lesson

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Lesson Overview

Lesson overview

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?

Out of 100 Out of 10 Multiply by 100 every time Divide by 10 every time

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.

$32\%$ $3.2\%$ $0.32\%$ $320\%$

Hint: Multiply by 100 to convert a decimal to a percent.

Try it 2: Which decimal is equal to $25\%$?

$2.5$ $0.025$ $0.25$ $25$

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 $30$.

Method 2 (formula):
$\frac{15}{100}\times 200 = 0.15\times 200 = 30$.

Try it

Try it 1: What is 20 percent of 70?

Hint: Twenty percent is double ten percent.

Try it 2: What is $12.5\%$ of $80$?

8 10 12 16

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?

25 percent 20 percent 40 percent 80 percent

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?

30 percent 36 percent 40 percent 60 percent

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 $n$?

50 55 60 65

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. 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 $30\%$.

36 40 60 120

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 $64$?

72 70 74 80

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?

$\,25 - 0.08\times 25$ $\,25 \div 0.08$ $\,0.08 + 25$ $\,25 + 0.08\times 25$

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.