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5.2.1: Solving Percent Problems

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Learning Objectives

• Identify the amount, the base, and the percent in a percent problem.
• Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100, so they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

• The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.
• The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.
• The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price.

You will return to this problem a bit later. The following examples show how to identify the three parts: the percent, the base, and the amount.

Identify the percent, amount, and base in this problem.

30 is 20% of what number?

Percent: The percent is the number with the % symbol: 20%.

Base : The base is the whole amount, which in this case is unknown.

Amount: The amount based on the percent is 30.

Percent=20%

Base=unknown

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Identify the percent, base, and amount in this problem:

What percent of 30 is 3?

The percent is unknown, because the problem states " What percent?" The base is the whole in the situation, so the base is 30. The amount is the portion of the whole, which is 3 in this case.

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

\[\ \text { Percent } {\color{red}\cdot}\text { Base }{\color{blue}=}\text { Amount } \nonumber \]

In the examples below, the unknown is represented by the letter \(\ n\). The unknown can be represented by any letter or a box \(\ \square\) or even a question mark.

Write an equation that represents the following problem.

\(\ 20 \% \cdot n=30\)

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as \(\ 20 \% \cdot n=30\), you can divide 30 by 20% to find the unknown: \(\ n=30 \div 20 \%\).

You can solve this by writing the percent as a decimal or fraction and then dividing.

\(\ n=30 \div 20 \%=30 \div 0.20=150\)

What percent of 72 is 9?

\(\ 12.5 \% \text { of } 72 \text { is } 9\).

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

\(\ 10 \% \text { of } 72=0.1 \cdot 72=7.2\)

\(\ 20 \% \text { of } 72=0.2 \cdot 72=14.4\)

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

What is 110% of 24?

\(\ 26.4 \text { is } 110 \% \text { of } 24\).

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

18 is what percent of 48?

• \(\ 0.375 \%\)
• \(\ 8.64 \%\)
• \(\ 37.5 \%\)
• \(\ 864 \%\)

Incorrect. You may have calculated properly, but you forgot to move the decimal point when you rewrote your answer as a percent. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Incorrect. You may have used \(\ 18\) or \(\ 48\) as the percent, rather than the amount or base. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Correct. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives \(\ 37.5 \%\).

Incorrect. You probably used 18 or 48 as the percent, rather than the amount or base, and also forgot to rewrite the percent as a decimal before multiplying. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Using Proportions to Solve Percent Problems

Percent problems can also be solved by writing a proportion. A proportion is an equation that sets two ratios or fractions equal to each other. With percent problems, one of the ratios is the percent, written as \(\ \frac{n}{100}\). The other ratio is the amount to the base.

\(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\)

Write a proportion to find the answer to the following question.

30 is 20% of 150.

18 is 125% of what number?

• \(\ 0.144\)
• \(\ 694 \frac{4}{9}\) (or about \(\ 694.4\))

Incorrect. You probably didn’t write a proportion and just divided 18 by 125. Or, you incorrectly set up one fraction as \(\ \frac{18}{125}\) and set this equal to the base, \(\ n\). The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Correct. The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably put the amount (18) over 100 in the proportion, rather than the percent (125). Perhaps you thought 18 was the percent and 125 was the base. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably confused the amount (18) with the percent (125) when you set up the proportion. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price .

The coupon will take $33 off the original price.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

\(\ \begin{array}{l} 10 \% \text { of } 220=0.1 \cdot 220=22 \\ 20 \% \text { of } 220=0.2 \cdot 220=44 \end{array}\)

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Evelyn bought some books at the local bookstore. Her total bill was $31.50, which included 5% tax. How much did the books cost before tax?

The books cost $30 before tax.

Susana worked 20 hours at her job last week. This week, she worked 35 hours. In terms of a percent, how much more did she work this week than last week?

Since 35 is 175% of 20, Susana worked 75% more this week than she did last week. (You can think of this as, “Susana worked 100% of the hours she worked last week, as well as 75% more.”)

Percent problems have three parts: the percent, the base (or whole), and the amount. Any of those parts may be the unknown value to be found. To solve percent problems, you can use the equation, \(\ \text { Percent } \cdot \text { Base }=\text { Amount }\), and solve for the unknown numbers. Or, you can set up the proportion, \(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\), where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

Related Topics

• How to Find Percent of Increase and Decrease
• How to Find Discount, Tax, and Tip
• How to Do Percentage Calculations
• How to Solve Simple Interest Problems

Step by step guide to solve percent problems

• In each percent problem, we are looking for the base, or part or the percent.
• Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

• \(51\) is \(340\%\) of what?
• \(93\%\) of what number is \(97\)?
• \(27\%\) of \(142\) is what number?
• What percent of \(125\) is \(29.3\)?
• \(60\) is what percent of \(126\)?
• \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

• \(\color{blue}{15}\)
• \(\color{blue}{104.3}\)
• \(\color{blue}{38.34}\)
• \(\color{blue}{23.44\%}\)
• \(\color{blue}{47.6\%}\)
• \(\color{blue}{100}\)

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How to Calculate Percentages

Last Updated: July 18, 2023 Fact Checked

This article was co-authored by Jake Adams . Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University. There are 17 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 8,662,220 times.

Resources And Tools

Calculating percentage.

• A simple way to multiply a decimal by 100 is to move the decimal to the right two digits. • The percent symbol is then just tacked on at the end, like a unit of measurement would be.

• There are 12 months total in a year, so Jerry worked 7/12 months.
• Then, convert the fraction to a decimal: 7/12 = 0.58
• Next, convert the fraction to a percent: 0.58 x 100% = 58%
• Jerry the electrician worked 58% of the year.

• 35 correct answers + 10 incorrect answers = 45 answers total
• We can set this problem up as the fraction 35/45.
• 35/45 = 0.78
• 0.78 x 100 = 78%
• Donovan got 78% of the answers correct on his test.

What Is X Percent of Y?

You can also simply move the decimal to the left two places.

• In this example, $0.45 is the amount of interest accrued each day that you do not pay your friend back.
• If you need to further calculate the total due after 1 day, you would add the amount you borrowed to the amount of the interest times the number of days. So $15 + ($0.45 x 1 day) = $15.45.

• We can reword this problem as “What is 80% of 35?”
• Plug the values into the formula P/100 = Part/Whole
• 80/100 = X/35
• 35 x 0.8 = X
• The pitcher won 28 games.

• We can reword this problem as “What is 93% of 8.15?”
• 93/100 = X/8.15
• 0.93 = X/8.15
• 0.93 x 8.15 = X
• There are 7.58 ounces of silver.

P Percent of What Number Is Y?

• Part/Percent (in decimal form) = Whole
• Keep reading for a full walk-through if you’re not sure how to get there.

• 72/100 = 1,380 online sales/Y total sales
• 72/100 = 1,380/Y
• 0.72 = 1,380/Y
• 0.72 x Y = 1,380
• 1,380/0.72 = Y
• Y = 1916.66
• Acme Computers made 1917 total sales this year.
• 39/100 = 89/Y
• 0.39 = 89/Y
• 0.39 x Y = 89
• 89/0.39 = Y

Calculating Percent Increase

• New Amount - Original Amount = Difference
• $15.75 - $13.99 = $1.76
• (Difference / Original Amount) x 100% = Percent Increase
• ($1.76 / $13.99) x 100% = 12.5%
• The price of the game went up by 12.5%.

• $55 - $22 = $33
• ($33 / $55) x 100% = 60%
• The company has a 60% markup on sweaters.

Calculating Percent Decrease

• Original Amount - New Amount = Difference
• 42 - 39 = 3
• (3 / 42) x 100% = 7%
• Jane’s hours decreased by 7%.

• 563 - 542 = 21
• (21 / 563) x 100% = 3.7%
• Company A decreased their number of employees by 3.7%.

Percentage in Real Life

• Example: If your bill is $54, a 10% tip would be $5.4.
• Example: For a $54 bill, 10% is $5.4. Half of $5.4 is $2.7. Finally, $5.4 + $2.7 = $8.1.
• Example: For a $54 bill, double that is $108. If you move the decimal one place to the left, you'll get $10.80.

• Move the decimal two places to the left . In this example, 70%/100% = 70/100 = 7/10 = 0.7. [30] X Research source
• Multiply the original price by the new decimal. If the shirt you want is $20, multiply $20 by 0.7. This comes to $14, meaning the shirt is now on sale for $14. [31] X Research source
• Calculate your savings. Simply subtract the sale price from the original price ($20 - $14 = $6 saved)!

• Convert 9% to a decimal: 0.09
• Add the decimal to 1: 0.09 + 1 = 1.09
• Multiple that value by the original price: $15 x 1.09 = $16.35
• Mark will pay $16.35 at checkout.

Percentage Calculator

Expert q&a.

• x% of y is the same as y% of x. For example, 10% of 30 = 3 = 30% of 10. [33] X Research source Thanks Helpful 0 Not Helpful 3

You Might Also Like

• ↑ Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 24 July 2020.
• ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
• ↑ https://txwes.edu/media/twu/content-assets/images/academics/academic-success-center/Quick-Guide-to-Percentages-and-Decimals.pdf
• ↑ Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 20 May 2020.
• ↑ https://www.calculatorsoup.com/calculators/math/fraction-to-decimal-calculator.php
• ↑ https://www.whatcom.edu/home/showpublisheddocument/1760/635548017079270000/
• ↑ https://www.whatcom.edu/home/showpublisheddocument/1760/635548017079270000
• ↑ https://www.cnm.edu/depts/tutoring/tlc/res/accuplacer/8_Math_550_Percent_Word_Problems__2_.pdf
• ↑ https://www.mathsisfun.com/percentage-calculator.html
• ↑ https://www.omnicalculator.com/math/percentage
• ↑ https://www.calculatorsoup.com/calculators/algebra/percentage-increase-calculator.php
• ↑ https://www.omnicalculator.com/math/percentage-increase
• ↑ https://www.calculatorsoup.com/calculators/algebra/percentage-decrease-calculator.php
• ↑ https://www.omnicalculator.com/math/percentage-decrease
• ↑ https://sciencing.com/easy-ways-calculate-percentages-8362422.html
• ↑ https://www.calculator.net/discount-calculator.html
• ↑ https://edu.gcfglobal.org/en/percents/percentages-in-real-life/1/

About This Article

To calculate percentages, start by writing the number you want to turn into a percentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage. To learn how to calculate a discount using a percentage, scroll down! Did this summary help you? Yes No

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Home / United States / Math Classes / 6th Grade Math / Solving Problems Based on Percentage

Solving Problems Based on Percentage

Percent is an alternate method of representing fractions and decimals. Here we will learn different methods of calculati ng the percent and the steps involved in each method. We will also look at some examples that will help you gain a better understanding of the concept. ...Read More Read Less

Table Of Contents

What is meant by percentage?

Solving problems based on percentages, finding the percentage of a number, finding the whole number from the percent, finding the whole using the ratio method, solved examples.

• Frequently Asked Questions

In mathematics, a percentage is a number or ratio that represents a fraction of 100. The symbol “ % ” is frequently used to represent it, and it has a few hundred years of history. While we are on the topic of percentages, one example will be, the decimal 0.35, or the fraction \(\frac{7}{20}\) , which is equivalent to 35 percent, or 35%.

By solving problems based on percentages, we can find the missing values and find the values of various unknowns in a given problem.

Find 40% of 200.

\(\frac{40}{100}\times 200\)              Write the percentage as a fraction

\(\frac{2}{5}\times 200=800\)            Simplify

First, write the percentage as a fraction or decimal. Then, divide the fraction or decimal by the part. This method applies to any situation in which a percentage and its value are given. 

If 2 percent equals 80, multiply 80 by 100 and divide it by 2 to get 4000.

Prove that 20% of 120 is 24. 

20% =\(\frac{20}{100}\)       Write the percent as a fraction or decimal.

Using multiplication equation:

\(\frac{20}{100}\times 120=24\)      Simplify

To prove the reverse of this solution we use the  division equation:

\(\frac{24}{\frac{20}{100}}\)      Simplify

\(\frac{2400}{20}=120\)    

A ratio table is the table that shows the comparison between two units and shows the relationship between them.

Example 1: What is 25% of 50?

We have 25% of 50.

So, 25% of 50 = \(\frac{1}{4}\times 50\) Write the percentage as a fraction or decimal.

                       = \(\frac{50}{4}\)     Simplify.

                       = 12.5  

Example 2: Using the ratio table, answer the following question:

What is 60% of 200?

We have 60% of 200.

Now, we have to use the ratio table to find the part. Let one row represent the part and the other row represent the whole row in the table and find the equivalent ratio of 200.

The first column represents the percentage = \(\frac{60}{100}\)

So, 60% of 200 is 120.

Example 3: Find the whole of the number.

                  50% of what number is 45.

We have: 50% of what number is 45?

Use division equation

\(\frac{45}{50%}\)    Write the percentage as a fraction or decimal

\(=\frac{45}{\frac{1}{2}}\)  Simplify

So, \(45\times 2=90\)

Hence, 50% of 90 is 45

Example 4: Find the whole of the number using the ratio table.

140% of what number is 84

We have to find 140% of what number is 84.

Use the ratio table to find the part. Let one be the part and the other be the whole row in the table. Now, find the equivalent ratio of 200.

So, 140% of 60 is 84.

Example 5: A rectangular hall’s width is 60 percent of its length.

What are the room’s dimensions?

Solution:  

Calculate the width of the room by taking 60% of 15 feet.

\(60%\times 15\) Write the percentage as a fraction or decimal.

= \(0.6\times 15\)      Simplify

We can al so understand it with the help of a diagram:

The width is 9 feet.

Area of the rectangle = \(\text{length}\times \text{width}\)

                                    = \(15\times 9\)

                                    = 135

Hence, the area of the given room is 135 \(feet^2\).

Example 6: You have won a camping trip at an auction at your school fair that cost $80. Your bid is 40% of your maximum bid for the price of the camping trip. How much more would you be willing to pay for the trip if you hadn’t already paid the full price?

You are given the winning camping bid that represents the maximum bid as well as the percentage of your maximum bid. You must calculate how much more you would have paid for the camping trip if you had known how much more you were willing to pay.

Your winning bid is the part, and your maximum bid is the whole.

Create a model based on the fact that 40% of the total is $80 to determine the highest bid. Then divide the winning bid by the maximum bid to find out how much more you were willing to pay.

The maximum bid is $200 and the winning bid is $80. So, you would be willing to bid $200 – $80 = $120 more for the tickets.

How do you calculate a percentage?

To calculate a percentage, divide the given value by the total value and multiply the result by 100. That is “(value/total value) x 100%”. This is the formula for calculating percentages.

In mathematics, a percentage is a number or ratio that represents a fraction of 100 in mathematics. Percentage is usually represented by the symbol “%”. It is also written simply as “percent” or “pct”. For example, the decimal 0.35, or the fraction \(\frac{35}{100}\), is equivalent to 0.35.

What is the purpose of percentages?

Percentages are used to figure out “how much” or “how many” of something is to be taken from a given value. Percentage makes it easier to calculate the exact amount or figure being discussed. In order to determine whether a percentage increase or decrease has occurred, a comparison of fractions is done. This aids in calculating percentages of profit and loss, for example in real life situations.

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PERCENTAGES

This section will explain how to apply algebra to percentage problems.

In algebra problems, percentages are usually written as decimals.

Example 1. Ethan got 80% of the questions correct on a test, and there were 55 questions. How many did he get right?

The number of questions correct is indicated by:

Ethan got 44 questions correct.

Explanation: % means "per one hundred". So 80% means 80/100 = 0.80.

Example 2. A math teacher, Dr. Pi, computes a student’s grade for the course as follows:

a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.

Darrel’s grade for the course is an 89.6, or a B+.

b. Suppose Selena has an 89 homework average and a 97 test average. What does Selena have to get on the final exam to get a 90 for the course?

The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam.

So instead of multiplying 30% times a number, multiply 30% times E. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.

Because Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.

Example 3. Sink Hardware store is having a 15% off sale. The sale price of a toilet is $97; find the retail price of the toilet.

a. Complete the table to find an equation relating the sale price to the retail price (the price before the sale).

Vocabulary: Retail price is the original price to the consumer or the price before the sale. Discount is how much the consumer saves, usually a percentage of the retail price. Sale Price is the retail price minus the discount.

b. Simplify the equation.

Explanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 = .85. In other words, the sale price is 85% of the retail price.

c. Solve the equation when the sale price is $97.

The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.)

The following diagram is meant as a visualization of problem 3.

The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So Retail Price = Sale Price + Discount If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. Sale Price = Retail Price - Discount

Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations.

Study Tip: Remember to use descriptive letters to describe the variables.

CHAPTER 1 REVIEW

This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.

Signed Numbers:

Informal Rules:

Adding or subtracting like signs: Add the two numbers and use the common sign.

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

Order of operations: P lease E xcuse M y D ear A unt S ally 1. Inside P arentheses, (). 2. E xponents. 3. M ultiplication and D ivision (left to right) 4. A ddition and S ubtraction (left to right)

Study Tip: All of these informal rules should be written on note cards.

Introduction to Variables:

Generate a table to find an equation that relates two variables.

Example 6. A car company charges $14.95 plus 35 cents per mile.

Simplifying Algebraic Equations:

Combine like terms:

Solving Equations:

1. Simplify both sides of the equation. 2. Write the equation as a variable term equal to a constant. 3. Divide both sides by the coefficient or multiply by the reciprocal. 4. Three possible outcomes to solving an equation. a. One solution ( a conditional equation ) b. No solution ( a contradiction ) c. Every number is a solution (an identity )

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.

a. Create a table to find the equation that relates cost and minutes.

c. If the call costs $23.50, how long were you on the phone?

If the call costs $23.50, then you were on the phone for approximately 79 minutes.

Literal Equations:

A literal equation involves solving an equation for one of two variables.

Percentages:

Write percentages as decimals.

Example 11. An English teacher computes his grades as follows:

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

Sue has to get a 78.36 in the final exam to get an 80 for the course.

Study Tips:

1. Make sure you have done all of the homework exercises. 2. Practice the review test on the following pages by placing yourself under realistic exam conditions. 3. Find a quiet place and use a timer to simulate the test period. 4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice. 5. Check your answers. 6. There is an additional exam available on the Beginning Algebra web page. 7. DO NOT wait until the night before the exam to study.

Math Topics

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Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Percentage Calculations

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

• Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

• Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

• Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
• Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
• Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
• Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
• Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
• Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

• Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
• Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
• Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
• Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

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Solving Percent Problems

Learning Objective(s)

·          Identify the amount, the base, and the percent in a percent problem.

·          Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.

The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.

The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price .

You will return to this problem a bit later. The following examples show how to identify the three parts, the percent, the base, and the amount.

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

Percent · Base = Amount

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as 20% · n = 30, you can divide 30 by 20% to find the unknown: n =  30 ÷ 20%.

You can solve this by writing the percent as a decimal or fraction and then dividing.

n = 30 ÷ 20% =  30 ÷ 0.20 = 150

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

10% of 72 = 0.1 · 72 = 7.2

20% of 72 = 0.2 · 72 = 14.4

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

Using Proportions to Solve Percent Problems

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

10% of 220 = 0.1 · 220 = 22

20% of 220 = 0.2 · 220 = 44

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

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Solving Percent Application Problems

Math: basic tutorials : solving percent application problems.

• Introduction to Fractions
• Equivalent Fractions
• Simplifying Fractions
• Mixed Numbers & Improper Fractions
• Multiplying Fractions
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• Adding Fractions
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• Decimals and Rounding
• Introduction to Percentage
• Simple Operations with Percent
• Solving Percent Change Problems
• Equation Basics
• One-Step Linear Equations
• Multiple-Step Linear Equations
• Rearranging Formulas
• Solving Systems of Linear Equations
• Addition and Subtraction of Polynomials
• Multiplying Polynomials
• Introduction to Factoring Polynomials
• Division of Algebraic Expressions
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Once you know the basics of how to solve operations with percent, you can use those methods to solve application problems. This section explains how to find the base, part, and percent in a word problem, and use them to solve the problem.

Example and Activity

What is the sale price of a coat that is normally 95 dollars and is discounted by 20 percent.

Line 1: What are you being asked to find. We are being asked to find the sale price.

Line 2: Choose a variable to represent it. Let s be the sale price.

Line 3: Write a sentence that gives the information to write an equation to find s. If the discount is 20 percent, this means the sale price is 80 percent of the original price.

Line 4: Translate the words into algebra, so the equation is s equals 0 decimal 8 0 times 95.

Line 5: Multiply to solve for s, so s equals 76.

Line 6: Write a statement that answers the question. The sale price of the coat is 76 dollars.

A cupcake contains 480 calories, and 240 of those calories are from fat. What percent of the total calories come from fat?

Line 1: What are you being asked to find? We are being asked to find the percent of the calories that from fat.

Line 2: Choose a variable to represent it. Let p be the percent from fat.

Line 3: Write a sentence that gives the information to find p. What percent of 480 is 240?

Line 4: Translate the words into algebra, so the equation is p time 480 equals 240.

Line 5: Divide both sides of the equation by 480 to solve for p, so the equation is 480p divided by 480 equals 240 divided by 480.

Line 6: Simplify to get p equals 0 decimal 5.

Line 5: Convert the decimal to a percent by multiplying by 100 percent so p = 50 percent.

Line 7: Write a statement that answers the question. Therefore, 50 percent of the calories in the cupcake are from fat.

Source: " Prealgebra - opens in a new window " by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet

• Summary: Solving Percent Application Problems - PDF - Opens in a new window This document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
• Worksheet: Solving Percent Application Problems - PDF - Opens in a new window This document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
• << Previous: Simple Operations with Percent
• Next: Solving Percent Change Problems >>

Note: This material is meant as a general guide, if your professor's instructions differ from the information we've provided, always follow your professor's instructions. Also note, icons on this site are used through a Noun Project Pro license. Please be sure to provide proper attribution if you reuse them.

• Last Updated: Aug 22, 2023 3:28 PM
• URL: https://tlp-lpa.ca/math-tutorials

Solved Examples on Percentage

The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage.

Solved examples on percentage:

1.  In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.

Total number of invalid votes = 15 % of 560000

                                       = 15/100 × 560000

                                       = 8400000/100

                                       = 84000

Total number of valid votes 560000 – 84000 = 476000

Percentage of votes polled in favour of candidate A = 75 %

Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000

= 75/100 × 476000

= 35700000/100

2. A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.

Total number of fruits shopkeeper bought = 600 + 400 = 1000

Number of rotten oranges = 15% of 600

                                    = 15/100 × 600

                                    = 9000/100

                                    = 90

Number of rotten bananas = 8% of 400

                                   = 8/100 × 400

                                   = 3200/100

                                   = 32

Therefore, total number of rotten fruits = 90 + 32 = 122

Therefore Number of fruits in good condition = 1000 - 122 = 878

Therefore Percentage of fruits in good condition = (878/1000 × 100)%

                                                                 = (87800/1000)%

                                                                 = 87.8%

3. Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?

Solution:            

Let the money he took for shopping be m.

Money he spent = 30 % of m

                      = 30/100 × m

                      = 3/10 m

Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10

But money left with him = $ 2100

Therefore 7m/10 = $ 2100          

m = $ 2100× 10/7

m = $ 21000/7

Therefore, the money he took for shopping is $ 3000.

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

Ratio into Percentage

Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Problems on Percentage

Real Life Problems on Percentage

Word Problems on Percentage

Application of Percentage

8th Grade Math Practice From Solved Examples on Percentage to HOME PAGE

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Worksheet on Percentage of a Given Quantity

Worksheet on Word Problems on Percentage

Worksheet on Increase Percentage

Worksheet on Decrease Percentage

Worksheet on increase and Decrease Percentage

Worksheet on Expressing Percent

Worksheet on Percent Problems

Worksheet on Finding Percentage

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Percentage Worksheets Percentages of Numbers

Welcome to our Finding Percentage Worksheets. In this area, we have a selection of percentage worksheets for 6th graders designed to help children learn and practice finding percentages of numbers.

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Quicklinks to...

• How to Find Percentages of a Number
• Finding Simple Percentages Worksheets
• Finding Simple Percentages Online Quiz
• Finding Harder Percentages Worksheets
• Finding (Harder) Percentages Online Quiz
• More related Math resources

Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

• 50% = 0.5 = ½
• 25% = 0.25 = ¼
• 75% = 0.75 = ¾
• 10% = 0.1 = 1 ⁄ 10
• 1% = 0.01 = 1 ⁄ 100

Percentage Worksheets

How to work out percentages of a number.

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

• How to find percentage of numbers support

Finding Percentage Worksheets

Here you will find a selection of worksheets on percentages designed to help your child understand how to work out percentages of different numbers.

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

• finding simple percentages 1%, 10%, 50% and 100%;
• finding multiples of 5%;
• finding any percentage of a number.

The percentage worksheets have been designed for students in 6th grade, and all the sheets come with an answer sheet.

Finding Simple Percentages (1%, 10%, 50% and 100%)

These sheets are a great way to start off learning percentages.

All the questions involve finding either 1%, 10%, 50% or 100% of different numbers.

• Finding Simple Percentages 1
• PDF version
• Finding Simple Percentages 2
• Finding Simple Percentages 3

Finding Simple Percentages Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your understanding and skill at finding simple percentages of different amounts.

Fun Quiz Facts

• This quiz was attempted 1,329 times last academic year. The average (mean) score was 13.4 out of 19 marks.
• Can you beat the mean score?

Finding Harder Percentages

• Find Percentages 1
• Find Percentages 2
• Find Percentages 3
• Find Percentages 4
• Find Percentages 5

Finding Percentages Walkthrough Video

This short video walkthrough shows several problems from our Finding Percentages Worksheet 3 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Finding Percentages Quiz

This quick quiz tests your understanding and skill at finding a range of percentages of different amounts.

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

• Money Percentage Worksheets

Percentage Word Problems

Once your child is confident finding percentages of a range of numbers, they can start using their knowledge to solve problems involving percentages.

The worksheets in this section contain a range of percentage problems set in different contexts.

• Percentage Word Problems 5th Grade
• 6th Grade Percent Word Problems

How can I work out the percentage increase (or decrease)?

Take a look at our How to Work Out Percentage Increase/Decrease page.

This page is all about finding the percentage increase or decrease between two numbers.

We also have a percentage increase calculator that will work it all out for you at the click of a button.

• How to Work out the Percentage Increase or Decrease

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

• Converting Fractions to Percentages

• Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

• Online Percentage Practice

How to Print or Save these sheets 🖶

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Regulators keep on finding problems with safety at Boeing—and customers are paying the price

Good morning. Another terrible, no good, very bad day for Boeing . The New York Times got its hands on a slide presentation summarizing the Federal Aviation Administration’s six-week review of Boeing’s production of the 737 Max. The agency conducted 89 product audits, and Boeing failed 33 of them. It separately conducted 13 product audits on Spirit AeroSystems, which makes the 737 Max fuselage, and gave it seven failing grades. In one shocking incident, the FAA saw Spirit mechanics applying liquid Dawn soap to a door seal as a lubricant.

Meanwhile, Boeing’s customers continue to suffer the consequences.  Southwest said it would have to reevaluate its 2024 financial forecast because of Boeing’s delivery delays. United asked Boeing to stop building the 737 Max 10s it was working on. “It’s impossible to say when the Max 10 is going to get certified,” CEO Scott Kirby told an investor conference . Boeing’s problem “is not a 12-month issue, it’s a two-decade issue.”

And all that came a day after the whistleblower who worked for the company in South Carolina was found dead in his truck from what appeared to be a self-inflicted gunshot wound. Boeing stock fell another 5%. Airline stocks were also down.

Separately, I missed the taping of this week’s Leadership Next, but my cohost, Michal Lev-Ram, reports the following:

A little more than a decade ago, René Lacerte stumbled on an epiphany: His title was wrong—or rather, it was in the wrong order. Since starting his payments software company BILL in 2006, Lacerte had always called himself its “founder and CEO.” But as the company grew, and hit some growing pains, he realized he needed to start thinking of himself as BILL’s “CEO and founder.”

“The reason I flipped it was to remind me every day that my responsibility to the company is as the CEO,” Lacerte told me. “I’m always going to be the founder of BILL, no matter what, right? The heart and soul and culture, that’s the easy part of being a founder. The hard part of leading is actually changing and growing as the leader that the organization needs, and that’s the CEO role.”

This simple switch in title, or “trick” as Lacerte calls it, isn’t pure semantics. It’s a meaningful mind-shift in how founding CEOs should think about their role. The founder part, as Lacerte says, will always be there—even when the founder steps down. But the CEO is more dynamic, just as companies are ever-changing. Founders tend to think of companies as their “babies.” But CEOs? It’s the organization that they have to lead.

You can hear the entire interview on Apple or Spotify . Other news below.

Alan Murray @alansmurray [email protected]

Bumble changes things up

When it launched in 2014, Bumble touted its decision to let women make the first move on its dating app, saving them from the flood of low-effort inquiries from men found on competing services. But new CEO Lidiane Jones, faced with slowing interest in dating apps, is considering removing this key feature. “It feels like a burden for a subset of our customers today,” she tells Fortune ’s Emma Hinchliffe. Fortune

LGBTQ inclusion

Gen Z LGBTQ employees are giving their employers lower scores on inclusion and allyship compared to those from older generations, according to a new study from EY. Just 38% of survey participants who scored their workplaces poorly expected to stay for longer than a year. Mitch Berlin, vice chair of strategy and transactions at EY’s Americas practice, says companies need to give employees a safe environment: “Even if you weren’t doing it for altruistic reasons, you should be doing it for business reasons.” Fortune

Toyota hikes pay

Toyota Motor met its union’s pay demands for the fourth year in a row in a positive sign for wage growth in the Asian economy. While the union didn’t disclose exact figures, Toyota said wages were now at their highest level ever. Strong wage growth in Japan could increase the chance that the country's central bank hikes interest rates in April, ending the world’s last negative interest rate regime. Bloomberg

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Shrinkflation is coming for your home by Alena Botros

Billionaire Frank McCourt says the surgeon general is only half right about the social-media mental health crisis. It’s a crisis of personhood, not privacy by Frank McCourt and Michael Casey

T his edition of CEO Daily was curated by Nicholas Gordon. 

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Course: 6th grade   >   Unit 3

Finding a percent.

• Finding percents

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Video transcript

For more audio journalism and storytelling, download New York Times Audio , a new iOS app available for news subscribers.

• March 15, 2024   •   35:20 A Journey Through Putin’s Russia
• March 14, 2024   •   28:21 It Sucks to Be 33
• March 13, 2024   •   27:44 The Alarming Findings Inside a Mass Shooter’s Brain
• March 12, 2024   •   27:30 Oregon Decriminalized Drugs. Voters Now Regret It.
• March 11, 2024   •   29:07 The Billionaires’ Secret Plan to Solve California’s Housing Crisis
• March 10, 2024 The Sunday Read: ‘Can Humans Endure the Psychological Torment of Mars?’
• March 8, 2024   •   29:40 The State of the Union
• March 7, 2024   •   32:31 The Miseducation of Google’s A.I.
• March 6, 2024   •   23:07 The Unhappy Voters Who Could Swing the Election
• March 5, 2024   •   32:02 A Deadly Aid Delivery and Growing Threat of Famine in Gaza
• March 4, 2024   •   26:06 An F.B.I. Informant, a Bombshell Claim, and an Impeachment Built on a Lie
• March 3, 2024 The Sunday Read: ‘How Tom Sandoval Became the Most Hated Man in America’

A Journey Through Putin’s Russia

Our moscow-based reporter traveled around the country to gauge the mood before a presidential vote..

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Hosted by Sabrina Tavernise

Featuring Valerie Hopkins

Produced by Rob Szypko ,  Mary Wilson and Shannon Lin

With Summer Thomad

Edited by Brendan Klinkenberg and Michael Benoist

Original music by Dan Powell and Marion Lozano

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Russians go to the polls today in the first presidential election since their country invaded Ukraine two years ago.

The war was expected to carry a steep cost for President Vladimir V. Putin. Valerie Hopkins, who covers Russia for The Times, explains why the opposite has happened.

On today’s episode

Valerie Hopkins , an international correspondent for The New York Times.

Background reading

Mr. Putin, in pre-election messaging, was less strident on nuclear war .

What to know about Russia’s 2024 presidential vote.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

Fact-checking by Susan Lee and Milana Mazaeva .

Translations by Milana Mazaeva .

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Valerie Hopkins covers the war in Ukraine and how the conflict is changing Russia, Ukraine, Europe and the United States. She is based in Moscow. More about Valerie Hopkins

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Two Python problems to solve

Goodnight. I have two problems and I would like help from my colleagues to resolve them. Are they:

Problem 1) Suppose someone presents you with a bag containing an odd number of numbers, be it 2m+1, with m > 300,000,000. Also, be told that the numbers appear in pairs, with the exception of one of them. For example, inside the bag, S, there could be S = [[4, 6, 8, 6, 4]]. Find out what this different number is. Explain how much time and memory your algorithm takes to solve this problem.

Problem 2) Suppose you are asked to find the ranking of an integer m in the sequence L from 0 to n, be it r(n) in which chains with at least two consecutive 1’s are prohibited. For example, r(000) = 1; r(001) = 2, r(010) = 3, r(011) = 3 and r(100) = 4. Note that r(011) contains a prohibition and therefore, r(010) = r(011) = 3 .

By which you mean: You have homework.

What have you done so far?

I’m starting to work on this problem now and I need help unlocking a resolution for these 2 problems. I’m not experienced with Python and I just started a few months ago.

The problems are not Python-specific. It’s more about creating the methods to resolve them.

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