percentage increase and decrease problem solving questions

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Percent increase and decrease

Here you will learn about percent increase and decrease, including how to increase and decrease a value by a given percentage, use decimals to calculate percent increase and percent decrease and find percent change.

Students will first learn about percent increase and decrease as part of ratios and proportions in the 7 th grade.

What is the percent increase and decrease?

Percent increase and decrease is the change in a value compared to its original value. They are expressed as percentages.

Percent increase means to increase (make bigger) a value by a certain amount. To do this, you can either calculate the given percentage of the value and then add it on to the original value or use a percent as a decimal.

For example,

Increase \$ 50 by 30 \%.

Percent decrease means subtracting a given percentage of a value from the original value. To do this, you can either calculate the given percent of the value and then subtract it from the original or use a percent as a decimal.

Decrease \$ 20 by 20 \%.

When given two values, you can calculate the percent difference or percentage change. When the value goes down this may also be called percent decrease, percent loss, or a markdown.

You can calculate percent change using the percentage change formula:

\text { Percent change }=\frac{\text { amount of change }}{\text { original }} \times 100

Common Core State Standards

How does this relate to 7 th grade math?

• Grade 7: Ratios and Proportional Relationships (7.RP.3) Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How to increase or decrease a value by a percent

In order to increase or decrease a value by a given percent:

Calculate the given percent of the value.

Add or subtract the calculated percent to/from the original number.

[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

Use this quiz to check your grade 6 to 7 students’ understanding of percents. 10+ questions with answers covering a range of 6th and 7th grade percent topics to identify areas of strength and support!

Percent increase and decrease examples

Example 1: increase value by a percent.

Increase 500 by 50 \%.

You will first calculate 50 \% of 500.

You can calculate 10 \% (by dividing by 10 ) and then multiply by 5 to get to 50 \%.

10 \% of 500=50

50 \times 5=250

50 \% of 500 is 250.

Note: You can also calculate 50 \% of an amount by dividing it by 2 .

2 Add or subtract the calculated percent to/from the original number.

Because you are calculating a percent increase, add 250 on to the original value of 500.

500+250=750

The final answer is 750.

500 increased by 50 \% is 750.

Example 2: decrease value by a percent

Decrease \$ 1,200 by 25 \%.

First, you will calculate 25 \% of \$ 1,200.

You can calculate 25 \% by first finding 10 \% (dividing by 10 ), then multiplying by 2 to find 20 \%.

10 \% of \$ 1,200 is 120.

20 \% of \$ 1,200 is 240.

You can then find 5 \%, by dividing 120 by 2.

120 \div 2=60.

5 \% of \$ 1,200 is 60.

240+60=300.

25 \% of \$ 1,200 is 300.

Note: You can also calculate 25 \% of an amount by dividing it by 4 .

Because you are calculating a percent decrease, you will subtract \$ 300 from the original value, \$ 1,200.

1,200-300=900

The final answer is \$ 900.

A 25 \% decrease of \$ 1,200 is \$ 900.

Percent increase and decrease using a percent as a decimal

In order to increase a value by using a percent as a decimal:

Add the percent you are increasing by and \textbf{100\%} .

Convert the percent to a decimal.

Multiply the original amount by the decimal.

In order to decrease a value by using a percent as a decimal:

Subtract the percent you are decreasing from \textbf{100\%} .

Example 3: percent increase using a percent as decimal

Increase 2,200 \, ml by 20 \%.

100 \%+20 \%=120 \%

Divide the percentage by 100.

120 \% \div 100=1.2

Multiply 2,200 by 1.2.

2,200 \times 1.2=2,640 \mathrm{~ml}

2,200 \, ml increased by 20 \% is 2,640 \, ml.

Example 4: percent decrease using a percent as decimal

Kendra had a car payment of \$ 430. When she purchased a new car, her car payment decreased 15 \%. How much is Kendra’s car payment now?

This is a 15 \% decrease, so you will subtract 15 \% from 100 \%.

100 \%-15 \%=85 \%

Now divide the percentage by 100.

\begin{aligned}&85 \div 100=0.85\\\\ &85 \%=0.85\end{aligned}

Multiply the original price of \$ 430 by 0.85.

430 \times 0.85=\$ 365.50

Remember to always write money using two decimal places.

Kendra’s car payment decreased from \$ 430 to \$ 365.50.

Calculating percent increase and decrease

In order to calculate the percent increase or percent decrease after a percent change:

Find the amount of change using subtraction .

• Plug numbers into the percent change formula. \text { Percentage change }=\cfrac{\text { Change }}{\text { Original }} \times 100

Simplify the fraction, if necessary, using equivalent fractions.

Convert the fraction to a decimal.

Calculate percent change.

Example 5: percent decrease after a percent change

Karla weighed 67 \, kg in January. Over a period of time, her weight had decreased to 55 \, kg. Calculate the percent decrease in her weight.

Karla’s weight has changed from 67 \, kg to 55 \, kg. You will subtract her original new from her original weight.

67 \mathrm{~kg}-55 \mathrm{~kg}=12 \mathrm{~kg}

Plug numbers into the percent change formula.

The change is 12 \, kg and the original amount is 67 \, kg. Plug the numbers into the following formula:

\begin{aligned}& \text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100 \\\\ &\text { Percent change }=\cfrac{12}{67} \times 100\end{aligned}

\cfrac{12}{67} \, is already in simplest form.

\cfrac{12}{67}=0.1791

You can round this decimal number to 0.18 to solve.

\text { Percent change }=0.18 \times 100

0.18\times 100=18

\text { Percent change }=18 \%

The percent decrease is about 18 \%.

Example 6: percent increase after a percent change

The cost of a cup of coffee has increased from \$ 2.75 to \$ 3.50. Find the percent increase in cost of a cup of coffee.

The cost of a cup of coffee has changed from \$ 2.75 to \$ 3.50. You will subtract the old cost from the new cost.

\$ 3.50-\$ 2.75=\$ 0.75

Apply the percent change formula. The amount of increase is \$ 0.75 and the original price is \$ 2.75. Plug the numbers into the following formula:

\begin{aligned}& \text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100 \\\\ & \text { Percent change }=\cfrac{0.75}{2.75} \times 100\end{aligned}

\cfrac{0.75}{2.75} can be simplified to \cfrac{3}{11}.

\text{ Percent change }=\cfrac{3}{11} \times 100

\cfrac{3}{11}=0.2727...

You can round this decimal number to 0.27 to solve.

\text { Percent change }=0.27 \times 100

0.27\times 100=27

\text { Percent change }=27 \%

The percent increase is about 27 \%.

Teaching tips for percent increase and decrease

• Microsoft Excel provides a way to calculate percent change. Students who possess Excel proficiency can further enhance their understanding of percent change by exploring this additional teaching aspect.
• There are times when the figures used to calculate percent change can be large. To help them with calculating, students can use calculators or percentage change calculators.

Easy mistakes to make

• Believing that percents cannot exceed \textbf{100\%} Percent increase or decrease can be greater than 100 \%. It simply means that the value has more than doubled (in case of an increase) or more than halved (in case of a decrease).
• Incorrectly converting percentages to decimals The most common mistakes are with single digit percentages (for example, 7 \% ), multiples of 10 (for example, 50 \% ) and decimal percentages (for example 4.5 \% ). Remember to divide the percentage by 100 to find the decimal. For example, 7 \%=0.07,\, 50 \%=0.5, \, 4.5 \%=0.045.
• Using an incorrect value for the denominator in the percentage increase formula Use the new number instead of the original value for the denominator when calculating percent increase.

Related percent lessons

• Percent of a number
• Percent decrease
• Percent increase
• Percent change
• Simple interest
• Percent error
• Exponential decay
• Compound interest formula

Percent increase and decrease practice questions

1. Increase \$ 450 by 25 \%.

First, calculate 25 \% of \$ 450.

\begin{aligned}& 10 \% \text { of } 450=45 \\\\ & 20 \% \text { of } 450=90 \\\\ & 25 \% \text { of } 450=112.5\end{aligned}

Because you are calculating a percent increase, add 112.5 on to the original value of 450.

450+112.5=562.5

Remember when representing money, there should be two decimal places.

The final answer is \$ 562.50.

2. Decrease 120 \, m by 60 \%.

First, you will need to calculate 60 \% of 120 \, m.

10 \% of 120 \, m = 12 \, m

12 \times 6=72

60 \% of 120 \, m = 72 \, m

Then you will subtract 72 \, m from the original value.

120-72=48 \mathrm{m}

A 60 \% decrease of 120 \, m is 48 \, m.

3. Use a percent as a decimal to increase 43 by   21 \%.

Add the percentage you are increasing by, 21 \%, and 100.

100+21 =121

Next, you will convert the percentage to a decimal by dividing.

121 \div 100=1.21

Then multiply the original amount by the decimal.

43 \times 1.21=52.03

43 increased by 21 \% is 52.03.

4. Use a percent as a decimal to decrease \$ 800 by 30 \%.

This is a 30 percent decrease so start by subtracting 30 \% from 100 \%.

100 \%-30 \%=70 \%

Next, to convert a percent to a decimal, you divide the percent by 100.

70 \div 100=0.70

70 \% = 0.70

Then, you will multiply the original number , \$ 800, by the decimal.

800 \times 0.70=\$ 560.00

\$ 800 decreased by 30 \% is \$ 560.00.

5. Find the percent increase when 300 \, ml is increased to 560 \, ml.

First, you will calculate the change from 300 \, ml to 560 \, ml.

560-300=260

The change is 260 \, ml, so you can now plug the numbers into the percent change formula.

\text { Percent change }=\cfrac{260}{300} \times 100

After simplifying the fraction to \cfrac{13}{15}, you would convert it to the decimal 0.87.

\begin{aligned}& 0.87 \times 100=87 \\\\ & \text { Percentage increase }=87 \%\end{aligned}

6. Find the percent decrease when 725 \, kg is decreased to 575 \, kg.

Start by finding the amount of change by subtracting the original number from the new number.

The value has changed from 725 \, kg to 575 \, kg.

725-575=150 \mathrm{~kg}

Next, plug numbers into the percent change formula. The change is 150 \, kg and the original amount is 725 \, kg.

\begin{aligned}& \text { Percent change }=\cfrac{\text { Change }}{\text { Original }} \times 100 \\\\ &\text { Percent change }=\cfrac{150}{725} \times 100\end{aligned}

If the fraction can be simplified, do that next.

\cfrac{150}{725} can be simplified to \cfrac{6}{29}.

\text { Percent change }=\cfrac{6}{29} \times 100

Then you will convert the fraction to a decimal.

\begin{aligned}& \cfrac{6}{29}=0.21 \\\\ & \text { Percent change }=0.21 \times 100\end{aligned}

Then you will calculate the percent change.

0.21 \times 100=21

\text { Percent change }=21 \%

The percent change is a 21 \% decrease.

Percent increase and decrease FAQs

No, percent increase or decrease cannot be a negative value. The negative sign is used to indicate the direction of change (increase or decrease), but the percent itself is always a positive value.

A positive percent increase indicates growth or expansion, while a percent decrease represents a reduction or contraction. For example, a 20 \% increase means the value has grown by 20 \%, whereas a 10 \% decrease means the value has decreased by 10 \%.

The next lessons are

• Compound measures
• Converting fractions decimals and percentages

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Percentage Increase and Decrease Worksheets

Welcome to our Percentage Increase and Decrease Worksheets page. In this area, we have a selection of worksheets involving finding percentage increases and decreases and working out percentage change.

There are also links to our handy Percentage Increase Calculator and also our How to Find Percentage Change support page to help you with these skills.

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We have a wide range of worksheets on this page to help you learn and practice working with percentage increases and decreases.

Before you learn about percentage increases and decreases, you need to know how to find the percentage of a number.

The worksheets available on this page include:

• finding the final amount after a percentage increase or decrease;
• finding the percentage change between two different amounts;
• solving percentage increase and decrease word problems.
• solving percentage change word problems

Quicklinks to ...

• How to find the Percentage Increase and Decrease
• Percentage Increase Calculator
• Percentage Increase and Decrease Examples
• Percentage Change Worksheets
• Percentage Increase, Decrease and Change Worksheets
• More related Math resources

Find the Percentage Increase and Decrease Online Quiz

How to find the percentage change.

The percentage change is when we know the initial value and the final value and we need to find the percentage increase or decrease.

We have created a support page to help you understand how to find the percentage change.

There are some worked examples and clear step-by-step instructions on this page.

• How to Calculate Percentage Change

How to Find the Percentage Increase & Decrease

If we know the initial amount, and we need to find the final amount after a percentage increase or decrease, we just need to follow these two simple steps:

• Step 1) Work out the percentage of the original amount.
• Step 2a) If it is a percentage increase , then add this amount to the original amount.
• Step 2b) If it is a percentage decrease , then subtract this amount from the original amount.

We have now found our final amount after the percentage increase or decrease.

Percentage Increase and Decrease Worked Examples

Example 1) a laptop usually costs $750. it is reduced by 15% in a sale. what is the sale price.

Step 1) Work out the percentage.

15% of $750 = $112.50

Step 2) Subtract the amount from the original price.

$750 - $112.50 = $637.50

The sale price of the laptop is $637.50.

Example 2) I have $6000 which I leave in a savings account for a year. The interest rate is 3%. How much money will I have at the end of a year?

3% of $6000 = $180

Step 2) Add the amount to the original price.

$6000 + $180 = $6180

At the end of a year, I have $6180.

Example 3) A bag of rice weighs 40 ounces. A larger bag weighs 35% more. How much does the larger bag weigh?

35% of 40 = 14

40 + 14 = 54

The larger bag weighs 54 ounces.

Example 3) An uncut version of a film lasts 150 minutes. The released version lasts 18% less time. How long does the released version last?

18% of 150 = 27

150 - 27 = 123

The released version lasts 123 minutes.

Here you will find a selection of worksheets on percentage increase and decrease.

We have split the worksheets into 3 different sections:

• Set 1) Percentage Increase and Decrease - finding the final amount when a percentage and an initial amount are given;
• Set 2) Percentage Change worksheets - finding the percentage change between an intial amount and a final amount are given;
• Set 3) Percentage Increase / Decrease / Change - finding the final amount after percentage increases and decreases, as well as the percentage change.

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

Set 1) Percentage Increase and Decrease Worksheets

These worksheets involve finding a final amount, when an initial amount and a percentage increase or decrease are given.

• Percentage Increase and Decrease Worksheet 1
• PDF version
• UK Version PDF
• Percentage Increase and Decrease Worksheet 2
• Percentage Increase and Decrease Worksheet 3
• Percentage Increase and Decrease Worksheet 4
• Percentage Increase and Decrease Word Problems 1

Set 2) Percentage Change Worksheets

• Find the Percentage Change Sheet 1
• Find the Percentage Change Sheet 2
• Percentage Change Word Problems Sheet 1
• Percentage Change Word Problems Sheet 2

Set 3) Percentage Increase, Decrease & Change Worksheets

• Percentage Increase, Decrease & Change Sheet 1
• Percentage Increase, Decrease & Change Sheet 2
• Percentage Increase, Decrease & Change Word Problems 1
• Percentage Increase, Decrease & Change Word Problems 2

More Recommended Math Resources

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

This is the calculator to use if you want to find a percentage increase or decrease.

There are two different calculators on the page:

• one calculator will work out the percentage change given an initial and final amount;
• the other calculator will find the final amount given a percentage increase (or decrease) and an initial amount.

The calculator will not just find the answer for you, but also show you the working out for each step.

Reverse Percentage Calculator

Sometimes you are told what the percentage increase/decrease is, and you are also told the final number.

Your task is then to find the original number before the percentage increase or decrease.

Our reverse percentage calculator will help you to find the original number.

• Reverse Percentages Calculator

Percentage Word Problems

The sheets in this area are at a harder level than those on this page.

The problems involve finding the percentage of numbers and amounts, as well as finding the amounts when the percentage is given.

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

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 of Number Worksheets

If you would like some practice finding the percentage of a range of numbers, then try our Percentage Worksheets page.

You will find a range of worksheets starting with finding simple percentages such as 1%, 10% and 50% to finding much trickier ones.

• Percentage of Numbers Worksheets

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

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Percentage Increase and Decrease Word Problems

• To find 10%, divide a number by 10.
• The original mass of chocolate is 200 grams.
• 200 ÷ 10 = 10 and so 10% of 200 grams in 20 grams.
• To increase an amount by 10%, add 10% to the original amount.
• 200 + 20 = 220. Therefore the new mass is 220 grams

• To find 40%, first find 10% and then multiply it by 4.
• 10% is found by dividing the number by 10. £50 ÷ 10 = £5 and so, 10% is £5.
• We multiply 10% by 4 to get 40%. £5 × 4 = £20 and so, 40% is £20.
• In a sale, the price is decreased.
• To decrease by a percentage, subtract the percentage from the original number.
• £50 – £20 = £30 and so, the new price is £30.

• Percentages of Amounts

Percentage Change Word Problems

How to work out percentage change.

• Work out the percentage by dividing the original number by 100 and multiplying by the percentage.
• For a percentage increase, add this percentage to the original number.
• For a percentage decrease, subtract this percentage from the original number.

• To find 1%, divide by 100.
• To find 5%, divide by 20.
• To find 10%, divide by 10.
• To find 20%, divide by 5.
• To find 25%, divide by 4.
• To find 50%, divide by 2.

Percentage Increase Word Problems

Percentage Decrease Word Problems

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Percentage Increase and Decrease

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The following math revision questions are provided in support of the math tutorial on Percentage Increase and Decrease. In addition to this tutorial, we also provide revision notes, a video tutorial, revision questions on this page (which allow you to check your understanding of the topic) and calculators which provide full, step by step calculations for each of the formula in the Percentage Increase and Decrease tutorials. The Percentage Increase and Decrease calculators are particularly useful for ensuring your stet-by-step calculations are correct as well as ensuring your final result is accurate.

Not sure on some or part of the Percentage Increase and Decrease questions? Review the tutorials and learning material for Percentage Increase and Decrease

Percentage Increase and Decrease Revision Questions

1. . A boy is 160 cm tall now but three years ago, he was 148 cm tall. What is the percentage increase of his height in the last three years expressed to one decimal place?

Reveal Answer Correct Answer: B

2. . An item that previously cost $30 became $24 after a discount. What is the percentage decrease of the item's price?

Reveal Answer Correct Answer: C

3. . An employee now earns $3,200 in a month after a 2% tax cut approved by the government. What was his previous salary before the tax cut?

Reveal Answer Correct Answer: D

4. . The GDP (gross domestic product) per capita (for person) of a country decreased by 3% during 2021 because of the negative impact Covid-19 had on employment. The actual GDP per capita of the given country is $16,328. What was the GDP per capita in the previous year?

Reveal Answer Correct Answer: A

5. . The price of an item was $300 initially. The owner raised the price by 10% but since the item could not be sold, he lowered the price by 10%. What is the actual price of the item?

6. . A mobile phone that previously cost $460 now costs $390. What is the percentage decrease of the mobile phone's price?

7. . A political party won 36.39% of popular votes in the last election, experiencing a percentage increase of 2.49% compared to previous elections. By what percentage did the given party win in the previous elections?

8. . The population of a city is 320,054 inhabitants where 137,427 are of Caucasian origin, 86,248 people are Hispanic and the origin of the rest of the population is unspecified. Which of the following percentage distributions is correct?

• Caucasian = 26.95%; Hispanic = 62.76%; Other = 10.21%
• Caucasian = 20.21%; Hispanic = 62.76%; Other = 16.95%
• Caucasian = 42.94%; Hispanic = 26.95%; Other = 69.89%
• Caucasian = 42.94%; Hispanic = 26.95%; Other = 30.11%

9. . 78 out of 200 passengers in an airplane speak English, 57 passengers speak French and the rest speak other languages. What is the percentage of distribution of these three categories?

• English speakers = 34%; French = 28.5%; Other = 65.0%
• English speakers = 34%; French = 28.5%; Other = 62.5%
• English speakers = 34%; French = 28.5%; Other = 37.5%
• English speakers = 78%; French = 14.25%; Other = 37.5%

10. . The price of an item that originally cost $40 dropped by 25% and then it increased again by 25%. What is the final price of the item?

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• Practice Questions Feedback. Helps other - Leave a rating for this practice questions (see below)
• Percentages Math tutorial: Percentage Increase and Decrease . Read the Percentage Increase and Decrease math tutorial and build your math knowledge of Percentages
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• Check your calculations for Percentages questions with our excellent Percentages calculators which contain full equations and calculations clearly displayed line by line. See the Percentages Calculators by iCalculator™ below.
• Continuing learning percentages - read our next math tutorial: Applications of Percentage in Banking. Simple and Compound Interest

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Percentages Calculators by iCalculator™

• Percentage Change Calculator
• Compound Percentage Change Calculator
• Ratio To Percentage Calculator
• Which Ratio Or Percentage Is Bigger
• Which Fraction Or Percentage Is Bigger
• Percentage To Ratio Calculator
• Percentage Difference Calculator
• Percentage Calculator
• Percent Error Calculator

Problems involving percent increase and decrease

Want more practice with percents and related concepts?

• Changing Decimals to Percents
• Changing Percents to Decimals
• Writing Expressions Involving Percent Increase and Decrease
• Calculating Percent Increase and Decrease
• More Problems Involving Percent Increase and Decrease

Here, you will practice solving problems involving percent increase and decrease. You may use a calculator for these exercises.

Why? To increase any amount by $\,19\%\,,$ just multiply by $\,1.19\,$:

Notice that when you increase , you multiply by a number greater than $\,1\,.$

If you decrease any amount by $\,30\%\,,$ then $\,70\%\,$ remains:

Thus, to decrease any amount by $\,30\%\,,$ just multiply by $\,0.7\,.$ Notice that when you decrease , you multiply by a number less than $\,1\,.$

Combining these ideas:

What if we switch the order of applying the increase/decrease?

Same result! Since $\,(1.19)(0.7) = (0.7)(1.19)\,,$ you can do the multiplication in whatever order you prefer.

In this exercise, all answers are rounded to two decimal places.

Concept Practice

All answers are rounded to two decimal places.

PERCENTAGE INCREASE AND DECREASE WORD PROBLEMS

Formula to find percentage increase/decrease

Problem 1 :

The price of a TV is $260. In a sale the price is decreased by 20%. Work out the price of the TV sale.

Price of the TV = $260

It is given that the price of the TV is decreased by 20%.

Then, the selling price of the TV :

= 80% of 260

= 0.80(260)

Problem 2 :

The value of a painting rises from $120000 to $192000. Work out the percentage increase in the value of painting.

Original price of the painting = $120000

After increase, the new price = $192000.

Price increase = 192000 - 120000

Percentage increase :

= ⁷²⁰⁰⁰⁄₁₂₀₀₀₀   ⋅ 100%

=  ⅗   ⋅ 10 0%

The value of the paiting is increased by 60%.

Problem 3 :

A puppy weighed 2 kg. Eight weeks later the puppy weighed 3.5 kg. What was the percentage increase in the Puppy's weight?

Weight of puppy = 2 kg.

Puppy's weight after eight weeks = 3.5 kg.

Increase in weight in eight weeks :

= (1.5/2) ⋅ 100% 

= 0.75 ⋅ 100%

Puppy's weight was increased by 75%.

Problem 4 :

Peter's weight decreases from 80 kg. to 64 kg. Calculate the percentage decrease in Peter's weight.

Old weight = 80 kg.

New weight = 64 kg.

Decrease in weight :

Percentage decrease :

=  ¹⁶⁄₈₀   ⋅ 100%

=  ⅕   ⋅ 100%

Peter has reduced 20% of his weight.

Problem 5 :

Alice buys a book for $19.80 A year later she sells the book for $12.87 Calculate the percentage decrease in the value of the book.

Cost price of the book = $19.80

Selling price = $12.87

Decrease in the price :

= 19.80 - 12.87

= (6.93/19.80) ⋅ 100%

The value of the book is decaresed by 35%.

Problem 6 :

The volume of juice in a can is increased from 250 ml. to 330 ml. Work out the percentage increase.

Original volume of juice in a can = 250 ml.

Volume of juice in can after increase = 330 ml.

Increase in volume :

= 330 - 250

= ⁸⁰⁄₂₅₀   ⋅ 100%

=  ⁸⁄₂₅ ⋅ 100%

Volume of juice in can is increased by 32%.

Problem 7 :

Sarah bought a TV for $250. Three years later she sold it for $180. Work out her percentage loss.

Cost price of the TV = $250

Selling price = $180

Cost price > Selling price ----> Loss

Loss = Cost price - Selling price

= 250 - 180

Percentage loss :

= ⁷⁰⁄₂₅₀   ⋅ 100%

= ⁷⁄₂₅  ⋅ 100%

= 7  ⋅ 4%

Problem 8 :

A car is travelling at 40 kilometers per hour. The car increases its speed to 56 kilometers per hour. Calculate the percentage increase in the speed of the car.

Initial speed of car = 40 km. per hour

Increased speed = 56 km. per hour

Increase in speed :

= 16 km. per hour

Percentage increase in speed of the car :

= ¹⁶⁄₄₀   ⋅ 100%

= ⅖  ⋅ 100%

Problem 9 :

Susan buys an antique for $120 and sells it for $216. Work out her percentage profit.

Cost price of an item = $120

Selling price of an item = $216

Selling price > Cost price ----> Profit

Profit  = Sleeing price - Cost price

= 216 - 120

Percentage profit :

= ⁹⁶⁄₁₂₀   ⋅ 100%

=  ⅘  ⋅ 100%

Problem 10 :

Holly bought a table for $80 She sold the table for $108 Find the percentage profit

Cost price = $80

Selling price = $108

Profit = Selling price - Cost price

=  ²⁸⁄₈₀ ⋅ 100%

=  ⁷⁄₂₀ ⋅ 100%

= 7 ⋅ 5%  

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For an explanation and everyday examples of using percentages generally see our page Percentages: An Introduction . For more general percentage calculations see our page Percentage Calculators .

To calculate the percentage increase:

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number

Then:   divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100 .

If your answer is a negative number, then this is a percentage decrease.

To calculate percentage decrease:

First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

If your answer is a negative number, then this is a percentage increase.

If you wish to calculate the percentage increase or decrease of several numbers then we recommend using the first formula. Positive values indicate a percentage increase whereas negative values indicate percentage decrease.

Percentage Change Calculator

More: Percentage Calculators

Further Reading from Skills You Need

The Skills You Need Guide to Numeracy

This four-part guide takes you through the basics of numeracy from arithmetic to algebra, with stops in between at fractions, decimals, geometry and statistics.

Whether you want to brush up on your basics, or help your children with their learning, this is the book for you.

Examples - Percentage Increase and Decrease

In January Dylan worked a total of 35 hours, in February he worked 45.5 hours – by what percentage did Dylan’s working hours increase in February?

To tackle this problem first we calculate the difference in hours between the new and old numbers.  45.5 - 35 hours = 10.5 hours.  We can see that Dylan worked 10.5 hours more in February than he did in January – this is his increase .  To work out the increase as a percentage it is now necessary to divide the increase by the original (January) number:

10.5 ÷ 35 = 0.3  (See our division page for instruction and examples of division.)

Finally, to get the percentage we multiply the answer by 100.  This simply means moving the decimal place two columns to the right.

0.3 × 100 = 30

Dylan therefore worked 30% more hours in February than he did in January.

In March Dylan worked 35 hours again – the same as he did in January (or 100% of his January hours).  What is the percentage difference between Dylan’s February hours (45.5) and his March hours (35)? 

First calculate the decrease in hours, that is: 45.5 - 35 = 10.5

Then divide the decrease by the original number (February hours) so:

10.5 ÷ 45.5 = 0.23 (to two decimal places).

Finally multiply 0.23 by 100 to give 23%.  Dylan’s hours were 23% lower in March than in February.

You may have thought that because there was a 30% increase between Dylan’s January hours (35) and February (45.5) hours, that there would also be a 30% decrease between his February and March hours. As you can see, this assumption is incorrect.

The reason is because our original number is different in each case (35 in the first example and 45.5 in the second). This highlights how important it is to make sure you are calculating the percentage from the correct starting point.

Sometimes it is easier to show percentage decrease as a negative number – to do this follow the formula above to calculate percentage increase – your answer will be a negative number if there was a decrease.  In Dylan’s case the increase in hours between February and March is -10.5 (negative because it is a decrease). Therefore   -10.5 ÷ 45.5 = -0.23.  -0.23 × 100 = -23%.

Dylan's hours could be displayed in a data table as:

Calculating Values Based on Percentage Change

Sometimes it is useful to be able to calculate actual values based on the percentage increase or decrease.  It is common to see examples of when this could be useful in the media.

You may see headlines like:

UK rainfall was 23% above average this summer. Unemployment figures show a 2% decline. Bankers ’ bonuses slashed by 45%.

These headlines give an idea of a trend – where something is increasing or decreasing, but often no actual data.

Without data, percentage change figures can be misleading.

Ceredigion, a county in West Wales, has a very low violent crime rate.

Police reports for Ceredigion in 2011 showed a 100% increase in violent crime. This is a startling number, especially for those living in or thinking about moving to Ceredigion.

However, when the underlying data is examined it shows that in 2010 one violent crime was reported in Ceredigion. So an increase of 100% in 2011 meant that two violent crimes were reported.

When faced with the actual figures, perception of the amount of violent crime in Ceredigion changes significantly.

In order to work out how much something has increased or decreased in real terms we need some actual data.

Take the example of “ UK rainfall this summer was 23% above average ” – we can tell immediately that the UK experienced almost a quarter (25%) more rainfall than average over the summer. However, without knowing either what the average rainfall is or how much rain fell over the period in question we cannot work out how much rain actually fell.

Calculating the actual rainfall for the period if the average rainfall is known.

If we know the average rainfall is 250mm, we can work out the rainfall for the period by calculating 250 + 23%.

First work out 1% of 250, 250 ÷ 100 = 2.5. Then multiply the answer by 23, because there was a 23% increase in rainfall.

2.5 × 23 = 57.5.

Total rainfall for the period in question was therefore 250 + 57.5 = 307.5mm.

Calculating the average rainfall if the actual amount is known.

If the news report states the new measurement and a percentage increase, “ UK rainfall was 23% above average... 320mm of rain fell… ”.

In this example we know the total rainfall was 320mm. We also know that this is 23% above the average.  In other words, 320mm equates to 123% (or 1.23 times) of the average rainfall. To calculate the average we divide the total (320) by 1.23.

320 ÷ 1.23 = 260.1626.  Rounded to one decimal place, the average rainfall is 260.2mm .

The difference between the average and the actual rainfall can now be calculated: 320 - 260.2 = 59.8mm .

We can conclude that 59.8mm is 23% of the average rainfall amount (260.2mm), and that in real terms, 59.8mm more rain fell than average.

Continue to: Percentages Percentage Calculators Averages (Mean, Median and Mode)

See also: Fractions | Calculating Area | Polygons Employability Skills | Transferable Skills

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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Class 7 (Old)

Course: class 7 (old)   >   unit 7.

• Percent word problem: penguins
• Percent word problems
• Percent word problem: magic club

Percentage change word problems

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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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

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

Percentage Increase and Decrease - Question Page

• Math Article
• Percentage Increase Decrease

Percentage Increase Or Decrease

Percentage means ‘per 100’, which is a number expressed as a fraction of 100. So when you say 100% of something, it means it represents the whole of it. The percentage is used to compare quantities. Let us say you are required to find the increase or decrease in the value of a certain quantity over a while; instead of quoting the numbers, this comparison can be conveniently expressed as a percentage increase or a percentage decrease in quantity.

Also Check: How to Calculate Percentage

Percentage Increase

When comparing the increase in a quantity over a period of time, we first find the difference between the original value and the increased value. We then use this difference to find the relative increase against the original value and express it in terms of percentage. The formula for percentage increase is given by:

Percentage Decrease

When comparing the decrease in a quantity over a period of time, we first find the difference between the original value and the decreased value. We then use this difference to find the relative decrease against the original value and express it in the form of a percentage. The formula for percentage decrease is given by:

Percentage Increase or Decrease Examples

The annual salary of Suresh increased from Rs 18,00,000 to Rs 22,00,000. Find the percentage increase.

Solution : Original salary = Rs 18,00,000

Increased salary = Rs 22,00,000

Increase in salary = Rs 22,00,000 – Rs 18,00,000 = Rs 4,00,000

Thus, percentage increase in salary = (increase in salary/original salary) x 100

= (4,00,000/18,00,000) x 100 = 22.22%

The population of a small town decreased from 18,560 to 15,787 due to breakout of an epidemic. What is the percentage decrease in the population?

Solution : Original population = 18,560

Decreased population = 15,787

Decrease in population = 18,560 – 15,787 = 2773

Percentage decrease in population = (Decrease in population/ Original population) x 100

= ( 2773/18560) x 100 = 14.94%

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