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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.
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
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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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How to Solve Percent Problems? (+FREE Worksheet!)
Learn how to calculate and solve percent problems using the percent formula.
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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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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:
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte48.jpg)
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:
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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.
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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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte51.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte52.jpg)
b. Simplify the equation.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte53.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte54.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte55.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte56.jpg)
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.)
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte57.jpg)
Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte58.jpg)
Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte59.jpg)
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)
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte60.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte61.jpg)
Simplifying Algebraic Equations:
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte62.jpg)
Combine like terms:
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte63.jpg)
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 )
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte64.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte65.jpg)
c. If the call costs $23.50, how long were you on the phone?
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte67.jpg)
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.
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte68.jpg)
Percentages:
Write percentages as decimals.
Example 11. An English teacher computes his grades as follows:
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte69.jpg)
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?
![problem solving of percentage problem solving of percentage](https://quickmath.com/images/artimages/b2c1/chapte70.jpg)
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
More solvers.
- Add Fractions
- Simplify Fractions
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 problems with percentages
- Price difference I
- Price difference II
- How many students?
To solve problems with percent we use the percent proportion shown in "Proportions and percent".
$$\frac{a}{b}=\frac{x}{100}$$
$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$
$$a=\frac{x}{100}\cdot b$$
x/100 is called the rate.
$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$
Where the base is the original value and the percentage is the new value.
47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?
$$a=r\cdot b$$
$$47\%=0.47a$$
$$=0.47\cdot 34$$
$$a=15.98\approx 16$$
16 of the students wear either glasses or contacts.
We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.
The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?
We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.
$$240-150=90$$
Then we find out how many percent this change corresponds to when compared to the original number of students
$$90=r\cdot 150$$
$$\frac{90}{150}=r$$
$$0.6=r= 60\%$$
We begin by finding the ratio between the old value (the original value) and the new value
$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$
As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.
$$1.6-1=0.6$$
$$0.6=60\%$$
As you can see both methods gave us the same answer which is that the student body has increased by 60%
Video lessons
A skirt cost $35 regulary in a shop. At a sale the price of the skirtreduces with 30%. How much will the skirt cost after the discount?
Solve "54 is 25% of what number?"
- Pre-Algebra
- The mean, the median and the mode
- Stem-and-Leaf Plots and Box-and-Whiskers Plot
- Calculating the outcome
- Combinations and permutations
- Finding the odds
- Probability of events
- Geometry – fundamental statements
- Circle graphs
- Angles and parallel lines
- Quadrilaterals, polygons and transformations
- Measure areas
- Pyramids, prisms, cylinders and cones
- Square roots and real numbers
- The Pythagorean Theorem
- Trigonometry
- Algebra 1 Overview
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- SAT Overview
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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
![problem solving of percentage Calculating the Percent Rate of Whole Number Amounts and All Percents](https://math-drills.com/percentsworksheets/images/percents_calculate_rate_allpercents_regular_wholenumbers_001_300.1675735328.jpg)
Percentage Calculations
![problem solving of percentage](https://www.math-drills.com/percentsworksheets/images/percents_calculate_part_allpercents_regular_wholenumbers_001_300.004.jpg)
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
![problem solving of percentage](https://www.math-drills.com/percentsworksheets/images/percents_increase_decrease_whole_allpercents_001_300.004.jpg)
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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![problem solving of percentage GCSE Maths](https://thirdspacelearning.com/wp-content/uploads/2021/02/Component-15.png)
Percentages
Here is everything you need to know about percentages for GCSE maths (Edexcel, AQA and OCR). You’ll learn how to find the percentage of an amount and calculate with percentage multipliers.
You will also work out how to increase and decrease a number by a percentage, percentage change and reverse percentages.
Look out for the percentages worksheets and exam questions at the end.
What are percentages?
A percentage is a number which is expressed as a fraction of 100 .
Percent means “number of parts per hundred” and the symbol we use for percent is the percent sign % .
![problem solving of percentage What are percentages?](https://thirdspacelearning.com/wp-content/uploads/2022/05/Percentages-what-is-card.png)
There are different types of percentage questions.
- Percentage of an amount
This is where we are asked to find a certain percentage of an amount.
E.g. Find 25% of £32 .
This is the same as finding a ¼ of £32 .
The answer is £8
Step-by-step guide: Percentage of an amount
- Percentage conversions
Percentages, fractions and decimals can all be used to represent part of a whole.
For example,
![problem solving of percentage](https://thirdspacelearning.com/wp-content/uploads/2022/04/Percentage-conversions-paragraph-image-300x184.png)
It is useful to be able to convert between percentages, fractions and decimals.
To change a percentage into a fraction, write the percentage number as the numerator of a fraction and 100 as the denominator, and then simplify the resulting fraction if possible.
To change a fraction into a percentage, there are two methods.
First see if it is possible to write an equivalent fraction with a denominator of 100; then the numerator will be the percentage.
Eg. \frac{7}{20} = \frac{7\times5}{20\times5}=\frac{35}{100}=35\%
A second method is to carry out the division represented in the fraction and then multiply by 100.
To change a percentage into a decimal , divide the percentage number by 100.
73\% = 73 \div 100 = 0.73
To change a decimal into a percentage , multiply the decimal by 100.
- Percentage multipliers
This is where we can find a decimal number and use it as a multiplier to make calculating percentages more efficient.
E.g. Find 41% of £800 .
We can use 0.41 as a multiplier to find the amount needed.
The answer is £328
Step-by-step guide: Percentage multipliers
- Percentage as operator
In order to calculate a percentage of an amount, a percentage increase or a percentage decrease we can use a percentage multiplier. To do this we change the percentage that we want into a decimal, and then multiply the amount by that decimal to calculate the answer.
34% of 58.
Here we want 34% which as a decimal is 0.34
Therefore the calculation is
Increase 78 by 15%
Here we want an increase of 15% which means in total we want 115% , which as a decimal is 1.15
Decrease 45 by 20%
Here we want a decrease of 20% which means in total we want 80% , which as a decimal is 0.8
Therefore the calculation is 45 \times 0.8 = 36
- Percentage increase
This is where we are asked to increase (make bigger) a value by a certain amount.
E.g. Increase 40g by 10% .
We can find 10% and add it on.
10% of 40 is 4
The answer is 44g
Step-by-step guide: Percentage increase
- Percentage decrease
This is where we are asked to decrease (make smaller) a value by a certain amount.
E.g. Decrease 60kg by 10% .
We can find 10% and subtract it.
10% of 60 is 6
The answer is 54kg
Step-by-step guide: Percentage decrease
- Percentage change
When values change, we can express this change as a percentage of the original value.
E.g. Work out the percentage change of 26kg from 25kg .
The actual change from 25 to 26 is 1 .
The answer is 4%
Step-by-step guide: Percentage change
- Reverse percentages
This is where we are given a certain percentage of a number and we have to find the original number.
E.g. 20% of a number is 6 , what is the number?
To find the original number we need to find 100% or one whole.
The answer is 30
Step-by-step guide: Reverse percentages
- Percentage calculations
Let’s look at different methods that can be used to perform percentage calculations.
What is 40% of 70?
Method 1: The one percent method
Find 1% first by dividing the amount by 100 and then multiply the amount by the percent you want.
Method 2: The decimal multiplier method
Write the percent you want as a decimal and then multiply the amount by this decimal.
Method 3: Using equivalent fractions
Write the percent you want as a fraction in simplest form and then multiply the amount by this fraction.
Method 4: Building up an answer from simple percentages you know
Using simple percentages you can “
build up the answer to the question.
For this question if you know 10% of 70 then you can multiply this answer by 4 to find 40%.
Note, methods 1 and 2 lend themselves best to questions where you are allowed to use a calculator. Methods 3 and 4 are most helpful when calculators are not permitted.
See also: One number as a percentage of another
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What are the 6 different types of percentage questions?
![problem solving of percentage What are the 6 different types of percentage questions?](https://thirdspacelearning.com/wp-content/uploads/2021/05/Percentages-How-to-card.png)
How to work out percentage worksheet
Get your free how to work out percentages worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Equation to percentage
We could be asked to solve problems where we need to form and solve equations to find answers as percentages. We often see this when dealing with interest and depreciation calculations.
A car purchased for £36000 depreciates by x% each year. If after 3 years, the car has a value of £15187.50, what percentage does the car depreciate by annually?
If we were solving this as a depreciation question with the percentage value known and the car value unknown we would use the calculation
We need to work backwards to find the multiplier. Essentially solving the equation, for ease let’s call the multiplier, x.
The depreciation multiplier used for this calculation was 0.75, this tells us that the final car value of £15187.50 was 75% of its original value. 100% – 75% = 25%, so the value of the car depreciated by 25% each year.
Step-by-step guide: Percentage profit
How to find the percentage
![problem solving of percentage How to find the percentage](https://thirdspacelearning.com/wp-content/uploads/2022/05/Percentages-how-to-card.png)
Percentages examples
Example 1: percentage of an amount.
Find 23% of £160 .
Write down what you have and what you are trying to find.
100% is £160 .
We need to work out 23% of £160 .
2 Work out what you need.
3 Write down the final answer .
23% of £160 is £36.80
Example 2: percentage multipliers
Find 39% of £4700
100% is £4700
We want to find 39% of £4700
Work out what you need .
We can write the percentage as a decimal number.
This gives the percentage in decimal form which is the percentage multiplier.
Write down the final answer .
39% of £4700 is £1833
Example 3: percentage increase
Increase £200 by 30%
100% is £200
We want to find 130% of £200
You could also use the decimal multiplier.
£200 increased by 30% is £260
Example 4: percentage decrease
Decrease 700g by 20%
100% is 700 g
We want to find 80% of 700 g
You could use the decimal multiplier.
700g decreased by 20% is 560 g.
Example 5: percentage change
The price of a t-shirt increased from £10 to £12 . Work out the percentage change.
The original amount is £10 .
We need to find the change as a percentage of the original amount.
The actual change is
The actual change written as a fraction of the original is
The actual change is the numerator (top number). The original number is the denominator (bottom number).
Convert the fraction to an equivalent fraction where the denominator is 100 .
Write the actual change as a fraction of the original amount and multiply by 100 .
The percentage change of £12 from £10 is 20%
Example 6: reverse percentages
The price of a coat is £40 after a 20% price cut. Find the original price.
£40 represents 80% of the original price.
So 80% = £40
We need the original price which is 100% .
We can work out 10%
Then we can work out 100%
We can make an equation using x as the original number. Use the decimal multiplier and the new number.
The price after the cut is £40 . The original price was £50
Common misconceptions
- Money needs two digits for the pence
E.g. Find 34% of £620
The answer is £210.80
- The decimal multiplier to work out a percentage increase can be greater than 1
E.g. To increase 50km by 3% we can work 103% of 50
The answer is 51.5 km
- Percentages can be greater than 100%
E.g. Calculate the percentage change from 200 to 450.
The actual change is 450-200=250
So the percentage change from 200 to 450 is 125%
How to work out percentage practice questions
1. Find 40\% of \pounds 300 .
![problem solving of percentage GCSE Quiz False](https://thirdspacelearning.com/wp-content/uploads/2021/05/cancel.png)
10\% of \pounds 300 is \pounds 30 . We can multiply this by 4 to get 40\% .
2. Calculate 12.4\% of \pounds 3000 .
As a multiplier, 12.4\% is 0.124 . To get the answer we can calculate 0.124\times3000
3. Increase 600m by 30\% .
30\% of 600 is 180 . We can add this on to the original amount to find the quantity after the increase.
4. Decrease 80 kg by 5\% .
5\% of 80 is 4 . We can subtract this from the original amount to find the quantity after the decrease.
5. Calculate the percentage change from 400 kg to 600 kg .
The actual increase is given by
The percentage increase is then given by
6. A book costs \pounds 4 after a price reduction of 20\% . What was the original price?
\pounds 4 represents 80\% of the original amount, which means 10\% of the original amount is \pounds 0.50 .
Multiplying by ten to get 100\% means the original price was \pounds 5 .
Percentages GCSE exam questions
1. Work out 90\% of \pounds 70.
10\% is 7 , so 90\% is 9 × 7
(1)
2. Charlotte invests \pounds 3000 for 4 years.
She gets a simple interest rate of 2\% per year.
Work out the total interest Charlotte gets.
3. Last year Ron paid \pounds 450 for his car insurance.
This year he has to pay \pounds 603 for his car insurance.
Work out the percentage increase in his car insurance.
The change is
Learning checklist
You have now learned how to:
- How to work out the percentage of a number
- How to calculate percentage change
- How to work out a percentage increase or decrease
The next lessons are
- Simple interest
- Compound interest
Still stuck?
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This calculator is a free online math tool that solves eight types of percentage problems . Just input the values into the sentence that best describes the problem involving percentages, and the calculator will generate a step-by-step solution.
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How to solve percentage problems?
This calculator solves eight different types of percenatge problems. We will use some examples to show each type.
Type 1: What is x % of y?
Example: What is 40% of 60?
Step1: Change the word of to multiplication sign.
40% of 60 = 40% * 60
Step2: Change 40% to decimal number by dividing 40% by 100 [40% = 40/100 = 0.4]
40% * 60 = 0.4 * 60 = 24
Type 2: x is what percent of y?
Example: 16 is what percent of 40?
Step1: Translate the words into an equation
Step2: Solve for $ x $
Step3: Multiply x by 100% to convert the result to a percentage.
Type 3: Percentage increase
Example: Mark’s hourly salary is \$15. What is the percentage increase in the salary if it is raised to \$18?
To solve this problem, we apply the percentage increase formula :
After putting the initial amount to 15 and the final amount to 18, we get:
Type 4: Percentage decrease
Example: The workforce at a corporation decreased from 135 to 110 personnel. What is the percentage decrease in the number of employees?
To solve this problem we use percentage decrease formula :
After putting the initial amount to 135 and final amount to 110 we get:
Type 5: What percent of X is Y?
Example: What percent of 80 is 25?
Step3: Express $ x $ as a percentage by multiplying the result by 100%.
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Course: 6th grade > Unit 3
- Percent word problem: recycling cans
Percent word problems
- Rates and percentages FAQ
![problem solving of percentage](https://cdn.kastatic.org/images/google_classroom_color.png)
- 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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COMMENTS
Solution. 20 100 = amount base. The percent in this problem is 20%. Write this percent in fractional form, with 100 as the denominator. 20 100 = 30 n. The percent is written as the ratio 20 100, the amount is 30, and the base is unknown. 20 ⋅ n = 30 ⋅ 100 20 ⋅ n = 3, 000 n = 3, 000 ÷ 20 n = 150.
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.
Percent Problems Percent Problems - Example 1: \(2.5\) is what percent of \(20\)? Solution: In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\) The Absolute Best Books to Ace Pre-Algebra to Algebra II
25% is part of a whole 100%.*. *25% is 1/4 of 100%*. so, you know that (150) is 1/4 of the answer (100%) Add 150 - 4 times (Because we know that 25% X 4 = 100%) And that is equal to: (150 + 150 + 150 + 150) = *600. The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the ...
Percent word problem: recycling cans (Opens a modal) Practice. Percent word problems Get 5 of 7 questions to level up! Quiz 3. Level up on the above skills and collect up to 160 Mastery points Start quiz. Up next for you: Unit test. Level up on all the skills in this unit and collect up to 700 Mastery points!
Percentages (calculator) Click here for Questions. Click here for Answers. Practice Questions. Previous: Foundation Solving Quadratics. Next: Ratio Videos. The Corbettmaths Practice Questions on finding a percentage of an amount.
Calculating a percent value. There are two values that are important for finding a percentage: a part and a whole. To calculate a percentage, use the following formula: % = part whole ⋅ 100. For example, say you took a quiz in math class and got 21 out of the 24 questions correct. We could calculate the percentage of questions you got correct ...
Examples, solutions, and videos that will help GMAT students review how to solve percent word problems. The following diagram shows some examples of solving percent problems using the part, base, rate formula. Scroll down the page for more examples and solutions of solving percent problems. Solving Percent Problems. Show Step-by-step Solutions.
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?
A lot of percent problems turn out to be easy to solve when you give them a little thought. In many cases, just remember the connection between percents and fractions and you're halfway home. ... But an easy way of solving the problem is to switch it around: 88% of 50 = 50% of 88. This move is perfectly valid, and it makes the problem a lot ...
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.
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fr...
Method 1. We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change. 240 − 150 = 90 240 − 150 = 90. Then we find out how many percent this change corresponds to when compared to the original number of students. a = r ⋅ b a = r ⋅ b.
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.
Percent problems. A brand of cereal had 1.2 milligrams ( mg) of iron per serving. Then they changed their recipe so they had 1.8 mg of iron per serving. What was the percent increase in iron? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.
If we were solving this as a depreciation question with the percentage value known and the car value unknown we would use the calculation . 36000 \times \text { multiplier }^{3}=15187.50. We need to work backwards to find the multiplier. Essentially solving the equation, for ease let's call the multiplier, x. 36000 \times x^{3}=15187.50
Percent Proportion. Problems involving the percent equation can also be solved with the proportion: Percent Amount (is) =. 100 Base (of) When the percent is given, drop the percent sign and place the percent over 100. Cross multiply to solve the proportion. Example 2: 27 is 45% of what number?
Type 4: Percentage decrease Example: The workforce at a corporation decreased from 135 to 110 personnel. What is the percentage decrease in the number of employees? Solution: To solve this problem we use percentage decrease formula: $$ \text{% decrease} = \dfrac{ \text{initial amount} - \text{ final amount} }{ \text{ initial amount} } \times 100 $$
Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations. Add or subtract a percentage from a number or solve the equations. How to Calculate Percentages. There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100.
Finding a percent. Discover how to calculate percentages with this simple method. First, write the problem as a fraction, then simplify it. Next, convert the fraction to a percentage by making the denominator 100. Alternatively, divide the numbers to get a decimal and multiply by 100 to find the percentage. Master this skill for everyday use.
Apache Spark and Hadoop, Microsoft Power BI, Jupyter Notebook and Alteryx are among the top data science tools for finding business insights. Compare their features, pros and cons. By Aminu ...
Percent word problems. 2 % of the students at Hamilton Middle School have red hair. There are 700 students at Hamilton Middle School. How many students at Hamilton Middle School have red hair? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.