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## Unit 3: Lesson 3

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## Video transcript

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

· Find the unknown in a percent problem.

The percent of the base is the amount.

Percent of the Base is the Amount.

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

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

n = 30 ÷ 20% = 30 ÷ 0.20 = 150

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

Using Proportions to Solve Percent Problems

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.

1. In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

Therefore, Ashley got 332 marks out of 400 marks.

2. An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?

Let the quantity of alloy required = m g

Number of students absent on a particular day = 14 % of 50

Therefore, the number of students present = 50 - 7 = 43 students.

Let the total number of apples in the basket be m

12 % of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

Therefore, total number of apples in the basket is 75.

The number of students with first division = 28 % of 300

And, the number of students with second division = 54 % of 300

Therefore, the number of students who just passed = 300 – (84 + 162)

Questions and Answers on Word Problems on Percentage:

2. Emma scores 72 marks out of 80 in her English exam. Convert her marks into percent.

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## 5th Grade Percentage Worksheet | Finding Percentages | Answers

## Worksheet on Percentage of a Number | Find the Percent of a Number

## Worksheet on Percent Problems | Questions on Application of Percentage

## To Find the Percent of a Given Number | Word Problem on Percentage

## Convert a Decimal into Percentage | Conversion of Decimal into Percent

## To Convert a Fraction into a Percentage|Converting Fraction to Percent

## To Convert a Percentage into a Fraction | Percentage into a Fraction

## Percentage into Decimal | Percentage as Decimals|Percent into Fraction

## Percentage | Symbol of Percent | Fraction with Denominator 100

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Real Life Problems on Percentage

8th Grade Math Practice From Word Problems on Percentage to HOME PAGE

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## Solving problems with percentages

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

16 of the students wear either glasses or contacts.

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

## Video lessons

Solve "54 is 25% of what number?"

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## Article Categories

## How to Solve Percent Problems

Basic math & pre-algebra all-in-one for dummies (+ chapter quizzes online).

## Sign up for the Dummies Beta Program to try Dummies' newest way to learn.

Solve simple percent problems.

Finding 25% of a number: Remember that 25% equals 1/4, so to find 25% of a number, divide it by 4:

To find 20% of a number, move the decimal point one place to the left and double the result:

## Make tough-looking percent problems easy

Suppose someone wants you to figure out the following:

As another example, suppose you want to find

Again, finding 7% is tricky, but finding 200% is simple, so switch the problem around:

Above, you learned that to find 200% of any number, you just multiply that number by 2:

7% of 200 = 200% of 7 = 2 7 = 14

## Solve more-difficult percent problems

Here’s how to find any percent of any number:

Change the word of to a multiplication sign and the percent to a decimal.

So, to find 35% of 80, you would rewrite it as:

Solve the problem using decimal multiplication.

Here’s what the example looks like:

Now you can solve the problem with decimal multiplication:

## About This Article

This article can be found in the category:.

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- Basic Math and Pre-Algebra All-in-One For Dummies Cheat Sheet
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Enter the value(s) for the required question and click the adjacent Go button.

## PERCENTAGES

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

In algebra problems, percentages are usually written as decimals.

The number of questions correct is indicated by:

Ethan got 44 questions correct.

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

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

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

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

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

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

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

## CHAPTER 1 REVIEW

## Signed Numbers:

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

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

## Introduction to Variables:

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

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

## Simplifying Algebraic Equations:

## Solving Equations:

## Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

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

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

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

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

## Literal Equations:

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

## Percentages:

Write percentages as decimals.

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

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

## Study Tips:

## Math Topics

## Percentage Calculator

## Calculator Use

## How to Calculate Percentages

Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:

Read on to learn more about how to figure percentages.

## 1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y

- Convert the problem to an equation using the percentage formula: P% * X = Y
- P is 10%, X is 150, so the equation is 10% * 150 = Y
- Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
- Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y
- Do the math: 0.10 * 150 = 15
- So 10% of 150 is 15
- Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15

## 2. How to find what percent of X is Y. Use the percentage formula: Y/X = P%

Example: What percent of 60 is 12?

- Convert the problem to an equation using the percentage formula: Y/X = P%
- X is 60, Y is 12, so the equation is 12/60 = P%
- Do the math: 12/60 = 0.20
- Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.
- Converting 0.20 to a percent: 0.20 * 100 = 20%
- So 20% of 60 is 12.
- Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%

## 3. How to find X if P percent of it is Y. Use the percentage formula Y/P% = X

Example: 25 is 20% of what number?

- Convert the problem to an equation using the percentage formula: Y/P% = X
- Y is 25, P% is 20, so the equation is 25/20% = X
- Convert the percentage to a decimal by dividing by 100.
- Converting 20% to a decimal: 20/100 = 0.20
- Substitute 0.20 for 20% in the equation: 25/0.20 = X
- Do the math: 25/0.20 = X
- So 25 is 20% of 125
- Double check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125

## Remember: How to convert a percentage to a decimal

## Remember: How to convert a decimal to a percentage

## Percentage Problems

## What is P percent of X?

- Written as an equation: Y = P% * X
- The 'what' is Y that we want to solve for
- Remember to first convert percentage to decimal, dividing by 100
- Solution: Solve for Y using the percentage formula Y = P% * X

## Example: What is 10% of 25?

- Written using the percentage formula: Y = 10% * 25
- First convert percentage to a decimal 10/100 = 0.1
- Y = 0.1 * 25 = 2.5
- So 10% of 25 is 2.5

## Y is what percent of X?

- Written as an equation: Y = P% ? X
- The 'what' is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X
- Solution: Solve for P% using the percentage formula P% = Y ÷ X

## Example: 12 is what percent of 40?

- Written using the formula: P% = 12 ÷ 40
- P% = 12 ÷ 40 = 0.3
- Convert the decimal to percent
- P% = 0.3 × 100 = 30%
- So 12 is 30% of 40

## Y is P percent of what?

- The 'what' is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X, which is the same as X = Y ÷ P%
- Solution: Solve for X using the percentage formula X = Y ÷ P%

## Example: 9 is 60% of what?

- Writen using the formula: X = 9 ÷ 60%
- Convert percent to decimal
- 60% ÷ 100 = 0.6
- X = 9 ÷ 0.6
- So 9 is 60% of 15

## What percent of X is Y?

## Example: What percent of 27 is 6?

- Written using the formula: P% = 6 ÷ 27
- 6 ÷ 27 = 0.2222
- Convert decimal to percent
- P% = 0.2222 × 100
- P% = 22.22%
- So 22.22% of 27 is 6

## P percent of what is Y?

## Example: 20% of what is 7?

- Written using the formula: X = 7 ÷ 20%
- Convert the percent to a decimal
- 20% ÷ 100 = 0.2
- X = 7 ÷ 0.2
- So 20% of 35 is 7.

## P percent of X is what?

## Y of what is P percent?

- Written as an equation: Y / X = P%
- Multiply both sides by X to get X out of the denominator
- (Y / X) * X = P% * X becomes Y = P% * X
- Divide both sides by P% so that X is on one side of the equation
- Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X

## Example: 4 of what is 12%?

- Written using the formula: X = 4 ÷ 12%
- Solve for X: X = Y ÷ P%
- 12% ÷ 100 = 0.12
- X = 4 ÷ 0.12
- X = 33.3333
- 4 of 33.3333 is 12%

## What of X is P percent?

- Multiply both sides by X to get Y on one side of the equation
- (Y ÷ X) * X = P% * X becomes Y = P% * X

## Example: What of 25 is 11%?

## Y of X is what percent?

## Example: 9 of 13 is what percent?

- Written using the formula: P% = Y / X
- 9 ÷ 13 = P%
- 9 ÷ 13 = 0.6923
- Convert decimal to percent by multiplying by 100
- 0.6923 * 100 = 69.23%
- 9 ÷ 13 = 69.23%
- So 9 of 13 is 69.23%

## Related Calculators

Find the change in percentage as an increase or decrease using the Percentage Change Calculator .

Solve decimal to percentage conversions with our Decimal to Percent Calculator .

Convert from percentage to decimals with the Percent to Decimal Calculator .

Weisstein, Eric W. " Percent ." From MathWorld -- A Wolfram Web Resource.

Cite this content, page or calculator as:

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## Basic "Percent of" Word Problems

Basic Set-Up Markup / Markdown Increase / Decrease

## MathHelp.com

## Why does the percentage have to be converted to decimal form?

## How do you turn "percent of" word problems into equations to solve?

## What is an example of solving a "percent of" word problem?

Since x stands for a percentage, I need to remember to convert this decimal back into a percentage:

## What is the difference between "percent" and "percentage"?

Then (the sales tax) is (some percentage) of (the price), or, in mathematical terms:

0.66 ÷ 6.95 = x = 0.094964028... = 9.4964028...%

First, I have to find the absolute (that is, the actual numerical value of the) increase:

The price has gone up six cents. Now I can find the percentage increase over the original price.

This percentage increase is the relative change:

...or an 8% increase in price per pound.

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## IMAGES

## VIDEO

## COMMENTS

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