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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.

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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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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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Worksheet on Fraction into Percentage

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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:.

- Pre-Algebra ,
- Basic Math and Pre-Algebra All-in-One For Dummies Cheat Sheet
- Basic Math and Pre-Algebra Workbook For Dummies Cheat Sheet
- Multiplying with Scientific Notation
- How to Convert Fractions to Decimals
- How to Determine Likelihoods Using Basic Probability
- View All Articles From Category

## Module 1: Whole Numbers, Fractions, Decimals, Percents and Problem Solving

Solving problems using percents, learning outcome.

## Pieces of a Percent Problem

The amount is a percent of the base.

Let’s look at another example:

## Solving for the Amount

[latex]\text{percent}\cdot{\text{base}}=\text{amount}[/latex]

Find [latex]50\%[/latex] of [latex]20[/latex]

First identify each piece of the problem:

percent: [latex]50\%[/latex] or [latex].5[/latex]

Now plug them into your equation [latex]\text{percent}\cdot{\text{base}}=\text{amount}[/latex]

[latex].5\cdot{20}= 10[/latex]

Therefore, [latex]10[/latex] is the amount or part that is [latex]50\%[/latex] of [latex]20[/latex].

What is [latex]25\%[/latex] of [latex]80[/latex]?

## Solving for the Percent

[latex]\Large{\frac{\text{amount}}{\text{base}}}\normalsize=\text{percent}[/latex]

What percent of [latex]320[/latex] is [latex]80[/latex]?

[latex]\large\frac{80}{320}\normalsize=?[/latex]

[latex]\large\frac{80}{320}\normalsize=.25[/latex]

Therefore, [latex]80[/latex] is [latex]25\%[/latex] of [latex]320[/latex].

## Solving for the Base

[latex]\Large{\frac{\text{amount}}{\text{percent}}}\normalsize=\text{base}[/latex]

[latex]60[/latex] is [latex]40\%[/latex] of what number?

percent:[latex]40\%[/latex] or [latex].4[/latex]

[latex](60)\div(.4)=150[/latex]

Therefore, [latex]60[/latex] is [latex]40\%[/latex] of [latex]150[/latex].

base = [latex]30000\div(.15)=$200000[/latex]

The non-profit receives [latex]$200000[/latex] a year in donations

Here are a few more percent problems for you to try.

In the next video we show another example of finding how much tip to give based on percent.

## Contribute!

## 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:

- 1 Conversion to Fractions and Decimals
- 2 Percent of a Number
- 3 Percent Change
- 4 Percent Increase and Decrease
- 5.1 Introductory Problems
- 5.2 Intermediate Problems

## Conversion to Fractions and Decimals

## Percent of a Number

## Percent Change

## Percent Increase and Decrease

## Introductory Problems

## Intermediate Problems

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