math problem solving percentage

$In 5th grade percentage worksheet, students can practice the questions on percentage. The questions are based on convert percentages to fractions, convert percentages to decimals, convert fractions to percentages, convert decimals to percentages, find the percentage of$

5th Grade Percentage Worksheet | Finding Percentages | Answers

In 5th grade percentage worksheet, students can practice the questions on percentage. The questions are based on convert percentages to fractions, convert percentages to decimals, convert fractions to percentages, convert decimals to percentages, find the percentage of

$Practice the questions given in the worksheet on percentage of a number. We know, to find the percent of a number we obtain the given number and then multiply the number by the required percent i.e., x % of a = x/100 × a 1. Find the following: (i) 22 % of 140$

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

Practice the questions given in the worksheet on percentage of a number. We know, to find the percent of a number we obtain the given number and then multiply the number by the required percent i.e., x % of a = x/100 × a 1. Find the following: (i) 22 % of 140

$In worksheet on percent problems we will practice various types of questions on calculating percentage problems. To answer the questions review application of percentage before practicing the sheet. Fill in the blanks:(i)The symbol of percent is … (ii)The word ‘cent’ means …$

Worksheet on Percent Problems | Questions on Application of Percentage

In worksheet on percent problems we will practice various types of questions on calculating percentage problems. To answer the questions review application of percentage before practicing the sheet. Fill in the blanks:(i)The symbol of percent is … (ii)The word ‘cent’ means …

$What is 18% of 500? 18% of 500 represent 18 parts out of hundred, so 18% of 500 represents 18 parts for each hundred which is 18 + 18 + 18 + 18 + 18 = 90. Thus, 18% of 500 = 90 So, 18% of 500 = $\frac{18}{100}$ × 500 = 18 × 5 = 90. To find the percent of a given number$

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

What is 18% of 500? 18% of 500 represent 18 parts out of hundred, so 18% of 500 represents 18 parts for each hundred which is 18 + 18 + 18 + 18 + 18 = 90. Thus, 18% of 500 = 90 So, 18% of 500 = $\frac{18}{100}$ × 500 = 18 × 5 = 90. To find the percent of a given number

$How to convert a decimal into percentage? We will follow the following steps for converting a decimal into a percentage: Step I: Obtain the number in decimal form. Step II: Multiply the number in decimal form by 100 and put percent sign (%)$

Convert a Decimal into Percentage | Conversion of Decimal into Percent

How to convert a decimal into percentage? We will follow the following steps for converting a decimal into a percentage: Step I: Obtain the number in decimal form. Step II: Multiply the number in decimal form by 100 and put percent sign (%)

$To convert a fraction into a percent, we multiply the given fraction by 100 and add the percent symbol after the product. Let us consider how to change a fraction to a percent (i) 42/100 = 42% (ii) 73/100 = 73% (iii) 6/100 = 6%$

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

To convert a fraction into a percent, we multiply the given fraction by 100 and add the percent symbol after the product. Let us consider how to change a fraction to a percent (i) 42/100 = 42% (ii) 73/100 = 73% (iii) 6/100 = 6%

$To convert a percentage into a fraction, place the given number over 100 and reduce it to its lowest term. Consider the following example: (i) 20% [We know % = 1/100]$

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

To convert a percentage into a fraction, place the given number over 100 and reduce it to its lowest term. Consider the following example: (i) 20% [We know % = 1/100]

$How to convert a given percentage into decimal? We will follow the following steps for converting a percentage into a decimal: Step I: Obtain the percentage which is to be converted into decimal Step II: Remove the percentage sign (%) and divide it by 100.$

Percentage into Decimal | Percentage as Decimals|Percent into Fraction

How to convert a given percentage into decimal? We will follow the following steps for converting a percentage into a decimal: Step I: Obtain the percentage which is to be converted into decimal Step II: Remove the percentage sign (%) and divide it by 100.

$A fraction with denominator 100 is called percentage and is denoted by the symbol %. In our daily life, we see a lot of statements with numbers followed by a symbol %. A number followed by % is called a percentage or percent. The term percent comes from the Latin phrase per$

Percentage | Symbol of Percent | Fraction with Denominator 100

A fraction with denominator 100 is called percentage and is denoted by the symbol %. In our daily life, we see a lot of statements with numbers followed by a symbol %. A number followed by % is called a percentage or percent. The term percent comes from the Latin phrase per

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Solving problems with percentages

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

$$\frac{a}{b}=\frac{x}{100}$$

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

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

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%

100% of 5 is 5

100% of 91 is 91

100% of 732 is 732

Finding 50% of a number: Remember that 50% means half, so to find 50% of a number, just divide it by 2:

50% of 20 is 10

50% of 88 is 44

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

25% of 40 is 10

25% of 88 is 22

Finding 20% of a number: Finding 20% of a number is handy if you like the service you’ve received in a restaurant, because a good tip is 20% of the check. Because 20% equals 1/5, you can find 20% of a number by dividing it by 5. But you can use an easier way:

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

20% of 80 = 8 2 = 16

20% of 300 = 30 2 = 60

20% of 41 = 4.1 2 = 8.2

Finding 10% of a number: Finding 10% of any number is the same as finding 1/10 of that number. To do this, just move the decimal point one place to the left:

10% of 30 is 3

10% of 41 is 4.1

10% of 7 is 0.7

Finding 200%, 300%, and so on of a number: Working with percents that are multiples of 100 is easy. Just drop the two 0s and multiply by the number that’s left:

200% of 7 = 2 7 = 14

300% of 10 = 3 10 = 30

1,000% of 45 = 10 45 = 450

Make tough-looking percent problems easy

Suppose someone wants you to figure out the following:

Finding 88% of anything isn’t an activity that anybody looks forward to. 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 easier. As you learned above, 50% of 88 is simply half of 88:

88% of 50 = 50% of 88 = 44

As another example, suppose you want to find

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

7% of 200 = 200% of 7

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

35% of 80 = ?

Ouch — this time, the numbers you’re working with aren’t so friendly. When the numbers in a percent problem become a little more difficult, the tricks no longer work, so you want to know how to solve all 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.

Changing the word of to a multiplication sign is a simple example of turning words into numbers. This change turns something unfamiliar into a form that you know how to work with.

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

35% of 80 = 0.35 80

Solve the problem using decimal multiplication.

Here’s what the example looks like:

So 35% of 80 is 28.

12% of 31 = 0.12 31

Now you can solve the problem with decimal multiplication:

So 12% of 31 is 3.72.

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

The number of questions correct is indicated by:

Ethan got 44 questions correct.

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

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

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

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

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

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

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

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

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

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

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

b. Simplify the equation.

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

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

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

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

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

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

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

CHAPTER 1 REVIEW

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

Signed Numbers:

Informal Rules:

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

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

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

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

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

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

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

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

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

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

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

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

Literal Equations:

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

Percentages:

Write percentages as decimals.

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

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

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

Study Tips:

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

Math Topics

More solvers.

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Online Calculators

Read on to learn more about how to figure percentages.

Solution: Solve for P% using the percentage formula P% = Y / X

Example: 9 of 13 is what percent?

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 .

If you need to convert between fractions and percents see our Fraction to Percent Calculator , or our Percent to Fraction Calculator .

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

Cite this content, page or calculator as:

Furey, Edward " Percentage Calculator " at https://www.calculatorsoup.com/calculators/math/percentage.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

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Basic "Percent of" Word Problems

Basic Set-Up Markup / Markdown Increase / Decrease

When you learned how to translate simple English statements into mathematical expressions, you learned that "of" can indicate "times". This frequently comes up when using percentages.

Suppose you need to find 16% of 1400 . You would first convert the percentage " 16% " to its decimal form; namely, the number " 0.16 ".

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Percent Word Problems

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

When you are doing actual math, you need to use actual numbers. Percents, being the values with a "percent" sign tacked on, are not technically numbers. This is similar to your grade-point average ( gpa ), versus your grades. You can get an A in a class, but the letter "A" is not a numerical grade which can be averaged. Instead, you convert the "A" to the equivalent "4.0", and use this numerical value for finding your gpa .

When you're doing computations with percentages, remember always to convert the percent expressions to their equivalent decimal forms.

Once you've done this conversion of the percentage to decimal form, you note that "sixteen percent OF fourteen hundred" is telling you to multiply the 0.16 and the 1400 . The numerical result you get is (0.16)(1400) = 224 . This value tells you that 224 is sixteen percent of 1400 .

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

Percentage problems usually work off of some version of the sentence "(this) is (some percentage) of (that)", which translates to "(this) = (some decimal) × (that)". You will be given two of the values — or at least enough information that you can figure out what two of the values must be — and then you'll need to pick a variable for the value you don't have, write an equation, and solve the equation for that variable.

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

What percent of 20 is 30 ?

We have the original number 20 and the comparative number 30 . The unknown in this problem is the rate or percentage. Since the statement is "(thirty) is (some percentage) of (twenty)", then the variable stands for the percentage, and the equation is:

30 = ( x )(20)

30 ÷ 20 = x = 1.5

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

Thirty is 150% of 20 .

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

"Percent" means "out of a hundred", its expression contains a specific number, and the "percent" sign can be used interchangeably with the word (such as " 24% " and "twenty-four percent"); "percentage" is used in less specific ways, to refer to some amount of some total (such as "a large percentage of the population"). ( Source )

In real life, though, including in math classes, we tend to be fairly sloppy in using these terms. So there's probably no need for you to worry overmuch about this technicallity.

What is 35% of 80 ?

Here we have the rate (35%) and the original number (80) ; the unknown is the comparative number which constitutes 35% of 80 . Since the exercise statement is "(some number) is (thirty-five percent) of (eighty)", then the variable stands for a number and the equation is:

x = (0.35)(80)

Twenty-eight is 35% of 80 .

45% of what is 9 ?

Here we have the rate (45%) and the comparative number (9) ; the unknown is the original number that 9 is 45% of. The statement is "(nine) is (forty-five percent) of (some number)", so the variable stands for a number, and the equation is:

9 = (0.45)( x )

9 ÷ 0.45 = x = 20

Nine is 45% of 20 .

The format displayed above, "(this number) is (some percent) of (that number)", always holds true for percents. In any given problem, you plug your known values into this equation, and then you solve for whatever is left.

Suppose you bought something that was priced at $6.95 , and the total bill was $7.61 . What is the sales tax rate in this city? (Round answer to one decimal place.)

The sales tax is a certain percentage of the price, so I first have to figure what the actual numerical amount of the tax was. The tax was:

7.61 – 6.95 = 0.66

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

0.66 = ( x )(6.95)

Solving for x , I get:

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

The sales tax rate is 9.5% .

In the above example, I first had to figure out what the actual tax was, before I could then find the answer to the exercise. Many percentage problems are really "two-part-ers" like this: they involve some kind of increase or decrease relative to some original value.

Note : Always figure the percentage of change of increase or decrease relative to the original value.

Suppose a certain item used to sell for seventy-five cents a pound, you see that it's been marked up to eighty-one cents a pound. What is the percent increase?

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

81 – 75 = 6

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

Note this language, "increase/decrease over the original", and use it to your advantage: it will remind you to put the increase or decrease over the original value, and then divide.

This percentage increase is the relative change:

6 / 75 = 0.08

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

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