What is a percentage?

🏆Practice quantity, percentage, percentage value

What is a percentage?

A percentage is a number that expresses a part of 100100.
Quantity refers to the absolute number of something.
The percentage value refers to the quantity that corresponds to the specific percentage of the whole.

In order to solve questions about finding the quantity, percentage and percentage value, we use the following equation:
percentage100=percentage valuetotal quantity\frac{percentage}{100}=\frac{percentage~value}{total~quantity}

To solve percentage problems, we will use the following formula

We will always have 22 given values and one unknown that we need to determine.

Pay attention - The data in the question doesn't always direct us to what we're being asked. Therefore, we'll need to use logic and select the values that will provide us with the correct answer.

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Test yourself on quantity, percentage, percentage value!

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Calculate 30 over 100 as a percentage:

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What is a percentage? - Amount, percentage, percentage value and the relationship between them

What is a percentage?

Percentage is any number that represents a part of 100100.
Percentage value is the actual number that the percentage represents out of the quantity.
Quantity is the total amount.
You can see the relationship between all these values in the following equation:

percentage100=percentage valuetotal amount\frac{percentage}{100}=\frac{percentage~value}{total~amount}

Any question pertaining to percentages can be solved using this equation (which is an excellent trick!) so it's important that you memorize it!

How do you solve questions regarding percentage value (converting percentage to a number)?

Let's insert the data into the equation.

Let's look at examples:
25%25\% of students in class 8C study art. There are 4040 students in class 8C.
How many students from class 8C study art?

Solution:
We need to determine the percentage value - how many students does the 25%25\% actually represent.
Note - a different way to phrase the same question could look like this: what is 25%25\% of 4040.

Let's work according to the equation:

percentage100=percentage valuetotal amount\frac{percentage}{100}=\frac{percentage~value}{total~amount}

The percentage is 2525.
The percentage value is the unknown we are looking for and the total amount is 4040.
Let's insert the data and we should obtain the following:
25100=x40\frac{25}{100}=\frac{x}{40}
Let's solve the equation and determine the unknown:
100x=1000100x=1000
x=10x=10
The answer is 1010 students from class 8'3 study in the art track.

Another question:
Dana invited her entire class to her birthday.
There are 4040 students in the class. 35%35\% of the class are boys. How many girls are in Dana's class?

Solution:
Note - if we determine the percentage value of 35%35\% out of 4040 we will discover how many boys are in the class
However if we want to know how many girls are in the class we need to find the percentage value of 65%65\% given that it represents the number of girls in the class.
Therefore in the equation we will insert 6565 for the percentage and not the given number 3535.
We obtain the following:

65100=x40\frac{65}{100}=\frac{x}{40}

Let's determine the unknown:
100x=2600100x=2600
x=26x=26

There are 2626 girls in the class.

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How do you solve percentage problems?

Let's insert the data into the equation!

Examples:

There are 6060 flowers blooming in the garden. 1515 of these flowers are roses. Determine what percentage of the garden's flowers are roses?

Solution:
Note - We can also rephrase the question to ask what percentage is 1515 out of 6060.

In this question we are asked to find the percentage, therefore it will be our unknown. We are given the total amount as well as the percentage value.
Let's insert the known data into the equation:

1560=x100\frac{15}{60}=\frac{x}{100}

Let's determine the unknown:
60x=150060x=1500
x=25x=25
The answer is as follows - The percentage of roses in the garden is 25%25\%.

How do we solve questions regarding the total quantity?

We must insert the data into the equation.

Let's look at examples:
10%10\% of the contestants in the competition are American. In total, there are 55 American contestants in the competition.
How many contestants are there in total in the competition?

Solution:
We are given the percentage and the percentage value, therefore we need determine the total amount, this is our unknown.
Let's insert the known data into the formula:

10100=x5\frac{10}{100}=\frac{x}{5}
Let's determine the unknown:
10x=50010x=500
x=50x=50
There are a total of 5050 contestants in the competition.

Additional question:
By 16:0016:00 Danny had completed 60%60\% of his total homework for that day. In total, Danny completed 33 pieces of homework by 16:0016:00.
How many pieces of homework did Danny receive altogether?

Solution:
We are given the percentage and the percentage value therefore we only need to determine the total amount.
Let's insert the given data into the formula:

60100=3x\frac{60}{100}=\frac{3}{x}

60x=30060x=300
x=5x=5
Danny received a total of 55 homework assignments that day.

Do you know what the answer is?

Additional exercises:

Calculate 25%25\% of 300300?

Solution:
300300 is the whole.
25%25\% is the percentage we are asked to find.
The percentage value is what we are asked to calculate, meaning, the number that corresponds to 25%25\% of the whole 300300.
The calculation is done by multiplying the two numbers together. It's important to remember that in order to convert a percentage to a number, we must divide by 100100.

We obtain:

30025%300* 25\%
25100300=75\frac{25}{100}*300 = 75

In other words, the percentage value is 7575.

Calculate 20%20\% of 400400?

Solution:
400400 is the whole.
20%20\% is the percentage we are asked to find.
The percentage value is what we need to calculate, meaning, the number that corresponds to 20%20\% of the whole 400400.
The calculation is done by multiplying these two numbers together. Remember that in order to convert a percentage to a number, we must divide by 100100.

We get:

40020%=20100400=80400 *20\%=\frac{20}{100}*400=80

In other words, the percentage value is 8080.

Another example:

Michal bought 8080 cupcakes for her birthday party. She couldn't resist waiting for her friends to arrive, and ate 1515 cupcakes by herself before they came. Calculate the percentage of the cupcakes that she ate?

Total number of cakes: 8080

The number of cakes she ate: 1515

The calculation: 1580\frac{15}{80} times 100100 = 18.75%18.75\%

Another example:

Michal's friends wanted to treat her with a birthday gift! They were interested in a dress that cost 300300 Dollars, however the seller gave them a special discount of 6060 Dollars. What percentage discount did Michal's friends receive?

  • Initial price: 300300.
  • Discount: 6060 Dollars.
  • Calculation: 60300\frac{60}{300} times 100=20%100 = 20\%.

Additional examples:

Itay found an attractive deal for a summer vacation in Greece! The advertisement promised the first 5050 customers a discount of 480480 Dollars! The original vacation price before the discount is 24002400 Dollars. What percentage discount will Itay receive?
Initial price: 24002400 Dollars
Discount offered to Itai: 480480 Dollars.
Calculation: 4802400\frac{480}{2400} times 100100 = 20%20\% discount

Another example:
Dan and Dana wanted to buy Danit a birthday present - a floral dress! The dress costs 450450 dollars. Dan asked Dana to put 135135 dollars towards the dress, while he would pay the remainder. What percentage of the gift did Dana pay for?
Gift price: 450450 dollars
Dana's contribution: 135450\frac{135}{450} times 100100 = 30%30\%

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Examples with solutions for Quantity, percentage, percentage value

Exercise #1

Calculate 95% of 100:

Step-by-Step Solution

In order to calculate 15% of 100, start by converting the percentage into a decimal. Convert 15% to a decimal: 95%=0.95 95\% = 0.95

Then multiply the decimal by 100 to find the percentage value: 0.95×100=95 0.95 \times 100 = 95

So, 95% of 100 is 95 95 .

Answer

95 95

Exercise #2

Calculate 75% of 100:

Step-by-Step Solution

In order to calculate 75% of 100, we must first convert the percent into a decimal. Convert 75% to a decimal: 75%=0.75 75\% = 0.75 .

Then multiply by the whole number: 0.75×100=75 0.75 \times 100 = 75 .

Therefore, 75% of 100 is 75 75 .

Answer

75 75

Exercise #3

Calculate 20% of 100:

Step-by-Step Solution

In order to determine 20% of 100, we begin by converting the percentage into a decimal and then proceed to multiply by the whole number. First, convert 20% to a decimal: 20%=0.2 20\% = 0.2

Next, multiply this decimal by 100 to find the percentage of the whole number: 0.2×100=20 0.2 \times 100 = 20

Thus, 20% of 100 is 20 20 .

Answer

20 20

Exercise #4

Calculate 50% of 100:

Step-by-Step Solution

In order to determine 50% of 100, we first convert the percentage into a decimal. Convert 50% to a decimal: 50%=0.5 50\% = 0.5 .

Next, multiply the decimal by 100 to get the percentage value: 0.5×100=50 0.5 \times 100 = 50 .

Therefore, 50% of 100 is 50 50 .

Answer

50 50

Exercise #5

Calculate 75 over 100 as a percentage:

Step-by-Step Solution

In order to determine the percentage of 75 out of 100, apply the percentage formula:

Percentage=PartWhole×100 \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

Substitute the specific values:

Percentage=75100×100 \text{Percentage} = \frac{75}{100} \times 100

The equation simplifies to:

Percentage=75% \text{Percentage} = 75\%

Therefore, 75 out of 100 is equivalent to 75%.

Answer

75%

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