A percentage is a number that expresses a part of .
Quantity refers to the absolute number of something.
The percentage value refers to the quantity that corresponds to the specific percentage of the whole.
A percentage is a number that expresses a part of .
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:
We will always have 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.
Calculate 30 over 100 as a percentage:
Percentage is any number that represents a part of .
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:
Any question pertaining to percentages can be solved using this equation (which is an excellent trick!) so it's important that you memorize it!
Let's insert the data into the equation.
Let's look at examples:
of students in class 8C study art. There are 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 actually represent.
Note - a different way to phrase the same question could look like this: what is of .
Let's work according to the equation:
The percentage is .
The percentage value is the unknown we are looking for and the total amount is .
Let's insert the data and we should obtain the following:
Let's solve the equation and determine the unknown:
The answer is students from class 8'3 study in the art track.
Another question:
Dana invited her entire class to her birthday.
There are students in the class. of the class are boys. How many girls are in Dana's class?
Solution:
Note - if we determine the percentage value of out of 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 given that it represents the number of girls in the class.
Therefore in the equation we will insert for the percentage and not the given number .
We obtain the following:
Let's determine the unknown:
There are girls in the class.
Calculate 25 over 100 as a percentage:
Calculate 40 over 100 as a percentage:
Calculate 50 over 100 as a percentage:
Let's insert the data into the equation!
Examples:
There are flowers blooming in the garden. 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 out of .
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:
Let's determine the unknown:
The answer is as follows - The percentage of roses in the garden is .
We must insert the data into the equation.
Let's look at examples:
of the contestants in the competition are American. In total, there are 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:
Let's determine the unknown:
There are a total of contestants in the competition.
Additional question:
By Danny had completed of his total homework for that day. In total, Danny completed pieces of homework by .
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:
Danny received a total of homework assignments that day.
Calculate 10 over 100 as a percentage:
Calculate 75 over 100 as a percentage:
Calculate 65 over 100 as a percentage:
Calculate of ?
Solution:
is the whole.
is the percentage we are asked to find.
The percentage value is what we are asked to calculate, meaning, the number that corresponds to of the whole .
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 .
We obtain:
In other words, the percentage value is .
Calculate of ?
Solution:
is the whole.
is the percentage we are asked to find.
The percentage value is what we need to calculate, meaning, the number that corresponds to of the whole .
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 .
We get:
In other words, the percentage value is .
Another example:
Michal bought cupcakes for her birthday party. She couldn't resist waiting for her friends to arrive, and ate cupcakes by herself before they came. Calculate the percentage of the cupcakes that she ate?
Total number of cakes:
The number of cakes she ate:
The calculation: times =
Another example:
Michal's friends wanted to treat her with a birthday gift! They were interested in a dress that cost Dollars, however the seller gave them a special discount of Dollars. What percentage discount did Michal's friends receive?
Additional examples:
Itay found an attractive deal for a summer vacation in Greece! The advertisement promised the first customers a discount of Dollars! The original vacation price before the discount is Dollars. What percentage discount will Itay receive?
Initial price: Dollars
Discount offered to Itai: Dollars.
Calculation: times = discount
Another example:
Dan and Dana wanted to buy Danit a birthday present - a floral dress! The dress costs dollars. Dan asked Dana to put dollars towards the dress, while he would pay the remainder. What percentage of the gift did Dana pay for?
Gift price: dollars
Dana's contribution: times =
Calculate 75 over 100 as a percentage:
Calculate 8% of 100:
Calculate 15% of 100:
Calculate 95% of 100:
In order to calculate 15% of 100, start by converting the percentage into a decimal. Convert 15% to a decimal:
Then multiply the decimal by 100 to find the percentage value:
So, 95% of 100 is .
Calculate 75% of 100:
In order to calculate 75% of 100, we must first convert the percent into a decimal. Convert 75% to a decimal: .
Then multiply by the whole number: .
Therefore, 75% of 100 is .
Calculate 20% of 100:
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:
Next, multiply this decimal by 100 to find the percentage of the whole number:
Thus, 20% of 100 is .
Calculate 50% of 100:
In order to determine 50% of 100, we first convert the percentage into a decimal. Convert 50% to a decimal: .
Next, multiply the decimal by 100 to get the percentage value: .
Therefore, 50% of 100 is .
Calculate 75 over 100 as a percentage:
In order to determine the percentage of 75 out of 100, apply the percentage formula:
Substitute the specific values:
The equation simplifies to:
Therefore, 75 out of 100 is equivalent to 75%.
75%