How do you calculate the percentage value?

Quantity, percentage, percentage value - Examples, Exercises and Solutions
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How do you calculate the percentage value?

Although there's no real reason, quite a few students are somewhat apprehensive about topics involving percentage calculations. To calculate percentages, all you need to do is memorize basic formulas and apply calculation techniques. Maybe in your first encounter with percentages, you answered relatively simple questions, but as you progress through the curriculum and move to higher grades, the topics and questions become more complex.

Calculating the percentage value is one of the questions you will need to answer. What is the purpose of the question? To understand what percentage represents a certain part. Naturally, such a question will appear as part of various problems you will face, regardless of your study group or the learning units you are assigned to. So how do we calculate a percentage value?

Examples for calculating percentage value:

The formula you will use to calculate the percentage value is: divide the specific part by the total amount, and multiply by one hundred. And now? Examples:

First 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. What percentage of the cupcakes did she eat?

Solution

Total number of cakes: 8080

The number of cakes she ate: 1515

The calculation: 1580⋅100=18.75%\frac{15}{80} \cdot 100 = 18.75\%

Second example:

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

Solution

  • Initial price: 300300.
  • Discount: 6060 Dollars.
  • Calculation: 60300⋅100=20%\frac{60}{300} \cdot100 = 20\%.
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Test yourself on quantity, percentage, percentage value!

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Calculate 6% of 100:

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How do we calculate the percentage value?

Additional examples:

John found an attractive deal for a summer vacation in Greece! The advertisement promised a discount of 480480 Dollars to the first 5050 customers! The original vacation price before the discount is 24002400 Dollars. What percentage discount will John receive?

Solution

Initial price: 24002400 Dollars
The discount offered to John: 480480 Dollars
The calculation: 4802400⋅100=20% \frac{480}{2400}\cdot100= 20\%
20%20\% discount

Another example:
Jeramiah and Daniel wanted to buy Ember a birthday present - a floral dress! The dress costs 450450 Dollars. Jeramiah asked Daniel to invest only 135135 Dollars, while he would pay the remainder from his pocket. What percentage of the gift's cost did Daniel pay?

Solution

Gift price: 450450 Dollars
Daniel's required cost: 135450⋅100=30%\frac{135}{450}\cdot100= 30\%

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Question 1

Calculate 3% of 100:

Question 2

Calculate 32 over 100 as a percentage:

Question 3

Calculate 40 over 100 as a percentage:

Examples with solutions for Quantity, percentage, percentage value

Exercise #1

Calculate 6% of 100:

Video Solution

Step-by-Step Solution

To solve the problem of calculating 6% of 100, we follow these clear steps:

  • Step 1: Convert the percentage to a fraction. The percentage 6% is equivalent to the fraction 6100 \frac{6}{100} .
  • Step 2: Multiply the whole number by this fraction. We calculate 6100×100 \frac{6}{100} \times 100 .
  • Step 3: Perform the calculation. Simplifying 6100×100 \frac{6}{100} \times 100 , we find:
6×100100=6 \frac{6 \times 100}{100} = 6

Therefore, the solution to the problem is 6.

Answer

6

Exercise #2

Calculate 3% of 100:

Video Solution

Step-by-Step Solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Identify the given information
    We are given a percentage of 3% and a whole number of 100.
  • Step 2: Use the percentage formula
    The formula to calculate the percentage of a whole number is given by:
    Percentage value=percentage100×whole number \text{Percentage value} = \frac{\text{percentage}}{100} \times \text{whole number}
  • Step 3: Substitute the values and calculate
    Substituting the given values into the formula, we have:
    3100×100=3 \frac{3}{100} \times 100 = 3

Therefore, the 3% of 100 is 3 3 .

Answer

3

Exercise #3

Calculate 32 over 100 as a percentage:

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given fraction 32100 \frac{32}{100} .
  • Step 2: Recognize that the denominator of 100 aligns directly with the meaning of percentage.
  • Step 3: Conclude that when the fraction is Part100 \frac{\text{Part}}{100} , it equals Part% \text{Part}\% .

Now, let's work through each step:

Step 1: The problem gives us the fraction 32100 \frac{32}{100} .
Step 2: Since the denominator is 100, the fraction directly represents a percentage.
Step 3: This means that 32100 \frac{32}{100} is simply 32% 32\% .

Therefore, the solution to the problem is 32% 32\% .

Answer

32%

Exercise #4

Calculate 40 over 100 as a percentage:

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Use the percentage formula: (PartWhole)×100%\left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\%.
  • Step 2: Substitute the given numbers: (40100)×100%\left(\frac{40}{100}\right) \times 100\%.
  • Step 3: Calculate the division, 40100=0.4\frac{40}{100} = 0.4.
  • Step 4: Multiply by 100 to convert to a percentage: 0.4×100=40%0.4 \times 100 = 40\%.

Therefore, 40 over 100 as a percentage is 40%40\%.

Answer

40%

Exercise #5

Calculate 15% of 100:

Step-by-Step Solution

To find 15% of 100, you can convert the percentage to a decimal by dividing by 100:

15%=15100=0.15 15\% = \frac{15}{100} = 0.15

Next, multiply this decimal by 100:

0.15×100=15 0.15 \times 100 = 15

Thus, 15% of 100 is 15.

Answer

15 15

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