Percentages

๐Ÿ†Practice percentage

What are Percentages?

In order to recognise and calculate percentages, we need to understand two basic concepts:

  • How to determine a part of a whole without percentages
  • How to determine a part of a whole with percentages

When we are discussing percentages, one should always ask the question "percentage of what?", meaning, there must be some whole from which the percentage is calculated. The whole serves as a reference point for the percentages.

To solve percentage problems, we will use the following formula

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Test yourself on percentage!

Calculate 30 over 100 as a percentage:

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Let's demonstrate this using two examples.

Example 1.

What is 141\over4 of 2020?

Solution:

When we are asked to find a part (141\over4) of a whole (2020), we need to multiply the part by the whole.

Therefore we obtain the following: 14โ‹…20=204=5\frac{1}{4} \cdot 20 = \frac{20}{4} = 5

Example 2.

A shirt originally cost 4040 dollars and it's currently on sale with a 2020% discount.

We are asked to calculate the price of the shirt after the price reduction.

Solution:

After the price reduction, the shirt's price is 8080% (before the reduction the price was 100100%).

8080% is actually 80100=810=0.8\frac{80}{100}= \frac{8}{10}= 0.8.

In order to calculate 8080% of 4040, we perform a simple multiplication - 40โ‹…0.8=3240\cdot0.8 = 32.

In other words, the price of the shirt after the price reduction is 3232 dollars.

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Examples with solutions for Percentage

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: 0.95ร—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: 0.75ร—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: 0.2ร—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: 0.5ร—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=PartWholeร—100 \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

Substitute the specific values:

Percentage=75100ร—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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