Percentages

🏆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: 1420=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 - 400.8=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 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

Exercise #2

Calculate 35% of 100:

Step-by-Step Solution

To find 35% of 100, first convert the percentage into a decimal by dividing by 100: 35%=35100=0.35 35\% = \frac{35}{100} = 0.35 .

Then, multiply this decimal by 100: 0.35×100=35 0.35 \times 100 = 35 .

Therefore, 35% of 100 is 35 35 .

Answer

35 35

Exercise #3

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 #4

Calculate 45% of 100:

Step-by-Step Solution

To find 45% of 100, you can multiply the percentage as a decimal by the whole number. First, convert 45% into a decimal. This is done by dividing by 100: 45%=45100=0.45 45\% = \frac{45}{100} = 0.45 .

Then, multiply this decimal by 100: 0.45×100=45 0.45 \times 100 = 45 .

Therefore, 45% of 100 is 45 45 .

Answer

45 45

Exercise #5

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

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