Converting between fractions and percentages and vice versa

In order to convert between fractions and percentages and vice versa, it's important to remember that one percent - 1%=11001\% = \frac{1}{100}.
If you remember this principle, the calculations are simple.

Converting Percentages to Fractions

The first stage -

In the numerator, we write the given percentage number (without the percentage sign)
and in the denominator, we always write the number 100100.

The second stage -

We reduce the fraction that we obtained as much as possible in order to achieve the final answer.

Converting Fractions to Percentages

The first stage -

We expand or reduce the fraction so that the number 100100 appears in its denominator.
We will make sure to perform the expansion/reduction operation on both the numerator and denominator to maintain the value of the fraction.

The second stage -

What we obtained in the numerator will be the percentage and that will be the final answer.

Important note - not every fraction can be converted to percentages (without a calculator) since not every given denominator can be converted to 100100 through expansion or reduction.

Educational chart showing the relationship between percentage, fraction, and decimal using examples like 30%, 3/10, and 0.3, with a conversion path explaining how to turn a fraction into a decimal and then into a percentage.

Suggested Topics to Practice in Advance

  1. How to Calculate Percentage
  2. Percentages
  3. How do you calculate the percentage value?
  4. What is a percentage?

Practice Converting Fractions to Percentages and Vice Versa

Examples with solutions for Converting Fractions to Percentages and Vice Versa

Exercise #1

Convert the fraction 7100 \frac{7}{100} into a percentage.

Video Solution

Step-by-Step Solution

The fraction:

x100 \frac{x}{100} is actually x percent.

Therefore we use the formula:

x100=x% \frac{x}{100}=x\%

7100=7% \frac{7}{100}=7\%

Answer

7%

Exercise #2

Convert the fraction into a percentage:

2100=? \frac{2}{100}=\text{?}

Video Solution

Step-by-Step Solution

To convert the fraction 2100\frac{2}{100} into a percentage, follow these steps:

  • Step 1: Recognize that to convert a fraction to a percentage, you multiply the fraction by 100.
  • Step 2: Multiply the numerator of the fraction by 100:

2100×100=2 \frac{2}{100} \times 100 = 2

This tells us that 2100\frac{2}{100} is equivalent to 2%.

Therefore, the correct percentage is 2%.

Answer

2%

Exercise #3

Write the percentage 75% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

To express 75% as a fraction with a denominator of 100, follow these steps:

  • Step 1: Recall that a percentage is a fraction out of 100. This means that 75% represents 75 out of 100.
  • Step 2: Write the percentage as a fraction: Since 75% means 75 per hundred, this directly gives us the fraction 75100\frac{75}{100}.

Upon checking the given choices, the correct answer is 75100\frac{75}{100}, which matches option 4.

Therefore, the solution to the problem is 75100\frac{75}{100}.

Answer

75100 \frac{75}{100}

Exercise #4

Write the percentage 66% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

To solve the problem of converting 66% into a fraction with a denominator of 100, we follow these simple steps:

  • Step 1: Recognize that the percentage 66% means 66 per 100.
  • Step 2: Write this as a fraction directly as 66100 \frac{66}{100} .

Therefore, the percentage 66% expressed as a fraction with a denominator of 100 is 66100 \frac{66}{100} .

Answer

66100 \frac{66}{100}

Exercise #5

Write the percentage 54% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

To solve the problem of converting a percentage to a fraction, follow these steps:

  • Step 1: Recognize that the percentage given is 54%.
  • Step 2: Use the conversion principle that any percentage can be written as a fraction with a denominator of 100. Thus, 54% is written as 54100\frac{54}{100}.
  • Step 3: Check if further simplification is needed. In this case, since we were specifically asked for a denominator of 100, no simplification is required.

Therefore, the percentage 54% as a fraction with a denominator of 100 is 54100\frac{54}{100}.

Answer

54100 \frac{54}{100}

Exercise #6

Convert the fraction 75100 \frac{75}{100}

to a percentage:

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify that the fraction given is 75100 \frac{75}{100} .
  • Step 2: Recognize that a fraction with a denominator of 100 directly gives the percentage represented by its numerator.

Now, let's work through each step:
Step 1: We see that the fraction is 75100 \frac{75}{100} , where 100 is the denominator, which is the standard for percentages.
Step 2: Since percentages are essentially fractions out of 100, the numerator directly translates into the percentage.

Thus, the percentage represented by 75100 \frac{75}{100} is 75%.

Therefore, the solution to the problem is 75%.

Answer

75%

Exercise #7

Convert the fraction 200100 \frac{200}{100} to a percentage

Video Solution

Step-by-Step Solution

To solve this problem, let's convert the fraction 200100 \frac{200}{100} to a percentage.

We can perform this conversion using the following steps:

  • Step 1: Recall that to convert a fraction to a percentage, you multiply it by 100. Therefore, the formula to use is:

  • numeratordenominator×100% \frac{\text{numerator}}{\text{denominator}} \times 100\%

Let's apply this formula to our fraction:

200100×100% \frac{200}{100} \times 100\%

Step 2: Simplify the fraction. In this case, 200100\frac{200}{100} simplifies to 22.

Step 3: Multiply the simplified result by 100:

2×100%=200% 2 \times 100\% = 200\%

Therefore, the fraction 200100\frac{200}{100} is equivalent to 200%.

The correct answer is choice 2: 200% 200\% .

Answer

200%

Exercise #8

Convert the fraction into a percentage:

56100=? \frac{56}{100}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, let's convert the given fraction 56100\frac{56}{100} into a percentage using the standard conversion method:

  • Step 1: Recognize that converting a fraction to a percentage involves multiplying the fraction by 100. This is because a percentage is a way of expressing a number as a part out of 100.
  • Step 2: Multiply the fraction by 100 as follows:

56100×100%=56% \frac{56}{100} \times 100\% = 56\%

Thus, when you convert 56100\frac{56}{100} into a percentage, you obtain 56%.

Comparing this with the provided answer options, 56% matches option 4.

Therefore, the correct answer is 56% 56\% .

Answer

56%

Exercise #9

Write the percentage 118% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow a simple conversion:

  • Step 1: Recognize that a percentage represents a number out of 100. Thus, 118% is equivalent to 118 out of 100.
  • Step 2: Apply the conversion formula: Percentage=Percentage number100 \text{Percentage} = \frac{\text{Percentage number}}{100} .
  • Step 3: Directly convert 118% into a fraction using this formula: 118100\frac{118}{100}.

Since the problem asks for the fraction with a denominator of 100, we have arrived at the correct form.

Therefore, the fraction form of 118% with a denominator of 100 is 118100\frac{118}{100}.

Answer

118100 \frac{118}{100}

Exercise #10

Convert the fraction 157100 \frac{157}{100} to a percentage:

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given information: the fraction is 157100 \frac{157}{100} .
  • Step 2: Apply the conversion formula by multiplying the fraction by 100.
  • Step 3: Perform the calculation and check the correct multiple-choice answer.

Now, let's work through each step:
Step 1: The problem provides us with the fraction 157100 \frac{157}{100} .
Step 2: We'll use the formula Percentage=(NumeratorDenominator)×100 \text{Percentage} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100 . Plugging in our values, we get:

(157100)×100=157% \left( \frac{157}{100} \right) \times 100 = 157\%

Therefore, the percentage equivalent of the fraction 157100 \frac{157}{100} is 157% 157\% .

The correct answer from the given choices is: Choice 4: 157%

Answer

157%

Exercise #11

Convert the fraction into a percentage:

24100=? \frac{24}{100}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll use the conversion method to obtain the percentage representation of the fraction:

  • Step 1: Identify the given fraction 24100 \frac{24}{100} .
  • Step 2: Convert the fraction to a percentage by multiplying it by 100: (24100)×100%\left(\frac{24}{100}\right) \times 100\% .
  • Step 3: Calculate the expression: 24100×100=24\frac{24}{100} \times 100 = 24.
  • Step 4: Append the percentage symbol to the result: 24%24\% .

Thus, the fraction 24100 \frac{24}{100} is equivalent to 24%.

Answer

24%

Exercise #12

Convert the fraction 135100 \frac{135}{100} to a percentage:

Video Solution

Step-by-Step Solution

To solve this problem, we should first recognize the nature of the fraction 135100\frac{135}{100}. Since the denominator is 100, the fraction directly represents the percentage equivalent of the numerator.

Step-by-step:

  • Step 1: Understand that any fraction a100\frac{a}{100} can be interpreted as a%a\% in percentage form.
  • Step 2: In this instance, 135100\frac{135}{100} directly translates to 135% because the denominator is 100.

Therefore, the fraction 135100\frac{135}{100} is equivalent to 135%.

The correct choice from the options provided is choice 3: 135%.

Therefore, the solution to the problem is 135%.

Answer

135%

Exercise #13

Write the percentage 89% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

To solve this problem, we will convert the percentage to a fraction directly:

  • Step 1: Understand that when expressing a percentage as a fraction, the number is divided by 100. For example, 89% means 89 per 100.
  • Step 2: Write the fraction using the number 89 as the numerator and 100 as the denominator. The fraction thus becomes 89100\frac{89}{100}.

Therefore, the percentage 89% expressed as a fraction with a denominator of 100 is 89100\frac{89}{100}.

Hence, the correct answer to the problem is 89100 \frac{89}{100} .

Answer

89100 \frac{89}{100}

Exercise #14

Write the percentage 33% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

To solve this problem, we will employ the following straightforward steps:

  • Step 1: Identify the given percentage, which is 33%.
  • Step 2: Use the definition of percentage to convert it into a fraction. A percentage is a fraction out of 100. Therefore, 33% equals 33100\frac{33}{100}.

Therefore, the solution to the problem is 33100 \frac{33}{100} .
Comparing with the given choices, the correct option is .

Answer

33100 \frac{33}{100}

Exercise #15

Write the percentage 201% as a fraction with a denominator of 100.

Video Solution

Step-by-Step Solution

We use the formula:

x100=x% \frac{x}{100}=x\%

201100=201% \frac{201}{100}=201\%

Answer

201100 \frac{201}{100}

Topics learned in later sections

  1. Estimation