Converting Fractions to Percentages and Vice Versa - Examples, Exercises and Solutions

The fraction:

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

Therefore we use the formula:

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

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

To solve this problem, follow these steps:

• Step 1: Identify that the fraction given is $\frac{75}{100}$.
• 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 $\frac{75}{100}$, 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 $\frac{75}{100}$ is 75%.

Therefore, the solution to the problem is 75%.

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

Step-by-step:

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

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

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

Therefore, the solution to the problem is 135%.

To solve this problem, let's convert the fraction $\frac{200}{100}$ 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:

• $\frac{\text{numerator}}{\text{denominator}} \times 100\%$

Let's apply this formula to our fraction:

$\frac{200}{100} \times 100\%$

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

Step 3: Multiply the simplified result by 100:

$2 \times 100\% = 200\%$

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

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

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

• Step 1: Identify the given information: the fraction is $\frac{157}{100}$.
• 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 $\frac{157}{100}$.
Step 2: We'll use the formula $\text{Percentage} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100$. Plugging in our values, we get:

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

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

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 $\frac{75}{100}$.

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

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

We use the formula:

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

$\frac{87}{100}=87\%$

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 $\frac{54}{100}$.
• 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 $\frac{54}{100}$.

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 $\frac{89}{100}$.

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

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

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: $\text{Percentage} = \frac{\text{Percentage number}}{100}$.
• Step 3: Directly convert 118% into a fraction using this formula: $\frac{118}{100}$.

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 $\frac{118}{100}$.

We use the formula:

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

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

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 $\frac{33}{100}$.

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

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 $\frac{66}{100}$.

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

To convert the fraction $\frac{2}{100}$ 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:

$\frac{2}{100} \times 100 = 2$

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

Therefore, the correct percentage is 2%.

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

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

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