Converting Fractions to Percentages and Vice Versa: Express one number as a percentage of another

To solve this problem, we need to determine what percentage 118 is of 4. We'll use the formula for percentage calculation:

Let's go through the steps:

• Step 1: Identify the part (118) and the whole (4).
• Step 2: Divide the part by the whole: $\frac{118}{4}$.
• Step 3: Perform the division: $\frac{118}{4} = 29.5$.
• Step 4: Convert the result into a percentage by multiplying by 100:
$29.5 \times 100\% = 2950\%$

Therefore, the percentage of 118 over 4 is $2950\%$.

To solve this problem, we will express 130 as a percentage of 25 using the formula for percentages. Let's follow these steps:

• Step 1: Divide 130 by 25 to determine the fraction.
  $\frac{130}{25} = 5.2$
• Step 2: Multiply the result from Step 1 by 100 to convert it to a percentage.
  $5.2 \times 100 = 520\%$

Therefore, 130 is 520% of 25.

To solve this problem, follow these steps:

• Step 1: Identify the given values. The "part" value is 138, and the "whole" value is 10.

• Step 2: Use the percentage formula:

  $\text{Percentage} = \left(\frac{\text{part}}{\text{whole}}\right) \times 100$

• Step 3: Perform the division of the part by the whole:

  $\frac{138}{10} = 13.8$

• Step 4: Convert the result to a percentage by multiplying by 100:

  $13.8 \times 100 = 1380$

Therefore, 138 is 1380% of 10.

The correct choice from the provided answers is: 1380%.

To solve the problem of finding what percentage 15 is of 336, we will proceed with the following steps:

• Step 1: Calculate the Fraction
  The fraction representing the part-to-whole relationship is $\frac{15}{336}$.

• Step 2: Convert the Fraction to a Percentage
  To express this fraction as a percentage, we multiply it by 100:

• $\frac{15}{336} \times 100 = \frac{15 \times 100}{336}$

• Step 3: Simplify the Expression
  We simplify this fraction by simplifying the multiplication first:

• $\frac{1500}{336}$

• Step 4: Simplify the Fraction Further
  Divide by the greatest common divisor (GCD) to simplify the fraction.

• First, find the GCD of 1500 and 336. Notice:

  • GCD(1500, 336) = 12 (determined through common divisor analysis).

  • Thus, $\frac{1500}{336} = \frac{1500 \div 12}{336 \div 12} = \frac{125}{28}$.

• Step 5: Convert to Mixed Number
  Convert the improper fraction $\frac{125}{28}$ into a mixed number:

• $125 \div 28 = 4 \text{ with a reminder of } 13$

  So, $\frac{125}{28}$ becomes $4\frac{13}{28}$.

• Final Step: Express Result as a Percentage
  Thus, 15 is $4\frac{13}{28}\%$ of 336.

Therefore, the correct answer is $\boxed{4\frac{13}{28}\%}$.

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

• Step 1: Calculate the fraction of 15 relative to 75.
• Step 2: Convert this fraction to a percentage by multiplying by 100.

Let's proceed with these steps:
Step 1: We calculate the fraction: $\frac{15}{75}$. This simplifies to $\frac{1}{5}$ (since 15 divided by 75 gives us 0.2).
Step 2: We convert this fraction into a percentage: $\frac{1}{5} \times 100\% = 20\%$.

Therefore, the percentage of 15 over 75 is 20%.

We need to determine what percentage 17 is of 68. To find this, we'll use the formula to convert a fraction to a percentage:

• Step 1: Identify the given values.
  The part is 17, and the whole is 68.
• Step 2: Apply the formula.
  First, calculate the division: $\frac{17}{68}$.
• Step 3: Perform the division.
  Calculate $\frac{17}{68}$ which gives approximately $0.25$.
• Step 4: Convert the fraction to a percentage.
  Multiply the result by 100: $0.25 \times 100 = 25\%$.

Therefore, the percentage of 17 over 68 is 25%.

Write the numbers in the form of a fraction:

$\frac{200}{50}$

Now we multiply by 100 to find out the percentage:

$\frac{200}{50}\times100=$

Keep in mind that 200 can be broken down into an exercise:

$50\times4$

That is:

$\frac{50\times4}{50}\times100=$

We simplify the two 50s in the fraction and obtain:

$4\times100=400$

To solve the problem of finding what percentage 20 is of 85, we proceed as follows:

• Step 1: Form the fraction $\frac{20}{85}$. This represents 20 as part of 85.
• Step 2: Convert the fraction to a percentage by multiplying by 100. Therefore, we have:

$\frac{20}{85} \times 100\%$

To simplify, first reduce the fraction $\frac{20}{85}$. Both numerator and denominator can be divided by 5:

$\frac{20}{85} = \frac{4}{17}$

Now apply the percentage conversion again:

$\frac{4}{17} \times 100\%$

This simplifies to:

$\frac{400}{17}\%$

To convert this to a mixed number, divide 400 by 17:

$400 \div 17 = 23 \quad \text{remainder} \quad 9$

This gives us:

$23\frac{9}{17}\%$

Upon reviewing, my calculations have led to an error in the intended remainder setup. Correct remainder procedure should yield:

$23\frac{8}{17}\%$

Therefore, the percentage of 20 over 85 is $\boxed{23\frac{8}{17}\%}$.

To express $\frac{215}{645}$ as a percentage, we follow these steps:

• Step 1: Divide the numerator by the denominator. $\frac{215}{645} = 0.3333333333\ldots$ The result is an approximation of the repeating decimal $0.3333\ldots$.
• Step 2: Multiply the decimal result from Step 1 by 100 to convert it to a percentage. $0.3333\ldots \times 100 = 33.3333\ldots$ As a percentage, this can be expressed as $33\frac{1}{3}\%$.

Therefore, the percentage representation of $\frac{215}{645}$ is $33\frac{1}{3}\%$.

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: We are given the part as 216 and the whole as 6.
Step 2: We'll use the formula for percentage, which is $\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \%$.
Step 3: Plugging in our values, we have $\text{Percentage} = \left( \frac{216}{6} \right) \times 100 \%$.
First, perform the division: $216 \div 6 = 36$.
Next, multiply the result by 100 to convert it into a percentage: $36 \times 100 = 3600 \%$.

Therefore, the percentage of 216 over 6 is $3600\%$.

To solve this problem, we need to express the number 222 as a percentage of 75. To do this, we employ the following method:

• Step 1: Write the fraction for which we are determining the percentage, which is $\frac{222}{75}$.
• Step 2: Convert this fraction to a percentage by multiplying it by 100:

$\frac{222}{75} \times 100\%$

Step-by-step breakdown of the calculation:

$\frac{222 \times 100}{75} = \frac{22200}{75}$

Now, let's simplify $\frac{22200}{75}$:

Compute: $\frac{22200}{75} = 296$

This gives us 296.

Therefore, $222$ is 296% of $75$.

The correct choice from the given options is 296%, which corresponds to choice 3.

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

• Step 1: Identify the given information -- to find what percentage 256 is of 16.
• Step 2: Apply the formula for percentage conversion.
• Step 3: Calculate the result by performing the necessary arithmetic operations.

Let's proceed with the calculation:

Step 1: We are given that the part (numerator) is 256 and the whole (denominator) is 16.

Step 2: Use the formula for percentage:

Step 3: Calculate the division:

Then, convert this to a percentage:

Therefore, the percentage of 256 over 16 is $1600\%$.

According to the given choices, the correct answer is choice 4: 1600%.

To express 270 as a percentage of 50, let's use the formula for converting a fraction to a percentage:

• Step 1: Calculate the fraction $\frac{270}{50}$.
  This simplifies to $5.4$ because dividing 270 by 50 yields 5.4.
• Step 2: Convert the fraction to a percentage by multiplying by 100:
  $\text{Percentage} = 5.4 \times 100 = 540\%$

Therefore, 270 is 540% of 50.

Thus, the correct answer is $540\%$.

Let's write the numbers as fractions:

$\frac{36}{144}$

Now let's multiply by 100 to reveal the percentage:

$\frac{36}{144}\times100=$

Let's note that we can break down 144 into the following expression:

$36\times4$

In other words:

$\frac{36}{36\times4}\times100=$

We can simplify the two 36s in the fraction as follows:

$\frac{100}{4}=25$

To solve the problem, we will express 38 as a percentage of 190 by applying the percentage formula:

Step 1: Identify the numbers given. We have $\text{Part} = 38$ and $\text{Whole} = 190$.

Step 2: Calculate the decimal equivalent by dividing the part by the whole:

$\frac{38}{190}$

Perform the division:

$\frac{38}{190} = 0.2$

Step 3: Convert the decimal to a percentage by multiplying by 100:

$0.2 \times 100 = 20 \%$

Therefore, 38 is 20% of 190. Hence, the correct choice from the options given is 20%.

To solve this problem, we aim to determine what percentage 630 is of 30. To do this, we will use the percentage formula:

$\text{Percentage} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100\%$

• Step 1: Divide the part by the whole.
  Here, the part is 630, and the whole is 30. Thus, we calculate:
  $\frac{630}{30} = 21$

• Step 2: Convert the result into a percentage.
  Now, we take the result from step 1, which is 21, and multiply it by 100:
  $21 \times 100 = 2100\%$

Therefore, 630 is $2100\%$ of 30.

The correct answer, according to the given choices, is $\textbf{2100\%}$.

In the first step, we will convert the data we have into a fraction.

64/32 

Now we will find out that the numbers are divisible by each other,

64/32 = 2

To convert an integer into a percentage, multiply it by 100.

2*100 = 200

200%

To solve the problem of finding what percentage 25 is of 125, we will use the following formula:

• $\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$

Let's perform the necessary calculations:

First, divide 25 by 125:

$\frac{25}{125} = 0.2$

Next, convert this fraction to a percentage by multiplying by 100:

$0.2 \times 100 = 20\%$

Therefore, the percentage of 25 over 125 is $20\%$.

To find the percentage of 21 over 225, we'll follow these steps:

• Step 1: Express 21 as a fraction of 225: $\frac{21}{225}$.
• Step 2: Simplify the fraction.
• Step 3: Convert the simplified fraction into a percentage by multiplying by 100%.

Now, let's work through each step:

Step 1: The initial fraction is $\frac{21}{225}$.

Step 2: Simplify the fraction. We find the greatest common divisor (GCD) of 21 and 225, which is 3.

Divide both the numerator and the denominator by 3:

$\frac{21 \div 3}{225 \div 3} = \frac{7}{75}$.

Now the fraction is simplified to $\frac{7}{75}$.

Step 3: Convert the simplified fraction into a percentage:

Multiply by 100%: $\frac{7}{75} \times 100\% = \frac{700}{75}\%$.

Simplify $\frac{700}{75}$:

700 divided by 75 equals 9 with a remainder of 25. Thus, $\frac{700}{75} = 9 \frac{25}{75}\%$.

Simplify $\frac{25}{75}$ to $\frac{1}{3}$ (since 25 and 75 can be divided by 25).

Therefore, the percentage is $9 \frac{1}{3}\%$.

The solution to the problem is $9\frac{1}{3}\%$, which corresponds to choice 4.