Converting Fractions to Percentages Practice Problems

Master fraction to percentage conversion with step-by-step practice problems. Learn to convert percentages to fractions and vice versa with guided solutions.

📚Practice Converting Between Fractions and Percentages
  • Convert percentages like 25%, 67%, and 225% to simplified fractions
  • Transform fractions such as 4/5, 7/20, and 3/4 into percentages
  • Master the two-step process for percentage to fraction conversion
  • Learn when fractions cannot be converted to percentages without calculators
  • Practice reducing fractions to lowest terms after conversion
  • Apply conversion skills to mixed numbers and improper fractions

Understanding Converting Fractions to Percentages and Vice Versa

Complete explanation with examples

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.

Detailed explanation

Practice Converting Fractions to Percentages and Vice Versa

Test your knowledge with 29 quizzes

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

Examples with solutions for Converting Fractions to Percentages and Vice Versa

Step-by-step solutions included
Exercise #1

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

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}

Video Solution
Exercise #2

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

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}

Video Solution
Exercise #3

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

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}

Video Solution
Exercise #4

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

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}

Video Solution
Exercise #5

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

to a percentage:

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%

Video Solution

Frequently Asked Questions

How do you convert a percentage to a fraction?

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Use a two-step process: First, write the percentage number (without the % sign) in the numerator and 100 in the denominator. Second, reduce the fraction to its simplest form by dividing both numerator and denominator by their greatest common factor.

What is the easiest way to convert fractions to percentages?

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The easiest method is to convert the fraction so its denominator becomes 100, then use the numerator as the percentage. For example, 3/25 becomes 12/100 = 12% by multiplying both parts by 4.

Why can't all fractions be converted to percentages easily?

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Some fractions cannot be converted to percentages without a calculator because their denominators cannot be changed to 100 through simple multiplication or division. For example, 10/11 cannot be easily converted since 11 doesn't divide evenly into 100.

What does 1% equal as a fraction?

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1% equals 1/100 as a fraction. This is the fundamental relationship that makes all fraction-percentage conversions possible, since percent means 'per hundred.'

How do you convert percentages greater than 100% to fractions?

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Follow the same two-step process: write the percentage number over 100, then simplify. For example, 225% = 225/100 = 9/4 = 2¼ as a mixed number.

What are common fraction to percentage conversions to memorize?

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Key conversions include: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80%, 1/10 = 10%, and 1/25 = 4%.

How do you reduce fractions after converting from percentages?

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Find the greatest common factor (GCF) of the numerator and denominator, then divide both by this number. Continue until no common factors remain except 1. For example, 45/100 reduces to 9/20 by dividing both by 5.

Can you convert mixed numbers to percentages?

+
Yes, first convert the mixed number to an improper fraction, then follow the standard conversion process to get a percentage greater than 100%. For example, 2¼ = 9/4 = 225/100 = 225%.

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