Understanding percentages and their relationship to fractions is an essential skill in various fields, including mathematics, finance, and everyday life. Converting percentages to fractions allows for easier comparisons and calculations. In this step-by-step guide, we will explore the process of converting percentages to fractions, answering common questions along the way.

What is a percentage?

Before delving into converting percentages to fractions, let’s define what a percentage is. A percentage is a way to express a portion of a whole or a ratio out of 100. It is denoted using the symbol “%.” For instance, 50% represents 50 out of 100 or half of the whole.

How do we convert a percentage to a fraction with a denominator of 100?

To convert a percentage to fraction form with a denominator of 100, simply write the percentage as the numerator and the denominator as 100. For example, 25% can be written as 25/100. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 25. Therefore, 25/100 simplifies to 1/4.

What if the percentage is a decimal?

Sometimes, percentages are given in decimal form, such as 0.75. To convert a decimal percentage to a fraction, we need to move the decimal point two places to the right and place it over 100. In this case, 0.75 becomes 75/100, which simplifies to 3/4.

What if the fraction cannot be simplified further?

In certain instances, the fraction obtained from converting a percentage may not simplify further. For example, if the percentage is 33.33%, converting it to a fraction yields 33.33/100. However, this fraction does not simplify further, as there is no common factor between 33.33 and 100. So, the fraction remains 33.33/100.

Can percentages be converted to fractions with different denominators?

Yes, percentages can be converted to fractions with various denominators. To convert a percentage to a fraction with a different denominator, first, divide the percentage by 100. Then, multiply the resulting decimal by the new denominator. This will give you the numerator of the fraction. For example, converting 25% to a fraction with a denominator of 20, we divide 25 by 100 to get 0.25. Multiplying 0.25 by 20 yields 5. Therefore, 25% can be written as 5/20.

Converting percentages to fractions is a crucial skill that allows for easier comparisons and calculations. By following the step-by-step guide provided, anyone can convert percentages to fractions effortlessly. Remember that percentages can be converted to fractions with a denominator of 100, fractions that can be simplified, fractions that cannot be simplified further, and even fractions with different denominators. With this understanding, navigating percentages in various contexts becomes much simpler. So, the next time you come across a percentage, confidently convert it into a fraction and gain a clearer understanding of its underlying value.

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