Expressing a Percentage as a Fraction

Oct 13, 2025 by thesweetdesigns.com 30 views

Understanding Percentages and Fractions

Percentages and fractions are two ways to express proportions or parts of a whole. Percentages are often used in everyday life to express a value as a part of 100, while fractions are used in mathematics to express a part of a whole as a ratio. In this article, we will explore how to express a percentage as a fraction and vice versa.

Expressing a Percentage as a Fraction

(a) Express $3 \frac{1}{2} \%$ as a Fraction

To express a percentage as a fraction, we need to convert the percentage to a decimal first. We can do this by dividing the percentage value by 100.

$3 \frac{1}{2} \% = \frac{3 \frac{1}{2}}{100}$

To convert the mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator.

$3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}$

Now, we can rewrite the percentage as a fraction.

$\frac{3 \frac{1}{2}}{100} = \frac{\frac{7}{2}}{100} = \frac{7}{2} \times \frac{1}{100} = \frac{7}{200}$

Therefore, $3 \frac{1}{2} \%$ can be expressed as the fraction $\frac{7}{200}$ .

(b) Express $\frac{3}{20}$ as a Percent

To express a fraction as a percentage, we need to convert the fraction to a decimal first. We can do this by dividing the numerator by the denominator.

$\frac{3}{20} = 0.15$

Now, we can convert the decimal to a percentage by multiplying it by 100.

$0.15 \times 100 = 15\%$

Therefore, $\frac{3}{20}$ can be expressed as the percentage $15\%$ .

Expressing a Fraction as a Percentage

(c) Express $\frac{7}{25}$ as a Percent

To express a fraction as a percentage, we need to convert the fraction to a decimal first. We can do this by dividing the numerator by the denominator.

$\frac{7}{25} = 0.28$

Now, we can convert the decimal to a percentage by multiplying it by 100.

$0.28 \times 100 = 28\%$

Therefore, $\frac{7}{25}$ can be expressed as the percentage $28\%$ .

(d) Express $\frac{9}{10}$ as a Percent

To express a fraction as a percentage, we need to convert the fraction to a decimal first. We can do this by dividing the numerator by the denominator.

$\frac{9}{10} = 0.9$

Now, we can convert the decimal to a percentage by multiplying it by 100.

$0.9 \times 100 = 90\%$

Therefore, $\frac{9}{10}$ can be expressed as the percentage $90\%$ .

Expressing a Percentage as a Decimal

(e) Express $25\%$ as a Decimal

To express a percentage as a decimal, we need to divide the percentage value by 100.

$25\% = \frac{25}{100} = 0.25$

Therefore, $25\%$ can be expressed as the decimal $0.25$ .

(f) Express $50\%$ as a Decimal

To express a percentage as a decimal, we need to divide the percentage value by 100.

$50\% = \frac{50}{100} = 0.5$

Therefore, $50\%$ can be expressed as the decimal $0.5$ .

Conclusion

In this article, we have explored how to express percentages as fractions and vice versa. We have seen how to convert percentages to decimals and fractions, and how to convert fractions to percentages and decimals. By understanding these conversions, we can work with percentages and fractions more easily and accurately.

Key Takeaways

To express a percentage as a fraction, we need to convert the percentage to a decimal first.
To express a fraction as a percentage, we need to convert the fraction to a decimal first.
To convert a percentage to a decimal, we need to divide the percentage value by 100.
To convert a fraction to a decimal, we need to divide the numerator by the denominator.
To convert a decimal to a percentage, we need to multiply the decimal by 100.

Final Thoughts

Q: What is the difference between a percentage and a fraction?

A: A percentage is a way of expressing a value as a part of 100, while a fraction is a way of expressing a part of a whole as a ratio.

Q: How do I convert a percentage to a fraction?

A: To convert a percentage to a fraction, you need to divide the percentage value by 100 and then simplify the resulting fraction.

Q: How do I convert a fraction to a percentage?

A: To convert a fraction to a percentage, you need to divide the numerator by the denominator and then multiply the result by 100.

Q: What is the decimal equivalent of a percentage?

A: The decimal equivalent of a percentage is obtained by dividing the percentage value by 100.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, you need to multiply the decimal by 100.

Q: What is the relationship between percentages and decimals?

A: Percentages and decimals are related in that a percentage can be converted to a decimal by dividing the percentage value by 100, and a decimal can be converted to a percentage by multiplying the decimal by 100.

Q: How do I add or subtract percentages?

A: When adding or subtracting percentages, you need to first convert the percentages to decimals, perform the operation, and then convert the result back to a percentage.

Q: How do I multiply or divide percentages?

A: When multiplying or dividing percentages, you can simply multiply or divide the percentages as if they were numbers.

Q: What is the difference between a percentage increase and a percentage decrease?

A: A percentage increase is an increase in a value by a certain percentage, while a percentage decrease is a decrease in a value by a certain percentage.

Q: How do I calculate a percentage increase or decrease?

A: To calculate a percentage increase or decrease, you need to first find the difference between the original and new values, divide the difference by the original value, and then multiply the result by 100.

Q: What is the formula for calculating a percentage increase or decrease?

A: The formula for calculating a percentage increase or decrease is:

Percentage change = (New value - Original value) / Original value x 100

Q: How do I calculate a percentage of a value?

A: To calculate a percentage of a value, you need to multiply the value by the percentage.

Q: What is the formula for calculating a percentage of a value?

A: The formula for calculating a percentage of a value is:

Percentage of value = Value x Percentage

Conclusion

In this article, we have answered some of the most frequently asked questions about percentages and fractions. We have covered topics such as converting percentages to fractions, converting fractions to percentages, and calculating percentage increases and decreases. By understanding these concepts, you can work with percentages and fractions more easily and accurately.

Key Takeaways

To convert a percentage to a fraction, divide the percentage value by 100 and simplify the resulting fraction.
To convert a fraction to a percentage, divide the numerator by the denominator and multiply the result by 100.
To convert a decimal to a percentage, multiply the decimal by 100.
To calculate a percentage increase or decrease, find the difference between the original and new values, divide the difference by the original value, and multiply the result by 100.
To calculate a percentage of a value, multiply the value by the percentage.

Final Thoughts

Percentages and fractions are two important concepts in mathematics that are used to express proportions or parts of a whole. By understanding how to work with percentages and fractions, you can solve a wide range of problems in mathematics and everyday life. Whether you are working with percentages in finance or fractions in mathematics, these concepts are essential skills to have.