Which Of The Following Is Not An Equivalent Expression For $20 \%$?A. $\frac{1}{5}$B. 0.2C. \$\frac{1}{20}$[/tex\]D. $\frac{20}{100}$

Introduction

Percentages are a fundamental concept in mathematics, used to express a value as a fraction of a whole. In this article, we will explore equivalent expressions for the percentage 20%. We will examine each option and determine which one is not an equivalent expression.

What is a Percentage?

A percentage is a way to express a value as a fraction of a whole. It is calculated by dividing the value by the total and multiplying by 100. For example, if we have a value of 20 and a total of 100, the percentage would be 20/100 = 0.2 or 20%.

Equivalent Expressions for Percentages

Equivalent expressions for percentages are values that represent the same proportion. In other words, they are different ways of expressing the same value. Let's examine each option:

Option A: $\frac{1}{5}$

$\frac{1}{5}$ is an equivalent expression for 20% because it represents the same proportion. To see this, we can convert $\frac{1}{5}$ to a decimal by dividing the numerator by the denominator: $\frac{1}{5} = 0.2$. This is equal to 20%.

Option B: 0.2

0.2 is an equivalent expression for 20% because it represents the same value. In decimal form, 20% is equal to 0.2.

Option C: $\frac{1}{20}$

$\frac{1}{20}$ is not an equivalent expression for 20%. To see this, we can convert $\frac{1}{20}$ to a decimal by dividing the numerator by the denominator: $\frac{1}{20} = 0.05$. This is equal to 5%, not 20%.

Option D: $\frac{20}{100}$

$\frac{20}{100}$ is an equivalent expression for 20% because it represents the same proportion. To see this, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20: $\frac{20}{100} = \frac{1}{5}$. This is equal to 20%.

Conclusion

In conclusion, the correct answer is Option C: $\frac{1}{20}$. This is not an equivalent expression for 20% because it represents a different proportion. The other options, $\frac{1}{5}$, 0.2, and $\frac{20}{100}$, are all equivalent expressions for 20%.

Key Takeaways

• Equivalent expressions for percentages are values that represent the same proportion.
• To determine if an expression is equivalent to a percentage, convert it to a decimal or simplify the fraction.
• $\frac{1}{5}$, 0.2, and $\frac{20}{100}$ are all equivalent expressions for 20%.
• $\frac{1}{20}$ is not an equivalent expression for 20%.

Final Thoughts

Q: What is an equivalent expression for a percentage?

A: An equivalent expression for a percentage is a value that represents the same proportion. In other words, it is a different way of expressing the same value.

Q: How do I determine if an expression is equivalent to a percentage?

A: To determine if an expression is equivalent to a percentage, convert it to a decimal or simplify the fraction. If the resulting value is equal to the percentage, then the expression is equivalent.

Q: What are some common equivalent expressions for percentages?

A: Some common equivalent expressions for percentages include:

• Fractions: $\frac{1}{5}$, $\frac{1}{10}$, $\frac{1}{20}$
• Decimals: 0.2, 0.1, 0.05
• Percentages: 20%, 10%, 5%

Q: Can I have multiple equivalent expressions for a percentage?

A: Yes, you can have multiple equivalent expressions for a percentage. For example, 20% is equivalent to $\frac{1}{5}$, 0.2, and $\frac{20}{100}$.

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

A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert $\frac{1}{5}$ to a decimal, divide 1 by 5: $\frac{1}{5} = 0.2$.

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD. For example, to simplify $\frac{20}{100}$, find the GCD of 20 and 100, which is 20. Then, divide both numbers by 20: $\frac{20}{100} = \frac{1}{5}$.

Q: Why is it important to understand equivalent expressions for percentages?

A: Understanding equivalent expressions for percentages is important because it allows you to work with different representations of the same value, making it easier to solve problems and communicate ideas. It also helps you to simplify complex calculations and make math more accessible.

Q: Can I use equivalent expressions for percentages in real-life situations?

A: Yes, you can use equivalent expressions for percentages in real-life situations. For example, if you are calculating a tip at a restaurant, you can use a percentage to determine the amount of the tip. You can also use equivalent expressions to compare different rates of interest or to calculate the cost of an item.

Q: How do I apply equivalent expressions for percentages in real-life situations?

A: To apply equivalent expressions for percentages in real-life situations, follow these steps:

1. Identify the percentage or rate of interest.
2. Convert the percentage to a decimal or simplify the fraction.
3. Use the equivalent expression to calculate the amount or cost.
4. Compare the results to make informed decisions.

Conclusion

In conclusion, equivalent expressions for percentages are an important concept in mathematics. By understanding equivalent expressions, you can work with different representations of the same value, simplify complex calculations, and make math more accessible. We hope this article has helped you to understand equivalent expressions for percentages and how to apply them in real-life situations.