Equivalent Forms of a Percentage

Oct 13, 2025 by recoveryshake.com 101 views

When dealing with percentages, it's essential to understand the different forms in which they can be expressed. In this article, we will explore the equivalent forms of a percentage and apply this knowledge to solve a problem involving a discount on a jacket.

What is a Percentage?

A percentage is a way to express a value as a fraction of 100. It's denoted by the symbol "%" and is often used to represent a proportion or a ratio. For example, 25% means 25 out of 100, or 1/4.

Equivalent Forms of a Percentage

A percentage can be expressed in different forms, including:

Decimal form: A percentage can be written as a decimal by dividing the percentage value by 100. For example, 25% is equal to 0.25.
Fractional form: A percentage can be written as a fraction by dividing the percentage value by 100 and simplifying the fraction. For example, 25% is equal to 1/4.
Mixed number form: A percentage can be written as a mixed number by dividing the percentage value by 100 and expressing the result as a mixed number. For example, 25% is equal to 1 1/4.

Which Choice is Equivalent to $6 \frac{1}{4} \%$ ?

Let's analyze the given choices and determine which one is equivalent to $6 \frac{1}{4} \%$ .

Choice A: 6.25: This is a decimal form of the percentage. To convert $6 \frac{1}{4} \%$ to a decimal, we can divide the percentage value by 100: $6 \frac{1}{4} \% = 6.25\%$ . Therefore, choice A is equivalent to $6 \frac{1}{4} \%$ .
Choice B: $\frac{25}{4}$ : This is a fractional form of the percentage. To convert $6 \frac{1}{4} \%$ to a fraction, we can divide the percentage value by 100 and simplify the fraction: $6 \frac{1}{4} \% = \frac{25}{4} \%$ . Therefore, choice B is equivalent to $6 \frac{1}{4} \%$ .
Choice C: $\frac{6}{25}$ : This is not equivalent to $6 \frac{1}{4} \%$ .
Choice D: $\frac{1}{16}$ : This is not equivalent to $6 \frac{1}{4} \%$ .

Conclusion

In conclusion, the correct answer is A. 6.25 and B. $\frac{25}{4}$ . Both choices are equivalent to $6 \frac{1}{4} \%$ .

A Store is Offering a $25\%$ Off Sale. Find the Discount on a $\$70$ Jacket

To find the discount on a $\$70$ jacket, we need to calculate 25% of the original price.

Step 1: Convert the Percentage to a Decimal

To convert 25% to a decimal, we can divide the percentage value by 100: $25\% = 0.25$ .

Step 2: Multiply the Decimal by the Original Price

Now, we can multiply the decimal by the original price to find the discount: $0.25 \times \$70 = \$17.50$ .

Step 3: Calculate the Discount

The discount is the amount we calculated in step 2: $\$17.50$ .

Conclusion

In conclusion, the discount on a $\$70$ jacket is $\$17.50$ .

Final Answer

In this article, we will address some of the most common questions related to percentages, equivalent forms, and discounts.

Q: What is a percentage?

A: A percentage is a way to express a value as a fraction of 100. It's denoted by the symbol "%" and is often used to represent a proportion or a ratio.

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

A: To convert a percentage to a decimal, you can divide the percentage value by 100. For example, 25% is equal to 0.25.

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

A: To convert a percentage to a fraction, you can divide the percentage value by 100 and simplify the fraction. For example, 25% is equal to 1/4.

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

A: A percentage is a way to express a value as a fraction of 100, while a proportion is a statement that two ratios are equal. For example, 25% is equal to 1/4, which is a proportion.

Q: How do I calculate a discount?

A: To calculate a discount, you need to multiply the percentage value by the original price. For example, if you want to find the discount on a $70 jacket with a 25% discount, you can multiply 0.25 by $70 to get $17.50.

Q: What is the difference between a discount and a markdown?

A: A discount is a reduction in the price of an item, while a markdown is a reduction in the price of an item that is already on sale. For example, if a store is offering a 25% discount on a $70 jacket, the price would be $52.50. If the store is offering a markdown of 25% on the discounted price, the price would be $39.38.

Q: How do I calculate the discount on a sale item?

A: To calculate the discount on a sale item, you need to multiply the percentage value by the sale price. For example, if a store is offering a 25% discount on a $70 jacket that is already on sale for $50, you can multiply 0.25 by $50 to get $12.50.

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

A: A percentage increase is a rise in the value of an item, while a percentage decrease is a fall in the value of an item. For example, if a store increases the price of a $70 jacket by 25%, the new price would be $87.50. If the store decreases the price of the jacket by 25%, the new price would be $52.50.

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

A: To calculate a percentage increase or decrease, you need to multiply the percentage value by the original price. For example, if you want to find the new price of a $70 jacket with a 25% increase, you can multiply 0.25 by $70 to get $17.50. If you want to find the new price of the jacket with a 25% decrease, you can multiply 0.25 by $70 to get $17.50, and then subtract $17.50 from the original price to get $52.50.

Conclusion

In conclusion, we have addressed some of the most common questions related to percentages, equivalent forms, and discounts. We hope that this article has provided you with a better understanding of these concepts and how to apply them in real-world situations.