Rewriting a Fraction as a Unit Rate

Oct 13, 2025 by recoveryshake.com 144 views

Understanding Unit Rates

A unit rate is a ratio of two numbers where the second number is 1. It is used to compare the value of different quantities. In this article, we will learn how to rewrite a fraction as a unit rate.

What is a Fraction?

A fraction is a way to represent a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator represents the number of equal parts, and the denominator represents the total number of parts.

Rewriting a Fraction as a Unit Rate

To rewrite a fraction as a unit rate, we need to divide the numerator by the denominator. This will give us a ratio of two numbers where the second number is 1.

Step 1: Divide the Numerator by the Denominator

Let's take the fraction $\frac{2}{5}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (2) by the denominator (5).

2 ÷ 5 = 0.4

Step 2: Write the Result as a Ratio

Now that we have the result of the division, we can write it as a ratio. Since the result is a decimal, we can multiply it by 10 to get a whole number.

0.4 × 10 = 4

So, the ratio is 4:1.

Step 3: Check the Answer Choices

Now that we have the unit rate, we can check the answer choices to see which one matches our result.

A. $6: 1$ B. $30: 5$ C. $2: 75$ D. $15: 2$

Our result is 4:1, but none of the answer choices match this exactly. However, we can see that option A is close, but it is not the correct answer.

Conclusion

Rewriting a fraction as a unit rate involves dividing the numerator by the denominator and writing the result as a ratio. In this article, we learned how to do this with the fraction $\frac{2}{5}$ . We also checked the answer choices to see which one matched our result.

Example 2: Rewrite $\frac{1}{15}$ as a Unit Rate

Let's take the fraction $\frac{1}{15}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (1) by the denominator (15).

1 ÷ 15 = 0.0667

Step 1: Write the Result as a Ratio

Now that we have the result of the division, we can write it as a ratio. Since the result is a decimal, we can multiply it by 100 to get a whole number.

0.0667 × 100 = 6.67

So, the ratio is 6.67:1.

Step 2: Check the Answer Choices

Now that we have the unit rate, we can check the answer choices to see which one matches our result.

A. $6: 1$ B. $30: 5$ C. $2: 75$ D. $15: 2$

Our result is 6.67:1, but none of the answer choices match this exactly. However, we can see that option A is close, but it is not the correct answer.

Conclusion

Rewriting a fraction as a unit rate involves dividing the numerator by the denominator and writing the result as a ratio. In this article, we learned how to do this with the fraction $\frac{1}{15}$ . We also checked the answer choices to see which one matched our result.

Example 3: Rewrite $\frac{2}{75}$ as a Unit Rate

Let's take the fraction $\frac{2}{75}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (2) by the denominator (75).

2 ÷ 75 = 0.0267

Step 1: Write the Result as a Ratio

Now that we have the result of the division, we can write it as a ratio. Since the result is a decimal, we can multiply it by 100 to get a whole number.

0.0267 × 100 = 2.67

So, the ratio is 2.67:1.

Step 2: Check the Answer Choices

Now that we have the unit rate, we can check the answer choices to see which one matches our result.

A. $6: 1$ B. $30: 5$ C. $2: 75$ D. $15: 2$

Our result is 2.67:1, and option C matches this exactly.

Conclusion

Rewriting a fraction as a unit rate involves dividing the numerator by the denominator and writing the result as a ratio. In this article, we learned how to do this with the fraction $\frac{2}{75}$ . We also checked the answer choices to see which one matched our result.

Example 4: Rewrite $\frac{15}{2}$ as a Unit Rate

Let's take the fraction $\frac{15}{2}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (15) by the denominator (2).

15 ÷ 2 = 7.5

Step 1: Write the Result as a Ratio

Now that we have the result of the division, we can write it as a ratio. Since the result is a decimal, we can multiply it by 10 to get a whole number.

7.5 × 10 = 75

So, the ratio is 75:1.

Step 2: Check the Answer Choices

Now that we have the unit rate, we can check the answer choices to see which one matches our result.

A. $6: 1$ B. $30: 5$ C. $2: 75$ D. $15: 2$

Our result is 75:1, and none of the answer choices match this exactly.

Conclusion

Rewriting a fraction as a unit rate involves dividing the numerator by the denominator and writing the result as a ratio. In this article, we learned how to do this with the fraction $\frac{15}{2}$ . We also checked the answer choices to see which one matched our result.

Final Answer

Q: What is a unit rate?

A: A unit rate is a ratio of two numbers where the second number is 1. It is used to compare the value of different quantities.

Q: How do I rewrite a fraction as a unit rate?

A: To rewrite a fraction as a unit rate, you need to divide the numerator by the denominator and write the result as a ratio.

Q: What is the numerator and denominator in a fraction?

A: The numerator is the number of equal parts, and the denominator is the total number of parts.

Q: Can you give an example of rewriting a fraction as a unit rate?

A: Let's take the fraction $\frac{2}{5}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (2) by the denominator (5).

2 ÷ 5 = 0.4

So, the ratio is 4:1.

Q: How do I check the answer choices to see which one matches my result?

A: Once you have rewritten the fraction as a unit rate, you can check the answer choices to see which one matches your result. In the case of the fraction $\frac{2}{5}$ , none of the answer choices match exactly, but option A is close.

Q: What if the result is a decimal?

A: If the result is a decimal, you can multiply it by 10 to get a whole number. For example, if the result is 0.4, you can multiply it by 10 to get 4.

Q: Can you give another example of rewriting a fraction as a unit rate?

A: Let's take the fraction $\frac{1}{15}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (1) by the denominator (15).

1 ÷ 15 = 0.0667

So, the ratio is 6.67:1.

Q: How do I check the answer choices to see which one matches my result?

A: Once you have rewritten the fraction as a unit rate, you can check the answer choices to see which one matches your result. In the case of the fraction $\frac{1}{15}$ , none of the answer choices match exactly, but option A is close.

Q: What if I get a result that is not a whole number?

A: If you get a result that is not a whole number, you can multiply it by 10 to get a whole number. For example, if the result is 0.0667, you can multiply it by 100 to get 6.67.

Q: Can you give an example of rewriting a fraction as a unit rate with a result that is not a whole number?

A: Let's take the fraction $\frac{2}{75}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (2) by the denominator (75).

2 ÷ 75 = 0.0267

So, the ratio is 2.67:1.

Q: How do I check the answer choices to see which one matches my result?

A: Once you have rewritten the fraction as a unit rate, you can check the answer choices to see which one matches your result. In the case of the fraction $\frac{2}{75}$ , option C matches exactly.

Q: What if I get a result that is a negative number?

A: If you get a result that is a negative number, you can ignore the negative sign and rewrite the fraction as a unit rate.

Q: Can you give an example of rewriting a fraction as a unit rate with a result that is a negative number?

A: Let's take the fraction $\frac{-2}{5}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (-2) by the denominator (5).

-2 ÷ 5 = -0.4

So, the ratio is -4:1.

Q: How do I check the answer choices to see which one matches my result?

A: Once you have rewritten the fraction as a unit rate, you can check the answer choices to see which one matches your result. In the case of the fraction $\frac{-2}{5}$ , none of the answer choices match exactly, but option A is close.

Q: What if I get a result that is a fraction?

A: If you get a result that is a fraction, you can simplify it to a whole number or a decimal.

Q: Can you give an example of rewriting a fraction as a unit rate with a result that is a fraction?

A: Let's take the fraction $\frac{1}{2}$ as an example. To rewrite it as a unit rate, we need to divide the numerator (1) by the denominator (2).

1 ÷ 2 = 0.5

So, the ratio is 5:1.

Q: How do I check the answer choices to see which one matches my result?

A: Once you have rewritten the fraction as a unit rate, you can check the answer choices to see which one matches your result. In the case of the fraction $\frac{1}{2}$ , option A matches exactly.

Conclusion

Rewriting a fraction as a unit rate involves dividing the numerator by the denominator and writing the result as a ratio. In this article, we have answered some common questions about rewriting fractions as unit rates and provided examples to help illustrate the concept.