Choosing the Correct Ratios

Oct 13, 2025 by miodeya.com 54 views

In mathematics, a unit rate is a ratio in which the second term is 1. It is used to compare the quantities of two different units. Unit rates are essential in various mathematical operations, including comparison, conversion, and problem-solving. In this article, we will explore which ratios have a unit rate greater than 1.

What is a Unit Rate?

A unit rate is a ratio in which the second term is 1. It is a way to express a quantity in terms of a unit, making it easier to compare and convert between different units. For example, if we have a ratio of 5 miles to 1 hour, the unit rate is 5 miles per hour.

Choosing the Correct Ratios

Now, let's analyze the given ratios and determine which ones have a unit rate greater than 1.

A. 7 miles : $\frac{3}{4}$ hour

To find the unit rate, we need to divide the first term by the second term.

$\frac{7 \text{ miles}}{\frac{3}{4} \text{ hour}} = \frac{7}{\frac{3}{4}} = \frac{7 \times 4}{3} = \frac{28}{3} \approx 9.33$ miles per hour

The unit rate is approximately 9.33 miles per hour, which is greater than 1.

B. $\frac{1}{3}$ mile : $2\frac{3}{8}$ hours

To find the unit rate, we need to divide the first term by the second term.

$\frac{\frac{1}{3} \text{ mile}}{2\frac{3}{8} \text{ hours}} = \frac{\frac{1}{3}}{\frac{17}{8}} = \frac{1}{3} \times \frac{8}{17} = \frac{8}{51} \approx 0.157$ miles per hour

The unit rate is approximately 0.157 miles per hour, which is less than 1.

C. $\frac{9}{8}$ miles : $\frac{5}{6}$ hour

To find the unit rate, we need to divide the first term by the second term.

$\frac{\frac{9}{8} \text{ miles}}{\frac{5}{6} \text{ hour}} = \frac{\frac{9}{8}}{\frac{5}{6}} = \frac{9}{8} \times \frac{6}{5} = \frac{54}{40} = \frac{27}{20} = 1.35$ miles per hour

The unit rate is 1.35 miles per hour, which is equal to 1, not greater than 1.

D. 4 miles

This is not a ratio, so we cannot find a unit rate.

Conclusion

Based on the analysis, the ratio that has a unit rate greater than 1 is:

A. 7 miles : $\frac{3}{4}$ hour

In the previous article, we explored which ratios have a unit rate greater than 1. Now, let's answer some frequently asked questions about unit rates.

Q: What is the purpose of unit rates?

A: Unit rates are used to compare the quantities of two different units. They are essential in various mathematical operations, including comparison, conversion, and problem-solving.

Q: How do I find the unit rate of a ratio?

A: To find the unit rate of a ratio, you need to divide the first term by the second term. For example, if you have a ratio of 5 miles to 1 hour, the unit rate is 5 miles per hour.

Q: What is the difference between a unit rate and a ratio?

A: A ratio is a comparison of two quantities, while a unit rate is a ratio in which the second term is 1. For example, the ratio 5 miles to 1 hour is equivalent to the unit rate 5 miles per hour.

Q: Can a unit rate be a fraction?

A: Yes, a unit rate can be a fraction. For example, if you have a ratio of $\frac{1}{3}$ mile to 1 hour, the unit rate is $\frac{1}{3}$ mile per hour.

Q: How do I convert a unit rate to a decimal?

A: To convert a unit rate to a decimal, you need to divide the numerator by the denominator. For example, if you have a unit rate of $\frac{7}{4}$ miles per hour, the decimal equivalent is 1.75 miles per hour.

Q: Can a unit rate be greater than 1?

A: Yes, a unit rate can be greater than 1. For example, if you have a ratio of 7 miles to $\frac{3}{4}$ hour, the unit rate is approximately 9.33 miles per hour, which is greater than 1.

Q: Can a unit rate be less than 1?

A: Yes, a unit rate can be less than 1. For example, if you have a ratio of $\frac{1}{3}$ mile to $2\frac{3}{8}$ hours, the unit rate is approximately 0.157 miles per hour, which is less than 1.

Q: How do I use unit rates in real-life situations?

A: Unit rates are used in various real-life situations, such as:

Measuring speed: Unit rates are used to measure speed in miles per hour or kilometers per hour.
Measuring distance: Unit rates are used to measure distance in miles per hour or kilometers per hour.
Measuring time: Unit rates are used to measure time in hours per day or minutes per hour.

Conclusion

Unit rates are an essential concept in mathematics, and understanding them is crucial for problem-solving and real-life applications. By following the steps outlined in this article, you can easily find the unit rate of a ratio and apply it to various real-life situations.