Question

select the three correct answers. which rates are unit rates? \\(\frac{60\text{ miles}}{5\text{ hours}}\\) \\(\frac{20\text{ minutes}}{6\text{ kilometers}}\\) \\(\frac{\frac{3}{2}\text{ feet}}{1\text{ minute}}\\) \\(\frac{35\text{ miles}}{1\text{ gallon}}\\) \\(\frac{\\$120}{8\text{ hour}}\\) \\(\frac{\\$10.25}{1\text{ hour}}\\)

Explanation:

A unit rate is a rate in which the denominator is 1 unit. Let's analyze each option:

Step 1: Analyze $\frac{60 \text{ miles}}{5 \text{ hours}}$

The denominator is 5 hours, not 1. So this is not a unit rate.

Step 2: Analyze $\frac{20 \text{ minutes}}{6 \text{ kilometers}}$

The denominator is 6 kilometers, not 1. So this is not a unit rate.

Step 3: Analyze $\frac{\frac{3}{2} \text{ feet}}{1 \text{ minute}}$

The denominator is 1 minute. So this is a unit rate.

Step 4: Analyze $\frac{35 \text{ miles}}{1 \text{ gallon}}$

The denominator is 1 gallon. So this is a unit rate.

Step 5: Analyze $\frac{\$120}{8 \text{ hour}}$

The denominator is 8 hours, not 1. So this is not a unit rate.

Step 6: Analyze $\frac{\$10.25}{1 \text{ hour}}$

The denominator is 1 hour. So this is a unit rate.

Answer:

• $\boldsymbol{\frac{\frac{3}{2} \text{ feet}}{1 \text{ minute}}}$
• $\boldsymbol{\frac{35 \text{ miles}}{1 \text{ gallon}}}$
• $\boldsymbol{\frac{\$10.25}{1 \text{ hour}}}$