Unit rates
A unit rate tells you the rate for 'one' of something. It helps you compare deals and understand speed. Think 'miles per hour' or 'price per pound'. It's all about figuring out 'how much for one?'
Concept
A rate is a ratio that compares two quantities with different units. A **unit rate** is a special type of rate where the second quantity is **one**. **Finding the Unit Rate** To find a unit rate, you divide the first quantity by the second quantity. The goal is to make the denominator of the rate equal to 1. **Example 1: Finding Speed** A car travels 120 miles in 2 hours. What is its unit rate (speed)? 1. **Write the rate:** 120 miles / 2 hours 2. **Divide to get a denominator of 1:** * Divide both the top and bottom by 2. * (120 ÷ 2) / (2 ÷ 2) = 60 miles / 1 hour 3. **The Unit Rate:** The speed is 60 miles per hour (mph). **Example 2: Finding the Better Deal (Unit Price)** * Store A sells 10 apples for $5. * Store B sells 12 apples for $6. Which is the better deal? We need to find the unit price (price per apple) for each. * **Store A:** * Rate: $5 / 10 apples * Divide by 10: ($5 ÷ 10) / (10 ÷ 10) = $0.50 / 1 apple * Unit Price: 50 cents per apple. * **Store B:** * Rate: $6 / 12 apples * Divide by 12: ($6 ÷ 12) / (12 ÷ 12) = $0.50 / 1 apple * Unit Price: 50 cents per apple. In this case, both stores have the same unit price, so the deal is the same. **Key Idea:** The word "per" almost always indicates a unit rate (miles **per** hour, dollars **per** pound, points **per** game). To find it, you divide.
Try it
Practice: Unit rates.