Unit rates and equivalent rates

Learning Objectives Define and identify ratios, rates, and unit rates. Calculate unit rates from given information. Identify and create equivalent rates. Compare unit rates to determine the 'best deal' or most efficient option. Solve real-world problems involving unit rates and equivalent rates. Explain the meaning of a unit rate in various contexts. Have you ever wondered which box of cereal is a better deal at the grocery store, or how many miles your car can travel on just one gallon of gas? 🛒 In this lesson, you'll learn about unit rates and equivalent rates, which are super useful for comparing things and making smart choices in everyday life. We'll discover how to break down complex comparisons into simple 'per one' amounts. Real-World...

TermDefinitionExample RatioA comparison of two quantities. Ratios can be written as 'a to b', 'a:b', or a fraction a/b.If there are 3 red apples and 2 green apples, the ratio of red to green apples is 3 to 2, or 3:2, or 3/2. RateA ratio that compares two quantities with different units.Traveling 120 miles in 2 hours is a rate. The units are miles and hours. Unit RateA rate where the second quantity (the denominator) is 1 unit. It tells you 'how much per one' of something.If you travel 60 miles in 1 hour, your unit rate is 60 miles per hour. If 5 apples cost $2.50, the unit rate is $0.50 per apple. Equivalent RatesRates that represent the same relationship or value, even if the numbers look different. They are like equivalent fractions.Traveling 60 miles in 1...

Calculating a Unit Rate $$ \text{Unit Rate} = \frac{\text{Quantity 1}}{\text{Quantity 2}} $$ (where Quantity 2 becomes 1 unit) To find a unit rate, divide the first quantity by the second quantity. The goal is to make the second quantity equal to 1. For example, to find miles per hour, divide total miles by total hours. Finding Equivalent Rates $$ \frac{a}{b} = \frac{a \times c}{b \times c} \quad \text{or} \quad \frac{a}{b} = \frac{a \div c}{b \div c} $$ (where c is any non-zero number) To find an equivalent rate, multiply or divide both parts of the rate (numerator and denominator) by the same non-zero number. This is just like finding equivalent fractions. Comparing Unit Rates 1. Calculate the unit rate for each option. 2. Compare the unit values. When you want to...