Unit rates and equivalent rates

Learning Objectives Define a rate and a unit rate. Calculate unit rates from given information. Compare different rates by finding their unit rates. Identify and create equivalent rates. Solve real-world problems involving unit rates and equivalent rates. Use unit rates to find missing values in proportional relationships. Ever wonder how stores compare prices for different sized items? 🛒 Or how fast a cheetah runs? 🐆 These questions can be answered using unit rates! In this lesson, you'll discover how to find and use unit rates to make comparisons and solve everyday problems. Understanding unit rates helps you be a smart shopper, a better planner, and a confident problem-solver in many situations. Real-World Applications Comparing prices at the grocery store (e....

TermDefinitionExample RatioA comparison of two quantities by division. Ratios can be written as a:b, a to b, or a/b.The ratio of 3 apples to 2 bananas is 3:2. RateA ratio that compares two quantities with different units.Driving 120 miles in 2 hours is a rate of 120 miles/2 hours. UnitA single item or quantity used as a standard of measurement.In 'miles per hour', 'hour' is a unit of time, and 'mile' is a unit of distance. Unit RateA rate where the second quantity (denominator) is 1 unit. It tells you 'how much per one'.If you drive 60 miles in 1 hour, the unit rate is 60 miles per hour. Equivalent RatesRates that represent the same relationship between quantities. They can be simplified or scaled to show the same unit rate.120 miles in 2 hours and...

Calculating a Unit Rate \text{Unit Rate} = \frac{\text{Quantity 1}}{\text{Quantity 2}} To find a unit rate, divide the first quantity by the second quantity. The goal is to make the second quantity equal to 1 unit. The units of Quantity 1 will be 'per' the unit of Quantity 2. Finding Equivalent Rates (Multiplication) \frac{A}{B} = \frac{A \times C}{B \times C} To find an equivalent rate, you can multiply both the numerator and the denominator of a given rate by the same non-zero number (C). This scales the rate up while keeping the relationship the same. Finding Equivalent Rates (Division) \frac{A}{B} = \frac{A \div C}{B \div C} To find an equivalent rate, you can divide both the numerator and the denominator of a given rate by the same non-zero number (C)....