Unit rates

Learning Objectives Define the terms ratio, rate, and unit rate, and differentiate between them. Calculate a unit rate from a given rate with different units. Use unit rates to compare values and determine the 'better buy' in real-world scenarios. Solve multi-step problems involving speed, density, and other common unit rates. Convert rates from one set of units to another using dimensional analysis (e.g., km/h to m/s). Interpret the unit rate as the constant of proportionality (slope) in a linear relationship. You're at the store and see two different sizes of your favorite snack. Which one is the better deal? 🛒 Unit rates are the mathematical tool you need to become a savvy shopper! This tutorial will explore the concept of unit rates, which are a powerful...

TermDefinitionExample RatioA comparison of two or more quantities, often expressed with a colon or as a fraction. The quantities being compared may or may not have the same units.The ratio of teachers to students in a school is 1:25 or 1/25. RateA special type of ratio that compares two quantities measured in different units.A car travels 240 kilometers in 3 hours. The rate is 240 km / 3 hours. Unit RateA rate that has been simplified so that the second quantity (the denominator) is 1.The car's rate of 240 km in 3 hours simplifies to a unit rate of 80 km per 1 hour (or 80 km/h). ProportionAn equation stating that two ratios or rates are equivalent. Proportions are often used to solve for an unknown quantity.240 km / 3 hours = x km / 1 hour. Solving for x gives the unit rate. Dimensio...

Calculating a Unit Rate \text{Unit Rate} = \frac{\text{Quantity A}}{\text{Quantity B}} To find the rate 'per one unit' of Quantity B, divide Quantity A by Quantity B. The result will be 'some amount of A per 1 unit of B'. Proportional Relationship Formula y = kx This formula models a linear relationship where 'k' is the unit rate (constant of proportionality). 'x' is the independent variable (e.g., number of items, hours) and 'y' is the dependent variable (e.g., total cost, total distance). This shows that the unit rate is the slope of the line.