Unit rates and equivalent rates

Learning Objectives Define and identify rates and unit rates. Calculate unit rates from given information, including those involving decimals. Determine if two rates are equivalent. Find equivalent rates using unit rates or proportions. Apply unit rates to solve real-world problems involving comparisons and predictions. Perform division and multiplication with decimals accurately when working with rates. Ever wonder which cereal box is the better deal at the grocery store? 🛒 Or how much gas you're really using per mile? In this lesson, you'll learn about unit rates and equivalent rates, powerful tools for comparing quantities and making smart decisions. We'll focus on how to work with these rates, especially when decimals are involved, which is common in eve...

TermDefinitionExample RateA ratio that compares two quantities with different units.150 miles in 3 hours. Unit RateA rate where the second quantity (denominator) is 1 unit. It tells you 'how much per one.'50 miles per 1 hour (derived from 150 miles in 3 hours). Equivalent RatesRates that represent the same relationship between two quantities, even if the numbers are different.50 miles per hour is equivalent to 100 miles in 2 hours. RatioA comparison of two quantities by division. Rates are a specific type of ratio.The ratio of apples to oranges is 3:2. ProportionAn equation stating that two ratios or rates are equivalent.$\frac{50 \text{ miles}}{1 \text{ hour}} = \frac{100 \text{ miles}}{2 \text{ hours}}$ Decimal OperationsThe rules for adding, subtracting, multiplying, and divi...

Calculating a Unit Rate $\text{Unit Rate} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$ Use this rule to simplify any rate into a 'per one' value, making it easier to understand and compare. Finding Equivalent Rates using Unit Rates $\text{Equivalent Rate} = \text{Unit Rate} \times \text{New Quantity}$ Once you have a unit rate, you can easily calculate how much of the first quantity corresponds to any amount of the second quantity. Finding Equivalent Rates using Proportions $\frac{a}{b} = \frac{c}{d}$ (where $a, b, c, d$ are quantities and $b \neq 0, d \neq 0$) This rule is useful when you know three parts of an equivalent rate relationship and need to find the fourth. Cross-multiplication is often used to solve.