Unit 2: Ratios and Proportions
Explore the fascinating world of ratios and proportions, mastering real-world applications and mathematical relationships
Unit 2 Overview
In this unit, you will explore the thrilling world of rates, ratios, and proportions! You will learn how to compare quantities with a ratio, such as the ratio of cats to dogs that can be found in a pet store. You will also learn that rates compare two different things, such as the speed of the car in miles per hour.
You'll be learning about proportional reasoning to help you solve problems in which the quantities either increase or decrease in a fixed way, e.g., scaling a recipe up from a cookbook. Additionally, you are going to use tables, graphs, and diagrams to picture these relations and make many real-life math problems—for example, buying goods in a store or how fast one has to move to keep the appointment.
Get ready to really nail down these important skills to apply them in practical life.
Learning Objectives
- Understand what a ratio is and how it compares two quantities
- Write ratios in different forms: as fractions, with a colon, or using the word "to"
- Calculate unit rates in various contexts (e.g., miles per hour, price per item)
- Set up and solve proportions using cross-multiplication
- Apply proportional reasoning to real-world problems
Your Progress
Introduction to Ratios
What You'll Learn:
- Understanding what a ratio is and how it compares two quantities
- Writing ratios in different forms: as fractions, with a colon, or using the word "to"
- Identifying real-world examples of ratios (e.g., comparing boys to girls in a class)
- Simplifying ratios by dividing both terms by their greatest common factor
Khan Academy: Introduction to Ratios
This video introduces the concept of ratios, explaining how they compare two quantities and can be written in different forms. It provides clear examples to help you understand how to read, write, and solve ratio problems.
Watch on YouTubeMath Antics: Ratios and Rates
This video explores both ratios and rates, showing how they are used to compare quantities. It uses fun and simple examples, making it easy to understand the difference between a ratio and a rate.
Watch on YouTubeUnderstanding Unit Rates and Ratios
What You'll Learn:
- Defining a unit rate as a ratio where the second term is 1
- Calculating unit rates in various contexts (e.g., miles per hour, price per item)
- Using unit rates to compare different situations (e.g., which product is a better buy)
- Applying unit rates to real-life problems involving speed, density, and cost
Rates and Unit Rates
This video introduces rates, explaining how they compare two different quantities with different units. It shows how to calculate rates and use them to solve real-world problems.
Watch on YouTubeRates and Unit Rates
This video explains the difference between rates and unit rates. It shows how to calculate unit rates by dividing two quantities, making it easy to understand and solve problems.
Watch on YouTubeProportional Reasoning
What You'll Learn:
- Understanding proportional relationships between quantities
- Setting up and solving proportions (equations that state two ratios are equal)
- Using cross-multiplication to find unknown values in proportions
- Applying proportional reasoning to solve problems involving scale drawings, maps, and real-life comparisons
Khan Academy: Proportional Relationships
This video introduces proportional relationships, explaining how two quantities increase or decrease together at the same rate. It shows how to identify and represent proportional relationships using tables and graphs.
Watch on YouTubeMath Antics - Proportions
This video explains what proportions are and how to solve proportional problems using cross-multiplication. It provides simple, clear examples that make understanding proportions easy.
Watch on YouTubeUsing Equivalent Fractions in Ratios
What You'll Learn:
- Identifying equivalent fractions and how they relate to ratios
- Creating equivalent ratios by multiplying or dividing both terms by the same number
- Using equivalent fractions to simplify complex ratios
- Applying equivalent fractions in solving ratio problems and real-world situations
Math Antics: Simplifying Fractions
This video explains how to simplify fractions by dividing both the numerator and denominator by their greatest common factor (GCF). It uses clear visuals to show how fractions can be reduced to their simplest form.
Watch on YouTubeKhan Academy: Equivalent Fractions
This video introduces equivalent fractions, explaining how fractions that look different can represent the same value. It shows how to create equivalent fractions by multiplying or dividing both the numerator and denominator by the same number.
Watch on YouTube