5 Ratios and Proportion
Section Information
Outcome/Competency: You will be able to apply ratios and proportion to trade specific problems.
Timing: 6h
Rationale: Why is it important for you to learn this skill?
If you go 100 km/hr down the highway, how far will you travel in 2 hours? Three hours? If you are going the same speed throughout, the answer is simple: 200 kilometers, and 300 kilometers. This is a basic example of ratio and proportion. Examples of ratio and proportion are found everywhere in life. Even things we have already learned in this course are examples of ratio and proportion such as fractions, percentages, and unit conversions! Understanding the math behind ratio and proportion will be useful in helping you predict quantities based on information you already know.
Objectives:
To be competent in this area, the individual must be able to:
- Identify a situation as proportional
- Model a situation using a proportion equation
- Solve a proportion equation and interpret the solution
Learning Goals
- Identify, write, and solve proportional equations and scenarios
Introduction:
This module will cover proportionality concepts and situations, ratios, equivalent ratios, and proportion equations. You will also learn how to find the missing factor in a proportion. You will be presented with content and examples and then given opportunities to do practice exercises.
Chapter Contents:
- Topic 1: Proportionality Concept and Situations
- Topic 2: Proportion Equation Scenarios
- Topic 3: Other Situations of Proportionality
- Test: Outcome 5
Topic 1: Proportionality Concept and Situations
1.1 Ratio
A ratio is an association between two or more quantities. There are many ways to describe a situation in terms of ratios. For example, look at this collection:
Here are some correct ways to describe the collection:
- The ratio of squares to circles is 6:3
- The ratio of circles to squares is 3 to 6.
Notice that the shapes can be arranged in equal groups, which allow us to describe the shapes using other numbers.
- There are 2 squares for every 1 circle.
- There is 1 circle for every 2 squares.
A ratio is an association between two or more quantities.
For example, the ratio 3:2 could describe a recipe that uses 3 cups of flour for every 2 eggs, or a boat that moves 3 meters every 2 seconds. One way to represent the ratio 3:2 is with a diagram that has 3 blue squares for every 2 green squares.
1.1 Practice Exercises
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1.2 Equivalent Ratios
A recipe for fizzy juice says, “Mix 5 cups of cranberry juice with 2 cups of soda water.”
To double this recipe, we would use 10 cups of cranberry juice with 4 cups of soda water. To triple this recipe, we would use 15 cups of cranberry juice with 6 cups of soda water.
This diagram shows a single batch of the recipe, a double batch, and a triple batch:
We say that the ratios 5:2, 10:4, and 15:6 are equivalent. Even though the amounts of each ingredient within a single, double, or triple batch are not the sa