# CHAPTER 5 - RATIOS, PROPORTIONS, AND APPLICATIONS

### OBJECTIVES

- Identify ratios and rates to compare quantities.
- Set up ratios and use them to solve problems involving allocation and sharing of quantities.
- Solve problems by determining unknown quantities using proportions as equivalent sets of ratios.
- Allocate quantities on a proportional basis using pro-ration as an application of proportions.
- Convert currencies between countries using exchange rates.
- Determine index numbers and their applications.

### CHAPTER OUTLINE

5.1 Ratios

5.2 Proportions

5 Review Exercises

5 Self-Test Exercises

## Introduction

One of the ways in which we use mathematics in our daily lives is through the comparison of numbers and quantities of two or more items. Numbers and quantities are more meaningful and easier to work with when relevant comparisons can be made between them. A **ratio** is a comparison or relationship between two or more quantities. An example of how ratios can be used in our daily lives is in grocery shopping: if a 260 gram box of cereal costs $2.67, and a 400 gram box of the same cereal costs $3.99, we can use ratios to calculate the unit prices and determine which box of cereal is more economical.

When two sets of ratios are equal, we say that they are **proportional** to each other. We can use proportions to calculate unknown quantities that would otherwise be difficult to estimate. For example, if you wanted to calculate the amount of gas needed to travel 375 km, knowing that the fuel efficiency of your car is 9.8 litres per 100 km, then you could set up a proportion equation to determine the amount of gas needed for the trip.

In this chapter, we will learn the concepts related to ratios to be able to solve problems involving ratios, proportions, and pro-rations, including business applications such as currency conversions and index numbers.

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