Chapter 5 – Ratios, Proportions, and Applications
OBJECTIVES
- Identify ratios and rates to compare quantities.
- Set up ratios and use them to solve problems involving the allocation and sharing of quantities.
- Solve problems by determining unknown quantities using proportions as equivalent sets of ratios.
CHAPTER OUTLINE
5.1 Ratios
5.2 Proportions
5 Review Exercises
5 Self-Test Exercises
5. Case Study – Lightning Wholesale
Introduction
We use mathematics daily by comparing 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 your car’s fuel efficiency 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.
Unless otherwise indicated, this chapter is an adaptation of the eTextbook Foundations of Mathematics (3rd ed.) by Thambyrajah Kugathasan, published by Vretta-Lyryx Inc., with permission. Adaptations include supplementing existing material and reordering chapters.
