7 # 16 - Ratio and Proportional Relationships

Ratios and proportional relationships are essential to mathematics and to all of science, and they are useful in daily life. They are a foundation for understanding rate of change, slope, linear-relationships, and other relationships in mathematics and science. In this chapter, we will motivate and define the concepts of ratio and proportional relationship. We will then see ways of reasoning to solve proportion problems with the aid of tables, graphs, double number lines, and strip diagrams. We will see how unit rates arise from ratios, how they connect ratios to fractions, and how they are behind the common cross-multiplying method for solving proportions. We will see that graphs of proportional relationships are of a special type and we will develop equations for proportional relationships by reasoning quantitatively. We will distinguish proportional relationships from other kinds of relationships, including inversely proportional relationships. Finally, we will study percent increase and decrease.