2-7 Solving Proportions
Objective
To solve and apply proportions
Lesson Vocabulary
- proportion
- cross products
- Cross Products Property
In the Solve It, the number of red beads and the number of blue beads are quantities that have a proportional relationship. This means that the ratio of the quantities is constant even though the quantities themselves can change. For example, as you are making the necklace you will have 2 red beads and 3 blue beads, then 4 red beads and 6 blue beads, then 6 red beads and 9 blue beads, and so on. At each stage, the ratio of red beads to blue beads remains constant, 2 : 3.
A proportional relationship can produce an infinite number of equivalent ratios. Any two of these can be used to write a proportion. A proportion is an equation that states that two ratios are equal. For example,
Essential Understanding If two ratios are equal and a quantity in one of the ratios is unknown, you can write and solve a proportion to find the unknown quantity.
Think
How is this problem related to problems you've solved before?
Solving this proportion is similar to solving a one-step equation using multiplication. You can simply multiply by 12 to isolate m.
Problem 1 Solving a Proportion Using the Multiplication Property
What is the solution of the proportion
Table of Contents
- 2-1 and 2-2 Solving One- and Two-Step Equations
- 2-3 Solving Multi-Step Equations
- 2-4 Solving Equations With Variables on Both Sides
- 2-5 Literal Equations and Formulas
- 2-6 Ratios, Rates, and Conversions
- 2-7 and 2-8 Solving Proportions and Using Similar Figures
- 2-9 Percents
- 2-10 Change Expressed as a Percent
- 3-1 Inequalities and Their Graphs
- 3-2 Solving Inequalities Using Addition or Subtraction
- 3-3 Solving Inequalities Using Multiplication or Division
- 3-4 Solving Multi-Step Inequalities
- 3-5 Working With Sets
- 3-6 Compound Inequalities
- 3-7 Absolute Value Equations and Inequalities
- 3-8 Unions and Intersections of Sets
- Chapter 1 Foundations for Algebra
- Chapter 2 Solving Equations
- Chapter 3 Solving Inequalities
- Chapter 4 An Introduction to Functions
- Chapter 5 Linear Functions
- Chapter 6 Systems of Equations and Inequalities
- Chapter 7 Exponents and Exponential Functions
- Chapter 8 Polynomials and Factoring
- Chapter 9 Quadratic Functions and Equations
- Chapter 10 Radical Expressions and Equations
- Chapter 11 Rational Expressions and Functions
- Chapter 12 Data Analysis and Probability