📘intermediate algebra review

key term - Proportion

Definition

Proportion is a mathematical relationship between two or more quantities where the ratio between them remains constant. It is a fundamental concept that is crucial in understanding and solving problems related to mixture and uniform motion applications.

5 Must Know Facts For Your Next Test

  1. Proportions can be used to solve mixture problems by setting up equations that represent the relationships between the components.
  2. In uniform motion problems, proportions can be used to determine the relationship between time, distance, and speed.
  3. Proportions are often represented using the equality of two ratios, such as a/b = c/d.
  4. Solving proportions involves cross-multiplying the terms to find the unknown value.
  5. Proportions are essential in scaling and creating similar figures, as the ratios between corresponding sides must be equal.

Review Questions

  • How can proportions be used to solve mixture problems?
    • In mixture problems, proportions can be used to represent the relationships between the different components of the mixture. By setting up equations that express the ratios between the quantities of the components, you can solve for the unknown values. For example, if you have a mixture of two liquids, you can use a proportion to represent the ratio of the volumes or concentrations of the two liquids, and then solve for the unknown quantity.
  • Explain how proportions are used in uniform motion problems.
    • In uniform motion problems, proportions can be used to establish the relationships between time, distance, and speed. The fundamental proportion in these problems is $\text{distance} / \text{time} = \text{speed}$. By setting up proportions that relate the given information, such as the ratios of distances traveled or the ratios of speeds, you can solve for the unknown values in the problem.
  • Analyze the role of proportions in scaling and creating similar figures.
    • Proportions are essential in scaling and creating similar figures because the ratios between corresponding sides must be equal. This means that if you have two similar figures, the ratio of any two corresponding sides will be the same. By using proportions, you can determine the scale factor between the figures and use it to calculate the dimensions of one figure given the dimensions of the other. Proportions also play a crucial role in maintaining the correct aspect ratio when resizing images or objects.