Ratio, Proportion, and Rates of Change

• What are the two types of ratios mentioned in the study material?

  Part-to-part and part-to-whole
• What does simplifying ratios involve?

  Reducing the ratio to its simplest form
• How can you solve problems involving direct proportions?

  By setting up a proportion and solving for the unknown
• How can you solve problems involving inverse proportions?

  By multiplying the two quantities and setting them equal to a constant
• What is a proportion?

  A statement that two ratios are equal
• How do you solve proportion problems using cross-multiplication?

  By multiplying the means and the extremes of the proportion
• In what real-world contexts can proportions be applied?

  Scaling recipes or maps
• What are rates of change?

  Measurements of how one quantity changes in relation to another
• How can you calculate speed as a rate of change?

  By dividing distance by time
• How can density be calculated as a rate of change?

  By dividing mass by volume
• How can rates of change be interpreted in graphs?

  By analyzing the slope of the graph
• In what contexts can rates of change be interpreted?

  In economics or physics
• What are the key concepts related to ratios and proportions?

  • Understanding and simplifying ratios
  • Solving problems involving direct and inverse proportions
  • Solving proportion problems using cross-multiplication
  • Applying proportions in real-world contexts
• What are the key concepts related to rates of change?

  • Understanding and calculating speed, density, and other rates
  • Interpreting rates of change in graphs
  • Contexts such as economics or physics