Ratio and Proportion | Year 7 Mathematics (Cambridge) PDF Download

Understanding Ratios

• Definition of Ratio: A ratio is a comparison of two quantities by division.
• Writing Ratios: Ratios are written in the form a : b or a/b, where a and b are numbers.
• Interpreting Ratios: Ratios show the relationship between two quantities or parts of a whole.

Key Concepts in Ratios

• Equivalent Ratios: Ratios that express the same relationship, e.g., 2 : 3 is equivalent to 4 : 6.
• Simplifying Ratios: Divide both parts of the ratio by their greatest common factor to simplify it, e.g., 6 : 9 simplifies to 2 : 3.

Applications of Ratios

• Ratio Problems: Solving problems involving ratios, such as mixing ingredients in a recipe or dividing resources.

Understanding Proportions

• Definition of Proportion: A proportion is an equation stating that two ratios are equal, e.g., a/b = c/d.
• Solving Proportions: Cross-multiplication method to solve proportions, ensuring both sides are equal.

Key Concepts in Proportions

• Direct Proportion: When two quantities increase or decrease at the same rate, e.g., if a doubles, b also doubles.
• Inverse Proportion: When one quantity increases as the other decreases at a constant rate, e.g., if a doubles, b halves.

Examples

• Ratio Example: If there are 4 red marbles and 6 blue marbles, the ratio of red to blue marbles is 4 : 6 or simplified to 2 : 3.
• Proportion Example: A recipe requires 2 cups of flour for every 3 cups of milk. To make 6 cups of the mixture, how much flour is needed?
  
  Cross-multiplying gives 2⋅6 = 3x
  x = 12/3 = 4 cups of flour needed.

Summary

Understanding ratios involves comparing quantities, writing ratios in different forms, and applying them in various scenarios like recipes or resource allocation. Proportions extend this concept by stating equality between two ratios, useful in solving practical problems involving scaling or mixing quantities.