Ratio and Proportion | Year 8 Mathematics (Cambridge) PDF Download

Understanding Ratios

• Ratios compare quantities or amounts relative to each other.
• Written as a fraction, e.g., 3:5 or 3/5.
• Example: If there are 3 red balls and 5 blue balls, the ratio of red to blue balls is 3:5.

Key Concepts

• Ratios can be simplified like fractions.
• Ratios can be used to scale quantities up or down.

Solving Problems Involving Ratios

• Example: If a recipe calls for 2 cups of flour and 3 cups of sugar, and you want to make half the recipe, you need 1 cup of flour and 1.5 cups of sugar.

Working with Proportions

• Proportions are equations stating that two ratios are equal.
• Example: where a, b, c, and d are quantities.

Finding Missing Values

• Example: If 2 oranges cost $3, how much do 5 oranges cost? Set up the proportion  and solve for x.

Applications of Proportions

• Used in scaling drawings or maps.
• Example: If 1 inch on a map represents 10 miles, how many miles are represented by 3.5 inches on the map?

Using Ratios in Real Life

• Cooking recipes, where ingredients need to be adjusted based on servings.
• Example: Doubling a recipe that calls for 1 cup of flour and 1/2 cup of sugar.

Summary

Understanding ratios and proportions is essential for solving problems involving relative quantities and scaling. Ratios compare different quantities, while proportions establish equality between ratios. Both concepts are widely applicable in everyday life, from cooking to scaling maps.