Ratios and Proportional Relationships

A ratio compares two quantities. If a class has 12 boys and 18 girls, the ratio of boys to girls is 12:18, which simplifies to 2:3. A proportion is an equation stating that two ratios are equal: [formula] To solve a proportion, cross-multiply: a cdot d = b cdot c.

Example: A recipe calls for 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?

Part-to-Part ratio: compares one part to another part. Example: boys to girls = 2:3. Part-to-Whole ratio: compares one part to the total. Example: boys to total = 2:5 (since 2 + 3 = 5). The SAT often requires you to convert between these two types.

Example: In a bag of 40 marbles, the ratio of red to blue marbles is 3:5. How many red marbles are there?

When the SAT gives you a ratio like a:b:c, the total parts are a + b + c. If the total quantity is T, each part equals frac{T}{a+b+c}. This shortcut saves 20+ seconds on ratio problems.