Ratio and Proportion

Summary and Exam Tips for Ratio and Proportion

Ratio and Proportion is a subtopic of Numbers, which falls under the subject Mathematics in the IB MYP curriculum. This topic involves understanding and manipulating ratios and proportions to solve various mathematical problems.

• Ratios express the relative size of two or more values. For example, in a school with 50 boys and 70 girls, the ratio of boys to girls is $50:70$, which simplifies to $5:7$ by dividing both sides by 10.
• Equivalent Ratios can be found by multiplying or dividing both sides of a ratio by the same number. For instance, mixing orange squash in a $1:4$ ratio of orange to water can be scaled to $100:400$ or $200:800$.
• Proportion refers to the relationship where one quantity changes in relation to another. There are two types:
  • Direct Proportion: As one quantity increases, the other also increases (e.g., $A:B$).
  • Inverse Proportion: As one quantity increases, the other decreases (e.g., $A \propto \frac{1}{B}$).
• Practical applications include determining lengths, masses, and other quantities based on given ratios and proportions.

Exam Tips

• Simplify Ratios: Always reduce ratios to their simplest form by dividing both sides by their greatest common divisor.
• Understand Proportions: Recognize whether a problem involves direct or inverse proportion and apply the appropriate method.
• Practice with Real-Life Examples: Use practical scenarios, like mixing ingredients or dividing objects, to better understand ratios and proportions.
• Check Units: Ensure that the units are consistent when calculating ratios and proportions to avoid errors.
• Use Cross-Multiplication: For solving proportion problems, cross-multiplication can be a quick and effective method.

By mastering these concepts, you'll be well-prepared to tackle ratio and proportion questions in your exams.