Summary
Ratios and proportions involve comparing quantities and understanding their relationships. Ratios express the relationship between two or more quantities, while proportions indicate that two ratios are equivalent.
- Ratio — a comparison of two or more quantities in a set order. Example: The ratio of 3:2 can be expressed as 6:4 by multiplying both terms by 2.
- Equivalent Ratios — ratios that are the same when simplified or scaled. Example: 15:20 is equivalent to 3:4 when both terms are divided by 5.
- Direct Proportion — when two quantities increase or decrease at the same rate. Example: If y is directly proportional to x, doubling x will double y.
- Inverse Proportion — when one quantity increases as the other decreases. Example: If y is inversely proportional to x, doubling x will halve y.
Exam Tips
Key Definitions to Remember
- A ratio is a comparison of two or more quantities.
- Proportion is a constant ratio between two sets.
Common Confusions
- Confusing direct and inverse proportions.
- Misinterpreting the order of terms in a ratio.
Typical Exam Questions
- How do you simplify the ratio 1 hour : 24 minutes? Divide both terms by 24 to get 5:2.
- How many pieces of candy does Wali receive if shared in the ratio 5:9:11? Wali receives 36 pieces.
- What is the new ratio if Alex and Bobbie each spend $4? Calculate remaining money and simplify to find the new ratio.
What Examiners Usually Test
- Ability to simplify and calculate equivalent ratios.
- Understanding and solving problems involving direct and inverse proportions.