Study Notes
The topic of Ratio and Proportions involves understanding how quantities relate to each other and how they can be simplified or compared. Ratios can be expressed in different ways and simplified by dividing both sides by the same number. Proportions describe how one quantity changes in relation to another, either directly or inversely.
- Ratio — a comparison of two quantities by division.
Example: For every 6 toffees, there are 8 lollipops, which can be written as 6:8. - Simplifying Ratios — dividing both parts of a ratio by the same number to find an equivalent ratio.
Example: The ratio 50:70 can be simplified to 5:7 by dividing both numbers by 10. - Direct Proportion — when one quantity increases or decreases, the other does the same.
Example: If A increases, B increases proportionally. - Inverse Proportion — when one quantity increases, the other decreases.
Example: If A increases, B decreases proportionally.
Exam Tips
Key Definitions to Remember
- Ratio: A comparison of two quantities by division.
- Proportion: A statement that two ratios are equal.
- Direct Proportion: Both quantities increase or decrease together.
- Inverse Proportion: One quantity increases while the other decreases.
Common Confusions
- Mixing up direct and inverse proportions.
- Forgetting to simplify ratios by dividing by the same number.
Typical Exam Questions
- How do you simplify the ratio 50:70? Divide both numbers by 10 to get 5:7.
- If Bella needs 100g of flour for 4 cookies, how many cookies can she make with 200g? She can make 8 cookies.
- What happens to A if B increases in a direct proportion? A also increases.
What Examiners Usually Test
- Ability to simplify ratios correctly.
- Understanding of direct and inverse proportions.
- Application of ratios and proportions in real-life problems.