Study Notes
Ratios compare two quantities, showing how many times one value contains or is contained within the other. Proportions state that two ratios are equal.
- Ratio — a comparison of two quantities by division.
Example: For every 6 toffees, there are 8 lollipops, so the ratio is 6:8. - Simplifying Ratios — dividing both terms of a ratio by the same number to find an equivalent ratio in simplest form.
Example: The ratio of 50 boys to 70 girls simplifies to 5:7. - Equivalent Ratios — ratios that express the same relationship between numbers.
Example: 6:8 is equivalent to 3:4. - Proportion — an equation stating that two ratios are equal.
Example: If 100 grams of flour makes 4 cookies, 200 grams makes 8 cookies. - Direct Proportion — when one quantity increases, the other increases at the same rate.
Example: If A increases, B increases. - Inverse Proportion — when one quantity increases, the other decreases at the same rate.
Example: If A increases, B decreases.
Exam Tips
Key Definitions to Remember
- Ratio: A comparison of two quantities by division.
- Proportion: An equation stating that two ratios are equal.
- Direct Proportion: When one quantity increases, the other increases at the same rate.
- Inverse Proportion: When one quantity increases, the other decreases at the same rate.
Common Confusions
- Mixing up direct and inverse proportions.
- Forgetting to simplify ratios by dividing both terms by the same number.
Typical Exam Questions
- What is the simplified form of the ratio 50:70? 5:7
- If 100 grams of flour makes 4 cookies, how many cookies can be made with 200 grams? 8 cookies
- What happens to B if A increases in a direct proportion? B increases
What Examiners Usually Test
- Ability to simplify ratios correctly.
- Understanding of direct and inverse proportions.
- Application of equivalent ratios in problem-solving.