Summary
Ratios compare two quantities, showing how many times one value contains or is contained within the other. Proportions indicate 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 — reducing the terms of a ratio to their smallest whole numbers. Example: The ratio 50:70 can be simplified to 5:7 by dividing both numbers by 10.
- Equivalent Ratios — ratios that express the same relationship between numbers. Example: 6:8 is equivalent to 3:4 when both terms are divided by 2.
- Direct Proportion — when one quantity increases, the other increases at the same rate. Example: If A increases, B increases proportionally.
- Inverse Proportion — when one quantity increases, the other decreases at the same rate. Example: If A increases, B decreases proportionally.
Exam Tips
Key Definitions to Remember
- Ratio
- Proportion
- Direct Proportion
- Inverse Proportion
Common Confusions
- Mixing up direct and inverse proportions
- Forgetting to simplify ratios
Typical Exam Questions
- How do you simplify the ratio 50:70? Divide both numbers by 10 to get 5:7
- What is the equivalent ratio of 6:8? 3:4, by dividing both terms by 2
- If 100 grams of flour makes 4 cookies, how many cookies can be made with 200 grams? 8 cookies
What Examiners Usually Test
- Ability to simplify ratios
- Understanding of direct and inverse proportions
- Calculation of equivalent ratios