Study Notes
Ratios and proportions are mathematical concepts used to compare quantities and determine how they change relative to each other.
- Ratio — a comparison of two quantities by division. Example: The ratio of boys to girls is 50:70, which simplifies to 5:7.
- Equivalent Ratios — ratios that express the same relationship between numbers. Example: 1:4 is equivalent to 100:400 and 200:800.
- Proportion — an equation stating that two ratios are equal. Example: If one parameter changes according to another, they are proportional.
- 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. Example: If A increases, B decreases.
Exam Tips
Key Definitions to Remember
- Ratio: A comparison of two quantities by division.
- Equivalent Ratios: Ratios that express the same relationship.
- 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 to their simplest form.
Typical Exam Questions
- Write the ratio 40:28 in its simplest form? Answer: 10:7
- In a bracelet, for every yellow bead, there are 3 blue beads. How many blue beads will there be in a bracelet with 5 yellow beads? Answer: 15 blue beads
- A piece of timber 299 cm long is cut into three pieces in the ratio of 3:7:13. Determine the lengths of the three pieces? Answer: 39 cm, 91 cm, 169 cm
What Examiners Usually Test
- Ability to simplify and find equivalent ratios.
- Understanding of direct and inverse proportions.
- Application of ratios and proportions in real-world problems.