Ratio and Proportion

Summary and Exam Tips for Ratio and Proportion

Ratio and Proportion is a subtopic of Numbers and the Number System, which falls under the subject Mathematics in the Edexcel IGCSE curriculum.

The concept of a ratio describes the relationship in amount between two or more entities, expressed as $a : b$. Equivalent ratios are those that remain consistent when scaled up or down, such as $3 : 2 = 6 : 4$ (multiplied by 2) and $15 : 20 = 3 : 4$ (divided by 5). An example problem involves finding the ratio $a : c$ when given $a : b = 2 : 3$ and $b : c = 3 : 4$, resulting in $a : b : c = 2 : 3 : 4$.

Proportion involves two types: Direct Proportion and Inverse Proportion. In direct proportion, as one quantity increases or decreases, the other does so correspondingly, such as the relationship between gas prices and food prices. In inverse proportion, as one quantity increases, the other decreases, exemplified by the time taken to complete a task decreasing with more workers.

Exam Tips

• Understand Equivalent Ratios: Practice converting ratios to their simplest form and finding equivalent ratios by multiplying or dividing both terms by the same number.

• Solve Ratio Problems: Familiarize yourself with problems that require finding missing terms in a sequence of ratios, such as $a : b : c$.

• Direct vs. Inverse Proportion: Clearly distinguish between direct and inverse proportion scenarios. Remember, in direct proportion, both quantities move in the same direction, while in inverse proportion, they move in opposite directions.

• Practice Real-World Examples: Apply ratio and proportion concepts to real-world situations, such as scaling recipes or calculating speed and time, to enhance understanding.

• Use Visual Aids: Draw diagrams or use tables to visualize relationships in ratio and proportion problems, which can help in comprehending complex questions.