Ratios, Proportions, and Real-Life Applications

Introduction

Ratios and proportions are vital for solving problems in GCSE Maths and beyond. They’re practical, appearing in real-life contexts like recipes, map reading, and unit conversions.

This article will cover:

1. The basics of ratios and proportions.
2. Practical real-life applications.
3. Strategies to tackle ratio problems effectively in exams.

1. Understanding Ratios

   Simplifying Ratios

   Ratios can be simplified like fractions by dividing all terms by their highest common factor (HCF).

   Example: Simplify .

   1. HCF = 6.
   2. Simplify: .

   Sharing Amounts in a Given Ratio

   Split amounts proportionally based on the ratio.

   Example: Share £120 in the ratio .

   1. Total parts = .
   2. One part = .
   3. Shares: , .

2. Understanding Proportions

   Proportions compare two ratios and can be direct or inverse.

   Direct Proportion

   Quantities increase or decrease together.

   Example: If 5 apples cost £10, how much will 8 apples cost?

   1. Set up proportion: .
   2. Solve: .

   Inverse Proportion

   One quantity increases while the other decreases.

   Example: If 3 people take 12 hours to paint a house, how long will 6 people take?

   1. Use inverse proportion formula: .
   2. Solve: .

3. Real-Life Applications

   Recipes:

   • Scale ingredients up or down based on serving size.

   Example: A recipe for 4 people uses 200g of flour. How much is needed for 6 people?

      

   Maps and Scales:

   • Use ratios to interpret map distances.

   Example: On a map with a scale of , 2cm represents cm, or 1km.

   Currency Conversion:

   • Convert amounts using exchange rates.

   Example: £1 = €1.20. How many euros is £50?

      

Practice Question

Question: Divide £180 in the ratio .

Solution:

1. Total parts = .
2. One part = .
3. Shares: , .

Conclusion

Mastering ratios and proportions is essential for solving real-life problems in GCSE Maths. Practise these concepts regularly to gain confidence in your exams.

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