EDEXCEL GCSE FOUNDATION MATHS - What is Proportion

Edexcel GCSE Foundation Maths: What is Proportion?

Understanding Proportion

Proportion is a fundamental concept in mathematics that describes a relationship between two quantities. When two quantities are in proportion, they change at the same rate. In simpler terms, if one quantity doubles, the other quantity also doubles.

Types of Proportion

There are two main types of proportion:

1. Direct Proportion:

• Two quantities are directly proportional when they increase or decrease at the same rate.
• If one quantity doubles, the other quantity also doubles.
• Example: The cost of buying apples is directly proportional to the number of apples you buy.

2. Inverse Proportion:

• Two quantities are inversely proportional when one quantity increases as the other quantity decreases.
• If one quantity doubles, the other quantity halves.
• Example: The time taken to travel a fixed distance is inversely proportional to the speed.

Recognizing Proportional Relationships

You can identify proportional relationships by looking for the following patterns:

• Direct Proportion: The ratio between the two quantities remains constant.
• Inverse Proportion: The product of the two quantities remains constant.

Solving Proportion Problems

Proportion problems can be solved using the following steps:

1. Identify the type of proportion: Direct or inverse.
2. Set up a proportion equation: This equation will express the relationship between the two quantities.
3. Solve for the unknown quantity: This can be done using algebraic manipulation.

Example Problems

Direct Proportion:

• Problem: If 5 apples cost £2, how much will 15 apples cost?
• Solution:
  • Set up the proportion: 5 apples / £2 = 15 apples / x
  • Solve for x: x = (£2 * 15 apples) / 5 apples = £6
  • Answer: 15 apples will cost £6.

Inverse Proportion:

• Problem: If it takes 4 hours to travel 200 miles at a speed of 50 mph, how long will it take to travel the same distance at a speed of 100 mph?
• Solution:
  • Set up the proportion: 4 hours * 50 mph = x hours * 100 mph
  • Solve for x: x = (4 hours * 50 mph) / 100 mph = 2 hours
  • Answer: It will take 2 hours to travel the same distance at 100 mph.

Practice Makes Perfect

To master the concept of proportion, it is essential to practice solving various problems. You can find plenty of practice questions in your textbook or online resources.

Conclusion

Proportion is a fundamental concept in mathematics with applications in various real-world situations. Understanding proportion can help you solve problems involving quantities that change at a constant rate. By mastering this concept, you will gain a deeper understanding of mathematical relationships and improve your problem-solving skills.