The Order of Operations: Why Alec Got It Wrong

Let’s analyse a common mistake students make when dealing with simple arithmetic expressions. Here’s the problem:

Alec needs to work out the value of 2 + 3 × 4
He writes:
2 + 3 = 5 and 5 × 4 = 20, so 2 + 3 × 4 = 20
Alec is wrong.
Explain why.

The Correct Approach: The Order of Operations (BODMAS/PEMDAS)

Alec’s mistake stems from not following the correct order of operations. In mathematics, we have a set of rules that dictate the order in which we perform calculations to ensure everyone arrives at the same answer. This is often remembered by the acronyms BODMAS or PEMDAS:

• BODMAS:
  • Brackets (or Parentheses)
  • Orders (or Exponents)
  • Division
  • Multiplication
  • Addition
  • Subtraction
• PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

BODMAS/PEMDAS tells us the priority of different operations. Multiplication and division take precedence over addition and subtraction.

Why Alec’s Method is Wrong

Alec performed the addition (2 + 3) before the multiplication (3 × 4). This violates the order of operations. According to BODMAS/PEMDAS, multiplication should be done before addition.

The Correct Calculation

Here’s the correct way to calculate 2 + 3 × 4:

1. Multiplication First: Perform the multiplication: 3 × 4 = 12
2. Addition Second: Add the result to 2: 2 + 12 = 14

Therefore, 2 + 3 × 4 = 14

The Importance of Order

The order of operations is crucial for obtaining the correct answer in mathematical expressions. Without it, calculations would be ambiguous and lead to different results.

In Summary

Alec is wrong because he added 2 and 3 before multiplying 3 and 4. The correct order of operations (BODMAS/PEMDAS) dictates that multiplication must be performed before addition. The correct answer is 14.

Need Help Mastering Order of Operations?

If you’re struggling with the order of operations or other GCSE maths topics, consider getting some extra assistance. GCSE Maths Online Tuition can provide support and help you build a strong foundation in mathematics. A tutor can work with you to explain the rules, provide practice problems, and help you avoid common mistakes. They can help you develop a clear understanding of the order of operations and improve your overall maths skills.