Solving the Mathematical Quandary: What's the Answer to 8-4×5?

When we encounter a problem like 8–4×5, it's crucial to understand the order of operations. Let's delve into how to solve such a problem step-by-step, using the BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) rule.

Understanding the Order of Operations: BIDMAS

When faced with mathematical expressions, following the correct order of operations is essential. The acronym BIDMAS (or BODMAS in some regions) helps us remember the correct sequence.

Brackets Indices (or Orders) Division and Multiplication (performed from left to right) Addition and Subtraction (performed from left to right)

Let's apply BIDMAS to solve the expression 8–4×5:

Step-by-Step Solution Using BIDMAS

Multiplication first: According to BIDMAS, we start with multiplication. So, we calculate 4×5:

8 - 4×5
 8 - 20

Subtraction: Now we perform the subtraction as required by the problem statement.

 8 - 20
 -12

Therefore, the correct answer is -12.

Common Misinterpretations and Missteps

Some might approach the problem differently, leading to incorrect answers. For instance, the expression might be misunderstood as 8–45/5. Let's break it down:

Misinterpretation: 8–45/5

If interpreted as 8 - (45/5), the solution would be:

Brackets: Perform 45/5 first.

 8 - (45/5)
 8 - 9

Subtraction: Then, perform the subtraction.

 -1

Clearly, this is different from the original problem, demonstrating the importance of following the BIDMAS rule.

Written Expressions vs. Correct Syntax

For clarity and accuracy, mathematical expressions should be written in a way that avoids ambiguity. A clearer expression would be 8 x 4 - 5, based on the correct order of operations:

Calculate 8 x 4: Subtract 5 from the result:

This yields:

 32 - 5
 27

Thus, the final answer is 27 when written 8 x 4 - 5.

Further Proof of Solution

To further verify the solution, we can use the premise y 8 - 4×5 and ensure the inverse operation is correct:

Proof Using Premise y 8 - 4×5

The premise is given as:

Brackets and Indices: None in this case. Multiplication: 4×5 20. Subtraction: 8 - 20 -12.

Now, let's check the inverse:

Starting with y -12. Add 4×5 to both sides: 8 - 20 -12. This simplifies to 8 - 20 -12.

The proof confirms that the solution y -12 is correct.

Conclusion

The correct approach to solving 8–4×5, as per the BIDMAS rule, yields -12. Understanding and correctly applying the order of operations is crucial in ensuring accuracy in mathematical calculations. Always write expressions clearly to avoid misinterpretations and ensure the correct solution.