Understanding the Result of 111 × 0 2: A Deep Dive into Mathematical Operations

Welcome to our exploration of an intriguing mathematical problem. The apparent contradiction of '111 × 0 2' can be clarified through a detailed understanding of the order of operations, specifically the PEMDAS (Presented, Evaluated, Math Discovered, Applied, Simplified) and BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rules.

Order of Operations Explained

The order of operations, widely known as PEMDAS (or BODMAS in some regions), outlines the steps to correctly evaluate mathematical expressions. It includes the following steps:

Parentheses (or Brackets) Exponents (or Orders) Multiplication and Division (from left to right) Addition and Subtraction (from left to right)

Evaluating 111 × 0 2

At first glance, the statement 111 × 0 2 appears incorrect. Let's break down the expression step by step:

Step-by-Step Breakdown

Identify Operations: In the expression 111 × 0, we have multiplication and addition. Perform Multiplication First: According to PEMDAS, we first perform the multiplication 1 × 0, which equals 0. Substitute Back into the Expression: Substituting 0 back into the expression gives us 111 11 0. Perform Addition from Left to Right: We then perform the addition from left to right: First, 111 11 122. Then, 122 0 122.

However, the correct evaluation, assuming the original expression was meant to be another form, can be shown as follows:

Correct Addition and Reduction

Let's re-evaluate the expression as provided:

Combine the integers 1111111111111 and 2 first: 1111111111111 2 1111111111113. Then, apply multiplication by zero: 1111111111113 × 0 0. Finally, add the remaining values: 30 0 2 32.

Therefore, the final answer is 32.

Multiplication by Zero: A Fundamental Principle

When any number is multiplied by zero, the result is always zero. This is a fundamental principle of mathematics. The expression 111 × 0 0 is correct, and it doesn't cancel out the addition of the subsequent terms. Instead, it provides the result for the multiplication operation, which is then added in the correct sequence.

Conclusion

The key takeaway is that the order of operations and the principle of multiplication by zero are crucial in correctly evaluating mathematical expressions. Understanding these rules can help avoid common mistakes and ensure accurate results.

Key Points

PEMDAS (BODMAS): Order of operations including multiplication and addition. Multiplication by Zero: Any number multiplied by zero equals zero. Evaluation Sequence: Correct application of operations from left to right.

By following these rules, you can confidently solve complex mathematical expressions.