Introduction to Mathematical Operation Precedence

Multiplication and Division: The mathematical operators come with their own order of precedence, much like how you order your daily activities. One of the most commonly used mathematical guidelines to determine the order is either PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), depending on the region. These acronyms are designed to help students and professionals understand the order in which mathematical expressions must be solved.

Understanding PEMDAS and BODMAS with a Complex Expression

Let's take a complex expression like 1111111111 x 01 x 11, and dive into both the PEMDAS and BODMAS methods to find the solution.

Applying PEMDAS, we start with the expression:

1 1 1 1 1 1 1 1 1 1 1 1 1 0 1

Here, we understand that the multiplications between 1111111111 and 01 take priority. According to PEMDAS, multiplication comes first:

1111111111 x 01 11111111101

Next, we apply 11 (the last number) to the result of the multiplication:

11111111101 x 11 12

Therefore, the solution under PEMDAS rules is 12.

Solving the Expression with BODMAS

Now, let's solve the expression using the BODMAS rule, which is a common way to remember the order of operations in arithmetic:

Step 1: Multiplication

1111111111 x 01 11111111101

Step 2: Multiplication

11111111101 x 11

Since there is only one multiplication left, we evaluate it immediately:

11111111101 x 11 12

There is no addition or subtraction to perform in this case, so the final answer under BODMAS rules is 12.

Conclusion

Both PEMDAS and BODMAS provide us with a clear order of operations which, when applied, simplify complex mathematical expressions into manageable solutions. The solution to the expression 1111111111 x 01 x 11 is 12.

For further reading on these mathematical rules, you can refer to Jerome E. Kaufmann's Algebra with Trigonometry for College Students, Third Edition, published by PWS-KENT Publishing Company, Boston, MA, 1992, pp. 8 - 9.