Solving 5050-25×022: Exploring PEMDAS and BODMAS

Mathematics often relies on consistent and standardized rules, such as PEMDAS and BODMAS, to ensure that mathematical expressions are solved in a clear and unambiguous way. In this article, we will walk through the steps to solve the expression 5050-25×022, shedding light on the importance of following these order of operations.

PEMDAS and BODMAS: A Review

Before diving into the solution, it is essential to review the order of operations, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) in the United States (PEMDAS) or Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right) in the United Kingdom (BODMAS). Both rules are designed to ensure that mathematical expressions are evaluated consistently.

Solving 5050-25×022

Let's break down the expression 5050-25×022 step by step, adhering to the order of operations.

Step 1: Multiplication

According to PEMDAS/BODMAS, we start with the multiplication part of the expression:

25×022

First, we need to resolve the multiplication:

25×0 0

So, the expression simplifies to:

5050-022

Step 2: Substitution

Now, we substitute the result of the multiplication back into the original expression:

5050-022

Since 022 is a decimal number, we can simplify further:

5050-0.22

Step 3: Subtraction

Next, we perform the subtraction from left to right. First, we subtract 0.22 from 5050:

5050-0.22 5049.78

However, the original expression was 5050-25×022, and the multiplication part simplified to 0, so:

5050-0 5050

Then, we perform the subtraction:

5050-22 5028

But, if we follow the exact expression 5050-25×0.22, we get:

5050-0.22 5049.78

Conclusion and Verification

After carefully following the order of operations, the final result of the expression 5050-25×022 is 5049.78. This solution aligns with the principles of PEMDAS/BODMAS, ensuring that the expression is evaluated correctly.

Additional Insights

It is crucial to use parentheses to clearly separate parts of the equation, especially when dealing with complex expressions. Failure to do so can lead to ambiguous results, as shown in the variations of solutions discussed above.

Proof of Solution

To verify our solution, we can use the inverse of the expression:

5050-25×0.22 5049.78

If we substitute back:

5049.78 0.22 5050

This confirms that our solution is correct, as the original value is reestablished.

Thus, the final answer to the expression 5050-25×022 is 5049.78, adhering to the principles of order of operations.