Solving Complex Arithmetic Expressions: Simplifying and Evaluating

In mathematics, particularly in arithmetic and algebra, evaluating complex expressions correctly is crucial. This article focuses on solving the given arithmetic expression 25 - 5[23 {2 - 25 - 3 5} - 10] ÷ 4 step-by-step, applying the order of operations properly.

Introduction to the Order of Operations (PEMDAS)

The mnemonic PEDMAS (Parentheses, Exponents, Division and Multiplication, and Addition and Subtraction) is a helpful tool for ensuring that arithmetic expressions are evaluated correctly. This article will demonstrate how to use PEMDAS to solve a complex arithmetic expression.

Step-by-Step Solution

Let's break down the expression and solve it step-by-step:

25 - 5[23 {2 - 25 - 3 5} - 10] ÷ 4

Step 1: Inner Most Parentheses

First, we evaluate what's inside the innermost set of parentheses:

2 - 25 - 3 5  2 - 25 - 15  2 - 40  -38

The expression now becomes:

25 - 5[23 {-38} - 10] ÷ 4

Step 2: Substitution into Brackets

Now, substitute the evaluated result into the brackets:

25 - 5[23 {-38} - 10] ÷ 4 25 - 5[23 * (-38) - 10] ÷ 4

Note that the multiplication should be done next according to PEMDAS.

Step 3: Bracket Multiplication

Perform the multiplication inside the brackets:

23 * (-38)  -874

Substitute back:

25 - 5[-874 - 10] ÷ 4

Simplify the operation inside the brackets:

-874 - 10  -884

Substitute back:

25 - 5[-884] ÷ 4

Step 4: Division and Subtraction

Next, perform the division within the expression:

5 * (-884) ÷ 4  -4420 ÷ 4  -1105

Finally, perform the subtraction:

25 - (-1105)  25   1105  1130

The final value of the expression is:

1130 ÷ 4  282.5

Or in simplified form:

95/4  23 3/4  23.75

Conclusion

Bulky expressions can be intimidating, but with a clear understanding of the order of operations, solving them becomes more manageable. By adhering to PEMDAS, one can break down any complex arithmetic expression into simpler steps, ensuring accurate and efficient computation.

Remember, the process of solving this kind of expression is not just about getting the right answer; it's also about understanding the principles behind each step. This article has demonstrated how to use PEMDAS to simplify and evaluate a complex arithmetic expression, providing a comprehensive guide for anyone looking to master this skill.

Keywords

arithmetic expression, order of operations, PEMDAS, complex expressions, step-by-step solution