Solving Mathematical Expressions: A Guide to Order of Operations

Mathematical expressions often require a specific sequence of operations to find the correct solution. This article will guide you through the process of solving two expressions using the order of operations, commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Solving 12 ÷ 26 - 74 × 2

Let's solve the expression 12 ÷ 26 - 74 × 2 step-by-step using the order of operations.

Evaluate the expression inside the parentheses first: 6 - 7 × 4: This part of the expression appears to have a syntax error. Instead, we can assume the expression is 12 ÷ (26 - 7 × 4). 6 - 7 × 4 -1 × 4 -4 Substitute back into the expression:

12 ÷ (26 - 7 × 4) 12 ÷ (26 - 28)

Perform the division inside the parentheses: 26 - 28 -2 Now the expression is:

12 ÷ (-2) -6

However, if the original expression is meant to be 12 ÷ 26 - 74 × 2, let's solve it using the order of operations as written:

12 ÷ 26 - 74 × 2 Evaluate the division and multiplication from left to right:

12 ÷ 26 ≈ 0.4615

0.4615 - 74 × 2 0.4615 - 148 -147.5385

However, if the intended expression is 12 ÷ 26 - 74 × 2, we should evaluate each part:

Multiplication: 74 × 2 148 Division: 12 ÷ 26 ≈ 0.4615 Addition and Subtraction: 0.4615 - 148 -147.5385

For the correct interpretation, let's consider:

Evaluate 12 ÷ 26 - 74 × 2: 12 ÷ 26 0.4615 74 × 2 148 0.4615 - 148 -147.5385

Solving 12/26 - 742

Let's solve the expression 12/26 - 742 step-by-step using the order of operations.

Evaluate the division: 12/26 0.4615 Subtraction: 0.4615 - 742 -741.5385

Thus, the final answer is:

-741.5385

Order of Operations Explained: PEMDAS

The order of operations, commonly remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right), ensures that mathematical expressions are evaluated consistently. Here’s a breakdown:

Parentheses (brackets): Evaluate expressions inside parentheses first. Exponents: Evaluate any exponents next. Multiplication and Division: Perform these operations from left to right. Addition and Subtraction: Perform these operations from left to right.

Understanding these steps can help resolve any ambiguity in mathematical expressions, ensuring accurate calculations.

To Practice:

Expression 1: 12 ÷ 26 - 74 × 2 Expression 2: 12/26 - 742

Feel free to apply the order of operations to these expressions, and explore more mathematical problems to strengthen your understanding.

Note: The expressions provided may contain errors or ambiguities. Always double-check the original problem before solving it to avoid misinterpretation.