Solving the Mathematical Expression 33 × 3 - 33 Using the Order of Operations

Introduction

Solving mathematical expressions correctly is essential for students and professionals alike. In this article, we will walk through the process of solving a specific mathematical expression, i.e., (3^3 times 3 - 3^3), using the correct order of operations. This guide will help clarify any confusion and ensure that you get the right answer.

Understanding the Expression

The given expression is:

$$3^3 times 3 - 3^3$$

At first glance, this expression might seem a bit confusing. However, with the correct application of the order of operations (either PEMDAS or BODMAS), we can ensure a clear and accurate solution.

Step-by-Step Solution

1. Exponents (B.O.D of BODMAS, P.E of PEMDAS)

First, we need to evaluate the exponents.

$$3^3 27$$ Step 1: Calculate the exponent: 33 27 Step 2: Substitute the values back into the expression: 27 × 3 - 27

2. Multiplication

Next, we perform the multiplication.

$$27 times 3 81$$ Step 3: Perform the multiplication: 27 × 3 81 Step 4: Substitute the result back into the expression: 81 - 27

3. Subtraction

Finally, we perform the subtraction.

$$81 - 27 54$$ Step 5: Perform the subtraction: 81 - 27 54

Therefore, the final answer is 54.

Conclusion

When solving mathematical expressions, it's crucial to follow the correct order of operations. By using the principles of either PEMDAS or BODMAS, we can ensure a systematic approach to solving such expressions. In this case, the expression (3^3 times 3 - 3^3) simplifies to 54.

Additional Tips for Solving Mathematical Expressions

1. Parentheses: Always start with parentheses, if any, before moving on to other operations. 2. Exponents: Evaluate exponents next. 3. Multiplication and Division: Perform from left to right. 4. Addition and Subtraction: Perform from left to right.

By following these steps, you can solve any mathematical expression with confidence and accuracy. Remember, practice makes perfect!