Solving Complex Arithmetic Expressions: Case Study of 123×1×2×3÷1÷2÷3

Understanding and solving complex arithmetic expressions can be challenging, particularly when the order of operations is not clear. In this article, we will delve into the process of evaluating the expression 123×1×2×3÷1÷2÷3. By breaking down the problem and applying the proper rules, we can reach the correct answer.

Introduction to the Expression

The expression given is 1 2 3 × 1 × 2 × 3 ÷ 1 ÷ 2 ÷ 3. This format, without proper spacing or grouping, can lead to confusion, especially for those unfamiliar with the order of operations. To solve this problem, we will follow the PEMDAS rule, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Evaluating the Expression Step by Step

Let's start by rewriting the expression in a more readable format:

1 2 3 × 1 × 2 × 3 ÷ 1 ÷ 2 ÷ 3

To remove the ambiguity, we group the divisions together and then apply the multiplication and division steps from left to right:

Step 1: Group the divisions together:

1 2 3 × 1 × 2 × 3 ÷ (1 ÷ (2 ÷ 3))

Step 2: Simplify the innermost division first:

1 2 3 × 1 × 2 × 3 ÷ (1 ÷ 0.6666666666666666)

Step 3: Evaluate the division inside the parentheses:

1 2 3 × 1 × 2 × 3 ÷ 1.5

Step 4: Perform the multiplication and division from left to right:

(1 × 2 × 3) ÷ 1.5 6 ÷ 1.5 4

Conclusion: The value of the expression 123×1×2×3÷1÷2÷3 is 4.

Alternative Method: Grouping and Simplification

Another way to solve this expression is to simplify the multiplication and division step by step:

Step 1: Group the multiplications and divisions:

(123 × 1 × 2 × 3) ÷ (1 ÷ (2 ÷ 3))

Step 2: Simplify the division inside the parentheses:

(123 × 1 × 2 × 3) ÷ (1 ÷ 0.6666666666666666)

Step 3: Evaluate the division:

(123 × 1 × 2 × 3) ÷ 1.5

Step 4: Perform the multiplication and division:

123 × 1 × 2 × 3 738

738 ÷ 1.5 492 ÷ 3 4

Conclusion: The value of the expression is again 4.

Conclusion

Mastering the order of operations and applying PEMDAS can help solve complex arithmetic expressions accurately. The expression 123×1×2×3÷1÷2÷3 evaluates to 4, as shown through both methods. Understanding these steps can help in solving similar problems in the future.

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