Understanding the Order of Operations with Complex Mathematical Expressions

Understanding the order of operations, often abbreviated as BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction), is essential for solving complex mathematical expressions accurately. This article will break down a specific expression and demonstrate the importance of following the correct sequence of operations.

The Given Expression: 4 × [3 ÷ 4 {4 × 3 ÷ 3 × 3}]

To solve the expression 4 × [3 ÷ 4 {4 × 3 ÷ 3 × 3}], we need to carefully follow the order of operations:

Step-by-Step Solution

**Innermost Parentheses**: Start with the innermost parentheses. In this case, we have 3 × 3 9.

**Second Set of Parentheses**: Now evaluate the expression within the next set of parentheses, which is 4 × 3 ÷ 9.

3 ÷ 9 1/3 0.3333333333333333.

4 × 1/3 4/3 ≈ 1.333333333333333

**Division and Multiplication**: Next, evaluate the division within the { }: 3 ÷ 4 0.75.

**Multiplication**: Then, multiply the result from step 3 by the result from step 2: 0.75 × 1.333333333333333 1

**Final Step**: Multiply the result from step 4 by 4: 4 × 0.75 3.

A Different Expression

Another expression is given as:

4 × [3 ÷ 4 {4 × 3 ÷ 3 × 3}]

3 ÷ 3 1

4 × 3 ÷ 9 4 × 1/3 4/3 ≈ 1.333333333333333

3 ÷ 4 0.75

0.75 × 1.333333333333333 1

4 × 1 4

Conclusion

The order of operations is critical to solving mathematical expressions accurately. BODMAS helps ensure that expressions are solved in the correct order, leading to the correct answer. The correct solution to the given expression is 12, not 4, demonstrating the importance of the correct sequence of operations.

Related Keywords

BODMAS Order of Operations Mathematical Expressions