Solving 15 × 15 ÷ 5 – 3: The Correct Order of Operations

When dealing with mathematical expressions, understanding the correct order of operations is crucial. This guide will walk you through the process of solving the expression 15 × 15 ÷ 5 – 3 using the BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) rule. By following this method, you can ensure accuracy in your calculations.

Understanding the Order of Operations

The order of operations is a set of rules that specify the sequence in which operations should be performed to solve a mathematical expression. In the context of the given problem, 15 × 15 ÷ 5 – 3, these steps are essential for arriving at the correct answer.

Solving the Expression Using BODMAS

Let's break down the expression step by step using the BODMAS rule.

Step 1: Division and Multiplication

According to BODMAS, the first operation to perform is division, followed by multiplication. In the given expression 15 × 15 ÷ 5 – 3:

15 × 15 ÷ 5 – 3 225 ÷ 5 – 3 First, perform the division: 225 ÷ 5 45 So, the expression now becomes: 45 – 3

Step 2: Addition and Subtraction

Next, according to BODMAS, we perform subtraction (since there are no addition operations in this expression).

45 – 3 42

Therefore, the final answer is 42.

Alternative Partitioning Methods

Partitioning the problem can also help to better understand and solve it. Here are two alternative methods to verify the solution:

Method 1: Single Step Partitioning

15 × 15 ÷ 5 – 3 15 × 3 – 3 Perform the multiplication: 15 × 3 45 Then, perform the subtraction: 45 – 3 42

Method 2: Double Step Partitioning

First: 15 × 15 225 Then: 225 ÷ 5 45 Lastly: 45 – 3 42

Both methods confirm that the final answer is indeed 42.

Conclusion

Mastery of the order of operations is essential for solving mathematical problems accurately and efficiently. By following the BODMAS rule and partitioning the problem into manageable steps, you can solve complex expressions like 15 × 15 ÷ 5 – 3 easily and confidently.

References

Jerome E. Kaufmann. Algebra with Trigonometry for College Students. Third Edition. PWS-KENT Publishing Company, Boston, Ma. 1992, pp. 8 - 9.