Understanding the Solution to 45 ÷ 5 × 9 - 6 - 5 82

Mathematics involves a set of rules to solve expressions accurately. When dealing with expressions involving multiple operations, it's imperative to follow the correct order of operations. In this article, we will explore how to solve the expression 45 ÷ 5 × 9 - 6 - 5 by applying the BODMAS and BIDMAS rules. Let's dive in!

What is BODMAS / BIDMAS?

The BODMAS (Brackets Off, Division, Multiplication, Addition, Subtraction) or BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) rules provide a standardized order for performing arithmetic operations. This prevents ambiguity and ensures that everyone arrives at the same result when solving mathematical expressions.

Solving the Expression: 45 ÷ 5 × 9 - 6 - 5

Let's break down the expression step-by-step, adhering to the BODMAS and BIDMAS rules:

Step 1: Division

First, we perform the division operation, which is the first in the BODMAS/BIDMAS sequence.

45 ÷ 5 9

So, the expression now becomes 9 × 9 - 6 - 5

Step 2: Multiplication

Next, we perform the multiplication operation.

9 × 9 81

So, the expression now becomes 81 - 6 - 5

Step 3: Subtraction

Since there are no further operations left (no addition), we proceed with the subtraction operation, working from left to right as per the standard order.

81 - 6 75

75 - 5 82

Therefore, the final answer is 82.

Step-by-Step Calculation in Detail

Let's go through the entire process again for clarity:

45 ÷ 5 9 9 × 9 81 81 - 6 75 75 - 5 82

The expression resolves to:

45 ÷ 5 × 9 - 6 - 5 82

Solomon's Alternative Approach

Alternatively, we can simplify the expression in a single step. Let's take a look at another way to solve it correctly:

45 ÷ 5 × 9 - 6 - 5

First, we perform the division and multiplication:

9 × 9 - 6 - 5

Then, we perform the subtractions from left to right:

81 - 6 - 5

75 - 5

82

Thus, the final answer is still 82, confirming our initial solution.

Conclusion

By following the BODMAS and BIDMAS rules, we can ensure that we solve mathematical expressions accurately. This article has demonstrated how to solve the expression 45 ÷ 5 × 9 - 6 - 5, arriving at the correct answer of 82. Understanding these rules is crucial for anyone working with mathematical expressions or involved in fields that rely on precise calculations, such as engineering, finance, and science.