Understanding and Solving Complex Arithmetic Problems with the BODMAS Rule

When it comes to solving complex arithmetic problems, understanding the correct order of operations is crucial. One such rule that serves as a key to unraveling these calculations is the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, and Subtraction). In this article, we will break down a specific problem to demonstrate how the BODMAS rule can be applied to solve it in a structured and lucid manner.

Problem Breakdown: 6565 32×4-65÷5

To solve the expression 6565 32×4-65÷5, it is essential to follow the BODMAS rule. This rule helps us determine the correct sequence of operations to follow.

Brackets: There are no brackets in this expression. BODMAS dictates that we should move on to the next operation in the sequence. Orders: Orders (powers and roots) are not present in this expression. Again, we move on to the next operation. Division and Multiplication: We will handle these operations from left to right as per the BODMAS rule. First, we will break down the expression into smaller parts and solve for multiplication and division.

The expression can be broken down into two parts for clarity:

6565 32×4 65÷5

6565 32×4 can be simplified to 6565 128 after performing the multiplication.

65÷5 can be simplified to 13 after performing the division.

Step-by-step Solution

Let's solve the simplified parts of the expression step-by-step:

6565 128 13

Now, we will handle the division as in the second part of the expression:

13 ÷ 5 13

Since there are no more operations to perform within the brackets, the next step according to the BODMAS rule is:

6565 128 - 13

Now, we will perform the subtraction:

6565 128 - 13 6565 - 13 16627

The Importance of BODMAS

The BODMAS rule ensures that calculations are performed in the correct order, making it easier to solve complex arithmetic problems. Understanding this rule can prevent errors and confusion.

Conclusion

While many people can solve such problems mentally, understanding the BODMAS rule and breaking down the problem step-by-step as demonstrated here helps in tackling more complex arithmetic problems. This article aims to provide clarity and a structured approach to solving such expressions.

Frequently Asked Questions

1. What is BODMAS?

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It is a mnemonic used to remember the order of operations in mathematics.

2. How is BODMAS applied in problem-solving?

BODMAS is applied by following the sequence of operations: Brackets first, then Orders, followed by Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right).

3. Why is it important to use BODMAS?

Using BODMAS ensures accuracy and consistency in solving mathematical problems, especially when dealing with complex expressions. It helps in avoiding errors and confusion.