Understanding the BODMAS Rule

Oct 13, 2025 by miodeya.com 16 views

Introduction

In mathematics, the BODMAS rule is a mnemonic device used to remember the order of operations in a mathematical expression. BODMAS stands for Brackets, Orders (or Exponents), Division, Multiplication, Addition, and Subtraction. It helps to simplify complex mathematical expressions by following a specific order of operations. In this article, we will use the BODMAS rule to simplify the expression (-10)×[{(60-8)÷4}+3×(5-7)].

Understanding the BODMAS Rule

The BODMAS rule is a simple way to remember the order of operations in a mathematical expression. It is as follows:

Brackets: Evaluate expressions inside brackets first.
Orders (or Exponents): Evaluate any exponential expressions next.
Division: Evaluate any division operations after that.
Multiplication: Evaluate any multiplication operations after division.
Addition: Evaluate any addition operations after multiplication.
Subtraction: Finally, evaluate any subtraction operations.

Simplifying the Expression

Now that we have a good understanding of the BODMAS rule, let's apply it to the given expression:

(-10)×[{(60-8)÷4}+3×(5-7)]

Step 1: Evaluate Expressions Inside Brackets

The first step is to evaluate the expressions inside the brackets. We have two sets of brackets: (60-8) and (5-7).

(60-8) = 52
(5-7) = -2

So, the expression becomes:

(-10)×[{52÷4}+3×(-2)]

Step 2: Evaluate Exponential Expressions

There are no exponential expressions in this expression, so we can move on to the next step.

Step 3: Evaluate Division Operations

The next step is to evaluate the division operation:

52÷4 = 13

So, the expression becomes:

(-10)×[{13}+3×(-2)]

Step 4: Evaluate Multiplication Operations

The next step is to evaluate the multiplication operation:

3×(-2) = -6

So, the expression becomes:

(-10)×[{13}+(-6)]

Step 5: Evaluate Addition Operations

The next step is to evaluate the addition operation:

13 + (-6) = 7

So, the expression becomes:

(-10)×[7]

Step 6: Evaluate Multiplication Operations

The final step is to evaluate the multiplication operation:

(-10)×7 = -70

Therefore, the simplified expression is:

-70

Conclusion

In this article, we used the BODMAS rule to simplify the complex mathematical expression (-10)×[{(60-8)÷4}+3×(5-7)]. We followed the order of operations as specified by the BODMAS rule and evaluated each operation in the correct order. The final simplified expression is -70.

Tips and Tricks

Always follow the order of operations as specified by the BODMAS rule.
Evaluate expressions inside brackets first.
Evaluate any exponential expressions next.
Evaluate any division operations after that.
Evaluate any multiplication operations after division.
Evaluate any addition operations after multiplication.
Finally, evaluate any subtraction operations.

Q: What is the BODMAS rule?

A: The BODMAS rule is a mnemonic device used to remember the order of operations in a mathematical expression. BODMAS stands for Brackets, Orders (or Exponents), Division, Multiplication, Addition, and Subtraction.

Q: Why is the BODMAS rule important?

A: The BODMAS rule is important because it helps to simplify complex mathematical expressions by following a specific order of operations. This ensures that mathematical expressions are evaluated consistently and accurately.

Q: What are the steps involved in using the BODMAS rule?

A: The steps involved in using the BODMAS rule are:

Evaluate expressions inside brackets first.
Evaluate any exponential expressions next.
Evaluate any division operations after that.
Evaluate any multiplication operations after division.
Evaluate any addition operations after multiplication.
Finally, evaluate any subtraction operations.

Q: How do I apply the BODMAS rule to a mathematical expression?

A: To apply the BODMAS rule to a mathematical expression, follow these steps:

Identify the expressions inside brackets and evaluate them first.
Identify any exponential expressions and evaluate them next.
Identify any division operations and evaluate them after that.
Identify any multiplication operations and evaluate them after division.
Identify any addition operations and evaluate them after multiplication.
Finally, identify any subtraction operations and evaluate them last.

Q: What if there are multiple sets of brackets in a mathematical expression?

A: If there are multiple sets of brackets in a mathematical expression, evaluate the expressions inside the innermost brackets first, and then work your way outwards.

Q: Can I use the BODMAS rule to simplify expressions with fractions?

A: Yes, you can use the BODMAS rule to simplify expressions with fractions. However, you need to follow the order of operations carefully to ensure that the fractions are evaluated correctly.

Q: How do I handle negative numbers when using the BODMAS rule?

A: When using the BODMAS rule, negative numbers are treated as any other number. You need to follow the order of operations carefully to ensure that the negative numbers are evaluated correctly.

Q: Can I use the BODMAS rule to simplify expressions with decimals?

A: Yes, you can use the BODMAS rule to simplify expressions with decimals. However, you need to follow the order of operations carefully to ensure that the decimals are evaluated correctly.

Q: What if I make a mistake when using the BODMAS rule?

A: If you make a mistake when using the BODMAS rule, re-evaluate the expression carefully and follow the order of operations again. You can also use a calculator or ask for help if you are unsure.

Conclusion

In this article, we have answered some frequently asked questions on using the BODMAS rule to simplify complex mathematical expressions. We have covered topics such as the importance of the BODMAS rule, the steps involved in using the BODMAS rule, and how to handle negative numbers and fractions when using the BODMAS rule. By following the BODMAS rule carefully, you can simplify complex mathematical expressions with ease and accuracy.

Tips and Tricks

Always follow the order of operations as specified by the BODMAS rule.
Evaluate expressions inside brackets first.
Evaluate any exponential expressions next.
Evaluate any division operations after that.
Evaluate any multiplication operations after division.
Evaluate any addition operations after multiplication.
Finally, evaluate any subtraction operations.
Use a calculator or ask for help if you are unsure.
Practice, practice, practice! The more you practice using the BODMAS rule, the more confident you will become.