A Comprehensive Guide to Simplifying Mathematical Expressions with Examples

Introduction:

Welcome to "Mastering BODMAS: A Comprehensive Guide to Simplifying Mathematical Expressions with Examples." In this tutorial, we will explore the BODMAS rule and its practical application in solving mathematical problems. BODMAS stands for Brackets, Orders (or Exponents), Division, Multiplication, Addition, and Subtraction. By understanding the order of operations and applying BODMAS correctly, you will gain proficiency in simplifying complex expressions and equations. Let's delve into the theory and learn through examples!

Understanding BODMAS:

BODMAS establishes a set of rules to determine the sequence of operations in mathematical expressions.

BODMAS prioritizes calculations in the following order: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

Each operation should be performed in the prescribed order to obtain the correct result.

Brackets:

Brackets are used to group numbers and operations within an expression.

The expression inside the brackets should be solved first, following the BODMAS rule.

Example: Simplify the expression (5 + 3) × 2.

First, solve the expression inside the brackets: 5 + 3 = 8.

Then, multiply 8 by 2, resulting in 16.

Orders (or Exponents):

Orders involve raising numbers to a power (exponent) or extracting roots.

The exponentiation operation is performed after solving any brackets and before proceeding to other operations.

Example: Simplify the expression 2³ + 4.

Here, 2³ means multiplying 2 by itself three times, resulting in 8.

Then, add 8 and 4, resulting in 12.

Division and Multiplication:

Division and multiplication operations are carried out from left to right, following the order of appearance.

It is crucial to perform these operations in the correct sequence to ensure accurate results.

Example: Simplify the expression 12 ÷ 3 × 2.

According to BODMAS, divide 12 by 3 first, resulting in 4.

Then, multiply 4 by 2, resulting in 8.

Addition and Subtraction:

Addition and subtraction operations are executed from left to right after brackets, orders, division, and multiplication.

These operations are straightforward but require attention to signs and precision.

Example: Simplify the expression 10 - 3 + 2.

Following BODMAS, subtract 3 from 10, resulting in 7.

Then, add 2 to 7, resulting in 9.

Practice Problems and Additional Examples:

Practice various problems, applying BODMAS to solve them step by step.

Example: Simplify the expression 3 × (4 + 2) ÷ 2 - 1.

First, solve the expression inside the brackets: 4 + 2 = 6.

Then, multiply 3 by 6, resulting in 18.

Next, divide 18 by 2, resulting in 9.

Finally, subtract 1 from 9, resulting in 8.

Conclusion:

By mastering the BODMAS rule, you will gain confidence in simplifying mathematical expressions accurately. Remember the order: Brackets, Orders, Division, Multip