bodmas rule

BODMAS Rule in Mathematics

The BODMAS rule is an acronym representing the order in which mathematical operations should be performed to correctly solve expressions. It stands for Brackets, Orders (powers and roots), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

Understanding the Components of BODMAS

• Brackets (B): This part includes everything in parentheses (), square brackets [], and curly braces {}. Operations inside brackets should always be solved first.
• Orders (O): Orders refer to powers and roots. After solving operations inside brackets, solve the exponents and roots next.
• Division (D) and Multiplication (M): These operations are treated equally and performed from left to right as they appear in the expression.
• Addition (A) and Subtraction (S): Like division and multiplication, addition and subtraction are performed from left to right.

Why BODMAS Rule is Important

The BODMAS rule ensures that all mathematicians will arrive at the same answer when solving an expression. Without this rule, the result of mathematical operations could vary, leading to confusion and inconsistency.

Examples of BODMAS in Action

Let's demonstrate the BODMAS rule with a few examples to understand how it influences the outcome of mathematical expressions.

Example 1:

Consider the expression: \(8 + 2 \times (2^2) - 4\).

Following the BODMAS rule:

• First, we solve the expression inside the brackets, which is \(2^2\). This equals \(4\).
• Next, we multiply \(2\) by \(4\) to get \(8\).
• We then add \(8\) to \(8\) achieving \(16\).
• Finally, we subtract \(4\) from \(16\) to get \(12\).

So, the solution to the expression \(8 + 2 \times (2^2) - 4\) is \(12\).

Example 2:

Consider another expression: \(\frac{36}{2(9 + 3)}\).

Following the BODMAS rule:

• Solve the expression inside the brackets first, which gives \(9 + 3 = 12\).
• Now, the expression becomes \(\frac{36}{2 \times 12}\).
• Next, perform the multiplication \(2 \times 12 = 24\).
• Finally, divide \(36\) by \(24\) to get \(1.5\).

Thus, the solution to the expression \(\frac{36}{2(9 + 3)}\) is \(1.5\).

Common Mistakes and Misconceptions

One common mistake is ignoring the left-to-right rule for operations of the same precedence, such as division and multiplication, or addition and subtraction. For example, in the expression \(18 \div 2 \times 3\), the correct approach is to divide \(18\) by \(2\) to get \(9\), and then multiply by \(3\) to obtain \(27\), not to multiply \(2\) and \(3\) first.

Another misconception is that multiplication always comes before division or addition always before subtraction. The BODMAS rule clarifies that division and multiplication, as well as addition and subtraction, are of equal priority and are simply resolved from left to right.

Example of a Common Mistake:

Consider: \(30 - 12 + 2\).

Incorrect approach: If one adds \(12\) and \(2\) first because they see addition as a priority, they would calculate \(12 + 2 = 14\), and then \(30 - 14 = 16\), which is incorrect.

Correct approach: Following BODMAS, first perform the subtraction \(30 - 12 = 18\), then add \(2\) to get \(20\). Thus, \(30 - 12 + 2 = 20\).

Experiments with BODMAS

Although we refer to these as "experiments," they're thought exercises to deepen your understanding of the BODMAS rule through various expressions.

Experiment 1:

Consider the expression: \(4 + 18 \div (3 - 1) \times 2\).

Following BODMAS, we first solve the brackets \(3 - 1 = 2\), then divide \(18\) by \(2\) obtaining \(9\), multiply by \(2\) to get \(18\), and finally add \(4\) to find that the expression equals \(22\).

Experiment 2:

Consider the expression: \(5^2 + 9 \times 3 - 4\).

Following BODMAS, orders come first, so \(5^2 = 25\). Then, multiplication \(9 \times 3 = 27\). We add these results to get \(52\), and subtract \(4\) to find the solution is \(48\).

The Importance of Practice in Understanding BODMAS

While we won't ask for practice in this lesson, it's worth noting the importance of actively working through various mathematical expressions to fully grasp the BODMAS rule. It enables one to understand how different operations interact and ensures accuracy in solving mathematical problems.

Conclusion

The BODMAS rule is a fundamental principle in arithmetic that guides the order of operations in mathematical expressions. By adhering to this rule, we ensure consistency and accuracy in solving problems. Understanding and applying the BODMAS rule is crucial for anyone dealing with mathematical operations, from students just learning the basics of arithmetic to professionals who engage with complex mathematical formulas.