Introduction to Mathematical Expression

Mathematical expressions can often lead to confusion if the correct order of operations is not followed. The term BODMAS (Brackets, Orders, Division/Multiplication, Addition, Subtraction) provides a clear sequence of steps to solve such expressions accurately. In this article, we will explore the expression 8 ÷ 2(2 2) and understand the correct answer using the BODMAS rule.

Understanding 8 ÷ 2(2 2)

The expression 8 ÷ 2(2 2) can be confusing due to the presence of both division and multiplication operators. To resolve this, we follow the BODMAS rule, which dictates the sequence of operations to be carried out in an expression.

BODMAS Rule

The BODMAS rule includes the following steps:

Brackets: Solve anything within brackets first. Orders: Perform operations such as square roots or exponents next. Division and Mmultiplication: These operations are then performed from left to right. Addition and Subtraction: These operations follow, again from left to right.

Applying the BODMAS Rule

Let's apply the BODMAS rule to the expression 8 ÷ 2(2 2):

Bracket: ((2 2) 4). The expression now becomes 8 ÷ 2 × 4. Division and Mmultiplication: Next, we perform division and multiplication from left to right. First, 8 ÷ 2 4. The expression then becomes 4 × 4. Finally, 4 × 4 16.

Therefore, the correct answer to 8 ÷ 2(2 2) is 16.

Alternative Interpretations and Situations

It is essential to understand that the interpretation of the expression can vary if not bracketed correctly. Two common situations are:

Situation 1: 8 ÷ (2(2 2))

Here, we follow BODMAS as follows:

Bracket: (2 2) 4. The expression becomes 8 ÷ 8. Next, 8 ÷ 8 1.

The answer in this situation is 1.

Situation 2: (8 ÷ 2)(2 2)

In this scenario, we again follow BODMAS:

Bracket: (2 2) 4. The expression becomes (4)(4). Next, (4)(4) 16.

Here, the answer is 16.

The difference in answers (16 or 1) highlights the importance of proper bracketing in mathematical expressions to avoid ambiguity.

Real-World Analogies

To make the concept more relatable, let's use a real-world analogy. Imagine a grandpa with 8 oranges who wants to distribute them equally among 2 families, each consisting of 2 children and 2 adults. If we use the BODMAS rule, the grandpa would first distribute 4 oranges to each family, making a total of 8 oranges (2 × 4). Then, each person would receive 2 oranges (4 ÷ 2).

Conclusion

The correct answer to the expression 8 ÷ 2(2 2) is 16 when following the BODMAS rule. However, if the expression is bracketed differently, the answer can change to 1. Understanding and applying the BODMAS rule correctly ensures accurate results in mathematical calculations.