Understanding the Solution to 12÷4 6÷3-2

Mathematics often plays a vital role in our daily lives, from simple calculations in the kitchen to complex equations in professional settings. One such problem that has sparked confusion is 12÷4 6÷3-2. This article will explore the solution to this equation by employing the BODMAS rule and breaking down the process step-by-step.

Let's start by understanding the acronym BODMAS, which stands for:

B - Brackets O - Orders (i.e., exponents) D - Division M - Multiplication A - Addition S - Subtraction

Step-by-Step Solution

Now, let's apply BODMAS to solve the equation 12÷4 6÷3-2.

Brackets: There are no brackets in this equation, so we can skip this step. Orders (Exponents): There are no exponents in this equation, so we can skip this step as well. Division: We should perform division operations first. In the equation, we have 12÷4 and 6÷3.

Solving the divisions first:

begin{align*} 12 div 4 3 6 div 3 2 end{align*}

After performing the division, our equation now looks like this:

begin{align*} 3 2 - 2 end{align*} Addition and Subtraction: Now, we perform the addition and subtraction from left to right. begin{align*} 3 2 - 2 5 - 2 3 end{align*}

Thus, the final answer is 3.

Alternative Interpretation: 12÷4 6÷3-2

It's important to note the alternative interpretation of the equation 12÷4 6÷3-2. This can also be interpreted as:

12 ÷ (4 (6 ÷ 3) - 2)

Let's break this down:

Brackets: We start by solving the innermost brackets first. Division and Addition/Subtraction: We continue solving in the order of operations.

Here's how to solve it step-by-step:

begin{align*} 6 div 3 2 4 2 - 2 4 12 div 4 3 end{align*}

Thus, the final answer is 3.

Different Interpretations of 12÷4 6÷3-2

Our initial interpretation of 12÷4 6÷3-2 is a straightforward application of the BODMAS rule, giving us a solution of 3. However, another way to interpret this equation is to group the divisions together and handle the arithmetic operations as follows:

12 ÷ (4 (6 ÷ 3) - 2) 12 ÷ (4 2 - 2) 12 ÷ 4 3

This method also yields the same result of 3.

Conclusion

In conclusion, the solution to the equation 12÷4 6÷3-2 is 3. Understanding the order of operations and the BODMAS rule is crucial for solving such equations accurately and efficiently. Whether you use the first interpretation or the alternative grouping, the answer remains consistent.

Further Reading

If you're interested in learning more about the order of operations and how they apply to other mathematical problems, consider exploring the following topics:

PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) Algebraic Expressions Linear Equations