Solving Mathematical Expressions Using Order of Operations

To solve the mathematical expression $24 \div (20 – 12 \div 3 \times 8)$, we need to follow the correct order of operations. This order is often remembered using acronyms like BODMAS or PEMDAS.

• Brackets (or Parentheses)
• Orders (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Let's break down the given expression step by step according to this rule.

The expression is:

$24 \div (20 – 12 \div 3 \times 8)$

Step 1: Solve the expression inside the Brackets (Parentheses)

We must first evaluate the expression inside the parentheses: $(20 – 12 \div 3 \times 8)$.

Inside the parentheses, we have subtraction, division, and multiplication. According to BODMAS/PEMDAS, Division and Multiplication come before Subtraction. We perform Division and Multiplication from left to right.

Step 2: Perform Division inside the Parentheses

Inside the parentheses, the first operation from the left among division and multiplication is division: $12 \div 3$.

$12 \div 3 = 4$

Now the expression inside the parentheses becomes: $(20 – 4 \times 8)$.

Step 3: Perform Multiplication inside the Parentheses

Next, perform the multiplication inside the parentheses: $4 \times 8$.

$4 \times 8 = 32$

Now the expression inside the parentheses becomes: $(20 – 32)$.

Step 4: Perform Subtraction inside the Parentheses

Finally, perform the subtraction inside the parentheses: $20 – 32$.

$20 – 32 = -12$

So, the expression inside the parentheses evaluates to $-12$.

Step 5: Substitute the result back into the original expression

Now, substitute the value of the expression inside the parentheses back into the original expression:

$24 \div (-12)$

Step 6: Perform the final Division

Now, perform the division: $24 \div (-12)$.

$24 \div (-12) = -2$

Therefore, the value of the expression $24 \div (20 – 12 \div 3 \times 8)$ is $-2$.

Comparing this result with the given options, we find that $-2$ matches Option 1.

Revision Table: Order of Operations (BODMAS/PEMDAS)

Additional Information: Importance of Order of Operations

The order of operations is crucial in mathematics to ensure that everyone gets the same result when evaluating a mathematical expression. Without a standard order, an expression like $24 \div (20 – 12 \div 3 \times 8)$ could be interpreted in many different ways, leading to different answers. Always remember to prioritize operations within parentheses and then follow the Division/Multiplication and Addition/Subtraction rules from left to right. Mistakes often happen when the left-to-right rule for operations of the same priority level (like division and multiplication, or addition and subtraction) is ignored.