Simplify: $5-48 \div 4 \times 2+3^2$

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03-11-2026
Mathematics

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Simplify: $5-48 \div 4 \times 2+3^2$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T06:52:27-05:00

Evaluate the exponent first: $3^2 = 9$.
Perform division and multiplication from left to right: $48 \div 4 = 12$, then $12 \times 2 = 24$.
Carry out subtraction and addition from left to right: $5 - 24 + 9$.
The simplified result is $\boxed{-10}$.

Explanation

Analysis and Order of Operations

The problem is to simplify the numerical expression $5 - 48 \div 4 \times 2 + 3^2$. This requires strictly adhering to the order of operations, often abbreviated as PEMDAS/BODMAS:

Parentheses/Brackets: None.
Exponents/Orders: Perform calculations involving powers or roots.
Multiplication and Division: Perform these from left to right as they appear.
Addition and Subtraction: Perform these from left to right as they appear.

Evaluating Exponents

First, we evaluate the exponent present in the expression, $3^2$.
Calculating $3^2 = 3 \times 3 = 9$.
Now, the expression becomes $5 - 48 \div 4 \times 2 + 9$.

Performing Multiplication and Division

Next, we process the multiplication and division operations from left to right.
First, divide 48 by 4: $48 \div 4 = 12$.
Now, the expression is $5 - 12 \times 2 + 9$.
Then, multiply the result by 2: $12 \times 2 = 24$.
Now, the expression is $5 - 24 + 9$.

Performing Addition and Subtraction

Finally, we handle the addition and subtraction from left to right.
Subtract 24 from 5: $5 - 24 = -19$.
Then, add 9 to that result: $-19 + 9 = -10$.

Final Result

By following the standard order of operations correctly, we determined that the expression $5 - 48 \div 4 \times 2 + 3^2$ simplifies to $-10$.
Therefore, the final result is $\boxed{-10}$.

Examples

Understanding the correct order of operations is essential in everyday life, such as when calculating total costs. For example, if you are buying 5 items, but then receive a discount where you subtract the cost of some returned items and add a service fee, you must perform these calculations in the correct sequence to ensure your final balance is accurate. Similar rules of precedence govern software programming, spreadsheet formulas, and engineering calculations, ensuring that complex tasks are executed reliably every time.