- Identify the order of operations: division and multiplication are evaluated from left to right before addition.
- Calculate the division: \(15 \div 3 = 5\).
- Multiply the result by 5: \(5 \cdot 5 = 25\).
- Add 9 to the product: \(25 + 9 = 34\).
- The final result is \(\boxed{34}\).
Explanation
- Analysis of the Order of Operations
The problem requires simplifying the arithmetic expression \(15 \div 3 \cdot 5 + 9\). To do this correctly, we must follow the standard order of operations, often known by the acronyms PEMDAS or BODMAS. This rule dictates the priority of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). In this expression, we have division, multiplication, and addition. Division and multiplication share the same precedence, so they must be performed in order from left to right. Once these are complete, we perform the addition.
- Performing the Division
The first operation, moving from left to right, is \(15 \div 3\). Calculating this gives:
\[15 \div 3 = 5.\]
Now, substitute this result back into the expression:
\[5 \cdot 5 + 9.\]
- Performing the Multiplication
Next, we address the multiplication:
\[5 \cdot 5 = 25.\]
Substituting this value back into the expression, we now have:
\[25 + 9.\]
- Performing the Addition and Final Result
Finally, we perform the last remaining operation, which is addition:
\[25 + 9 = 34.\]
Thus, the simplified result of the expression \(15 \div 3 \cdot 5 + 9\) is \(\boxed{34}\).
Examples
Order of operations is essential in everyday life, especially in fields like finance, engineering, and computer programming. For example, when calculating the total cost of a project, if you have a budget of \$100 and you need to pay for 3 different components each costing \$5, while also adding a fixed service fee of \$9, the order in which you calculate these items matters. If you perform calculations in the wrong sequence, you might arrive at a budget deficit or surplus. Mastering this ensures that your financial planning and project estimations are accurate and reliable.