Simplify the expression, using the rule for order of operations if necessary:
$3 \cdot 12-9 \cdot 8=$
$\square$
Answer (2)
The expression 3 ⋅ 12 − 9 ⋅ 8 simplifies to − 36 by performing the multiplications first and then subtracting. We first find 3 ⋅ 12 = 36 and 9 ⋅ 8 = 72 , and then subtract 72 from 36 . Therefore, the final result is − 36 .
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First, multiply 3 by 12 to get 36 .
Then, multiply 9 by 8 to get 72 .
Subtract 72 from 36 .
The final result is − 36 .
Explanation
Understanding the problem We need to simplify the expression 3 c d o t 12 − 9 c d o t 8 using the order of operations. The order of operations tells us to perform multiplication before subtraction.
First Multiplication First, we perform the multiplication 3 c d o t 12 , which equals 36.
Second Multiplication Next, we perform the multiplication 9 c d o t 8 , which equals 72.
Subtraction Now, we perform the subtraction 36 − 72 , which equals -36.
Final Answer Therefore, the simplified expression is -36.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or balancing a budget. For example, if you earn $3 per hour for 12 hours and then spend $9 per item on 8 items, the expression 3 ⋅ 12 − 9 ⋅ 8 helps you calculate your net earnings. This concept extends to more complex financial calculations, scientific experiments, and engineering designs, where the correct sequence of operations ensures accurate results.
