Evaluate $(24-(12 \div 9)+16)-8 \times 3$
Answer (2)
Evaluate the division: $12
div 9 =
\frac{4}{3}$.
Evaluate the parentheses: $24 -
\frac{4}{3} + 16 =
\frac{116}{3}$.
Evaluate the multiplication: 8 × 3 = 24 .
Perform the subtraction: $\frac{116}{3} - 24 =
\frac{44}{3} . T h e f ina l an s w er i s \boxed{\frac{44}{3}}$.
Explanation
Understanding the Problem We are asked to evaluate the expression $(24-(12
div 9)+16)-8 \times 3$. To do this, we will follow the order of operations (PEMDAS/BODMAS).
Evaluating the Division First, we evaluate the division within the parentheses: $12
div 9 = \frac{12}{9} = \frac{4}{3}$.
Evaluating the Parentheses Next, we evaluate the expression within the parentheses: $24 -
\frac{4}{3} + 16$. We can rewrite this as 40 − 3 4 . To combine these terms, we need a common denominator, which is 3. So, we have 3 120 − 3 4 = 3 116 .
Evaluating the Multiplication Now, we evaluate the multiplication: 8 × 3 = 24 .
Performing the Subtraction Finally, we subtract the result of the multiplication from the result of the parentheses: 3 116 − 24 . Again, we need a common denominator, which is 3. So, we have 3 116 − 3 72 = 3 44 .
Final Answer Therefore, the value of the expression is 3 44 .
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or managing time. For instance, if you're planning a trip, you might need to calculate the total cost, considering transportation, accommodation, and activities. If transportation costs $50, accommodation costs $100 per night for 3 nights, and activities cost $75, the total cost would be calculated as $50 + (100 \times 3) + 75 = $425. This demonstrates how the order of operations ensures accurate financial planning.
The evaluated expression results in 3 44 . We followed the order of operations by solving the division, multiplication, and then completing the addition and subtraction. The final answer is 3 44 .
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