Evaluate $(24-72 \div 9+16)-8 \times 3$
Answer (2)
Perform the division: $72
div 9 = 8$.
Perform the multiplication: $8
times 3 = 24$.
Evaluate the expression inside the parentheses: 24 − 8 + 16 = 32 .
Subtract the result of the multiplication from the result of the parentheses: 32 − 24 = 8 . The final answer is 8 .
Explanation
Understanding the Expression We are asked to evaluate the expression $(24-72
div 9+16)-8
times 3$. To do this, we will follow the order of operations (PEMDAS/BODMAS).
Performing the Division First, we perform the division $72
div 9 , w hi c h e q u a l s 8. S o t h ee x p ress i o nb eco m es (24-8+16)-8
times 3$.
Performing the Multiplication Next, we perform the multiplication $8
times 3 , w hi c h e q u a l s 24. S o t h ee x p ress i o nb eco m es (24-8+16)-24$.
Evaluating the Parentheses (Subtraction) Now, we evaluate the expression inside the parentheses from left to right. First, 24 − 8 = 16 . So the expression becomes ( 16 + 16 ) − 24 .
Evaluating the Parentheses (Addition) Then, 16 + 16 = 32 . So the expression becomes 32 − 24 .
Final Subtraction Finally, we subtract 24 from 32, which equals 8. So the expression is 32 − 24 = 8 .
Examples
Order of operations is a fundamental concept in mathematics and is used in various real-life scenarios, such as calculating expenses, determining the total cost of items with discounts, or even in programming to ensure operations are performed in the correct sequence. For example, if you buy 3 items that cost $5 each and have a discount of 2 , t h e t o t a l cos t c anb ec a l c u l a t e d a s (3 \times 5) - 2 = 13$. Without the correct order of operations, you might calculate 3 × ( 5 − 2 ) = 9 , which is incorrect.
The evaluation of the expression ( 24 − 72 ÷ 9 + 16 ) − 8 × 3 follows the order of operations leading to a final result of 8 . We calculated the division and multiplication while simplifying the parentheses step by step. The whole evaluation ends with the expression simplifying down to 8 .
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