$[(5,577)-2] \div 2 \cdot(8+18 \div 9)$
Answer (2)
Evaluate the expression inside the first parentheses: ( 5577 ) − 2 = 5575 .
Evaluate the expression inside the second parentheses: $8 + 18
div 9 = 8 + 2 = 10$.
Divide the result from the first parentheses by 2: $5575
div 2 = 2787.5$.
Multiply the result by the result from the second parentheses: $2787.5
cdot 10 = 27875 . T h e f ina l an s w er i s \boxed{27875}$.
Explanation
Understanding the Problem We are asked to evaluate the expression $[(5577)-2]
div 2
cdot(8+18
div 9)$. To do this, we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Evaluating the First Parenthesis First, we evaluate the expressions inside the parentheses. We have two sets of parentheses: ( 5577 ) − 2 and $(8 + 18
div 9)$.
For the first set, ( 5577 ) − 2 = 5575 .
Evaluating the Second Parenthesis For the second set, we need to perform the division before the addition. So, $18
div 9 = 2$. Then, we add this result to 8: 8 + 2 = 10 .
Performing Division Now we have $[5575]
div 2
cdot [10]$. We perform the division and multiplication from left to right. First, we divide 5575 by 2: $5575
div 2 = 2787.5$.
Performing Multiplication Finally, we multiply the result by 10: $2787.5
cdot 10 = 27875$.
Final Answer Therefore, the value of the expression is 27875.
Examples
Order of operations is a fundamental concept in mathematics and is used in various real-life scenarios. For instance, when calculating the total cost of items with discounts and taxes, the order of operations ensures the correct price is determined. Similarly, in programming, the order of operations is crucial for evaluating complex expressions and ensuring the program functions as intended. Understanding and applying the order of operations correctly is essential for accurate calculations and problem-solving in both mathematical and practical contexts.
To evaluate the expression [( 5577 ) − 2 ] ÷ 2 ⋅ ( 8 + 18 ÷ 9 ) , we first simplify inside the parentheses and then follow the order of operations. After calculations, we find that the final answer is 27875 .
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