$(17+4 \times 3=$
$9+2 \times(8-2)-3=$
Answer (2)
First, multiply 4 and 3, then add the result to 17: 17 + 4 × 3 = 17 + 12 = 29 .
Next, subtract 2 from 8, multiply the result by 2, add 9, and subtract 3: 9 + 2 × ( 8 − 2 ) − 3 = 9 + 2 × 6 − 3 = 9 + 12 − 3 = 21 − 3 = 18 .
The first expression evaluates to 29.
The second expression evaluates to 18. 29 , 18
Explanation
Understanding the Problem We are given two arithmetic expressions to evaluate. We need to follow the order of operations (PEMDAS/BODMAS) to get the correct results.
Evaluating the First Expression First, let's evaluate the expression 17 + 4 × 3 . According to the order of operations, we need to perform the multiplication before the addition.
Multiplication So, we calculate 4 × 3 = 12 .
Addition Now, we add the result to 17: 17 + 12 = 29 .
Evaluating the Second Expression Next, let's evaluate the expression 9 + 2 × ( 8 − 2 ) − 3 . According to the order of operations, we need to perform the operation inside the parentheses first.
Parentheses So, we calculate ( 8 − 2 ) = 6 .
Multiplication Now, we perform the multiplication: 2 × 6 = 12 .
Addition Next, we perform the addition: 9 + 12 = 21 .
Subtraction Finally, we perform the subtraction: 21 − 3 = 18 .
Conclusion Therefore, the results of the two expressions are 29 and 18.
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses, determining the total cost of items with discounts, or even in programming where the order of operations affects the outcome of calculations. For instance, if you are buying multiple items with different prices and quantities, you need to multiply the quantity by the price for each item and then add them up to find the total cost. Similarly, if you have a discount on some items, you need to subtract the discount amount after multiplying the quantity and price.
The first expression evaluates to 29 and the second expression evaluates to 18 by following the order of operations. In the first expression, multiplication is performed before addition, while in the second expression, the operations within parentheses are prioritized before multiplication and subtraction. Thus, the final results are 29 and 18.
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