Type the correct answer in the box. Use numerals instead of words.
Use the order of operations to evaluate this expression:
[tex]$7+(5-9)^2+3(16 \div 8)$[/tex]
The value of the expression is $\square$.
Answer (2)
Evaluate the expression inside the parentheses: ( 5 − 9 ) = − 4 and ( 16 ÷ 8 ) = 2 .
Evaluate the exponent: ( − 4 ) 2 = 16 .
Perform the multiplication: 3 ( 2 ) = 6 .
Perform the addition: 7 + 16 + 6 = 29 . The value of the expression is 29 .
Explanation
Understanding the Expression and Order of Operations We need to evaluate the expression $7+(5-9)^2+3(16
\div 8)$ using the order of operations (PEMDAS/BODMAS). This means we need to deal with Parentheses first, then Exponents, then Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).
Evaluating Parentheses First, we evaluate the expressions inside the parentheses:
( 5 − 9 ) = − 4
( 16 ÷ 8 ) = 2
Evaluating Exponent Next, we evaluate the exponent:
( − 4 ) 2 = ( − 4 ) × ( − 4 ) = 16
Performing Multiplication Now, we perform the multiplication:
3 ( 16 ÷ 8 ) = 3 ( 2 ) = 6
Performing Addition Finally, we perform the addition:
7 + ( 5 − 9 ) 2 + 3 ( 16 ÷ 8 ) = 7 + 16 + 6 = 29
Final Answer Therefore, the value of the expression is 29.
Examples
Order of operations is a fundamental concept in mathematics and is used in various real-life scenarios. For example, when calculating the total cost of items with discounts and taxes, you need to follow the order of operations to get the correct result. Imagine you are buying a shirt that costs $20, has a 10% discount, and then a 5% tax is applied. The correct calculation would be: $20 - (0.10 \times 20) + (0.05 \times (20 - (0.10 \times 20))) = $18 + $0.90 = $18.90. Following the order of operations ensures you apply the discount before the tax, giving you the correct final price.
The computed value of the expression 7 + ( 5 − 9 ) 2 + 3 ( 16 ÷ 8 ) is 29, after applying the order of operations. We evaluated the parentheses, exponent, multiplication, and completed the addition in sequence. Therefore, the final answer is 29.
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