Wapi simplified an expression. His work is shown below:
[tex]7(8.5-1.5)+8 \div 2[/tex]
Step 1: [tex]7(7)+8 \div 2[/tex]
Step 2: [tex]49+8+2[/tex]
Step 3: [tex]57 \div 2[/tex]
Step 4: 28.5
In which step did Wapi make his first mistake?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answer (2)
Wapi correctly simplifies the parentheses in Step 1.
In Step 2, Wapi incorrectly evaluates the division, leading to an incorrect expression.
The correct simplification should be 7 ( 7 ) + 8 d i v 2 = 49 + 4 = 53 .
Therefore, Wapi's first mistake is in Step 2. s t e p 2
Explanation
Analyzing the Problem Let's analyze Wapi's steps to identify the first mistake. The original expression is 7 ( 8.5 − 1.5 ) + 8 d i v 2 .
Evaluating Step 1 Step 1: Wapi simplifies the expression inside the parentheses: 8.5 − 1.5 = 7 . So the expression becomes 7 ( 7 ) + 8 d i v 2 . This step is correct.
Evaluating Step 2 Step 2: Wapi calculates 7 ( 7 ) = 49 . However, instead of correctly evaluating 8 d i v 2 = 4 , Wapi seems to have incorrectly written 8 + 2 . The expression should be 49 + 4 , but Wapi wrote 49 + 8 + 2 . Therefore, Step 2 is where Wapi made his first mistake.
Continuing Correct Calculation To confirm, let's continue the correct calculation: 49 + 4 = 53 . Then the expression becomes 53 .
Evaluating Step 3 Step 3: Wapi writes 57 d i v 2 , which is incorrect since the correct expression should be 53 .
Evaluating Step 4 Step 4: Wapi calculates 28.5 , which is also incorrect.
Conclusion Therefore, Wapi made his first mistake in Step 2.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a scientific experiment. For example, if you are calculating the total cost of items with discounts and taxes, you need to apply the discount before adding the tax. Similarly, in programming, the order in which operations are performed can significantly affect the result. Mastering the order of operations ensures accurate and reliable results in various fields.
Wapi's first mistake occurred in Step 2, where he incorrectly evaluated the division. The expression should have simplified to 49 + 4 instead of 49 + 8 + 2 . Therefore, the correct answer is Step 2.
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