The three steps below were used to find the value of the expression [tex]$[(-10+2)-1]+(2+3)$[/tex]
Step 1: ?
Step 2: [tex]$-9+2+3$[/tex]
Step 3: [tex]$-7+3$[/tex]
Which expression is missing from Step 1?
A. [tex]$[-10+-1+2]+(2+3)$[/tex]
B. [tex]$[-8-1]+(2+3)$[/tex]
C. [tex]$[8+1]+(2+3)$[/tex]
D. [tex]$[-10+1]+(2+3)$[/tex]
Answer (2)
Simplify the innermost parentheses: ( − 10 + 2 ) = − 8 .
Substitute the result into the original expression: [ − 8 − 1 ] + ( 2 + 3 ) .
Compare the simplified expression with the given options.
The missing expression in Step 1 is [ − 8 − 1 ] + ( 2 + 3 ) .
Explanation
Analyze the Problem We are given the expression [( − 10 + 2 ) − 1 ] + ( 2 + 3 ) and asked to find the missing expression in Step 1 of its evaluation. The given steps are:
Step 1: ? Step 2: − 9 + 2 + 3 Step 3: − 7 + 3
We need to determine which of the provided options correctly fills in Step 1.
Simplify the Innermost Parentheses First, let's simplify the innermost parentheses in the original expression:
( − 10 + 2 ) = − 8
Now, substitute this result back into the original expression:
[( − 10 + 2 ) − 1 ] + ( 2 + 3 ) = [ − 8 − 1 ] + ( 2 + 3 )
Compare with the Options Now, let's compare this expression, [ − 8 − 1 ] + ( 2 + 3 ) , with the given options:
Option 1: [ − 10 + − 1 + 2 ] + ( 2 + 3 ) Option 2: [ − 8 − 1 ] + ( 2 + 3 ) Option 3: [ 8 + 1 ] + ( 2 + 3 ) Option 4: [ − 10 + 1 ] + ( 2 + 3 )
We can see that Option 2, [ − 8 − 1 ] + ( 2 + 3 ) , matches the expression we derived.
Final Answer Therefore, the missing expression in Step 1 is [ − 8 − 1 ] + ( 2 + 3 ) .
Examples
When simplifying complex arithmetic expressions, it's crucial to follow the order of operations (PEMDAS/BODMAS). This problem demonstrates how to correctly simplify an expression by breaking it down into smaller, manageable steps. This approach is useful in various real-life scenarios, such as calculating expenses, managing budgets, or determining quantities in recipes. By simplifying expressions step by step, we can avoid errors and arrive at the correct solution.
The missing expression in Step 1 is [ − 8 − 1 ] + ( 2 + 3 ) , which corresponds to option B. This was determined by simplifying the expression from the inside out. After substituting the simplified values, this matches with the provided options.
;
