Let's evaluate the expression step by step to check if Eve's work is correct. The original expression is:
\[ 33 - 11 + 262 \div 34 \]
We'll follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
- Perform the division first:
\[ 262 \div 34 = 7.70588 \approx 7.71 (if rounded) \]
or \( 262 \div 34 \) can be simplified directly:
- \( 34 \times 7 = 238 \)
- \( 34 \times 8 = 272 \)(this is too much)
- So \( 262 \div 34 = 7 \) (exact, since 7 is the largest integer less than 7.71)
Replacing that in the original expression gives:
\[ 33 - 11 + 7 \]
- Then do the subtraction and addition from left to right: \[ 33 - 11 = 22 \]
So now we have:
\[ 22 + 7 = 29 \]
Let's summarize Eve's steps to see if she matches this:
- Original expression: \( 33 - 11 + 262 \div 34 \) (Correct)
- Step 1: \( 27 - 11 + 236 \div 34 \) (Incorrect, should not be 236)
- Step 2: \( 27 - 11 + 72 \div 34 \) (Incorrect, previous result was wrong)
- Step 3: \( 27 - 11 + 244 \) (Incorrect)
- Step 4: \( 27 - 11 + 96 \) (Incorrect)
- Step 5: \( 16 + 96 \) (Incorrect)
- Step 6: \( 112 \) (Incorrect)
Eve's calculation is incorrect from the very first step. The correct evaluation of the expression \( 33 - 11 + 262 \div 34 \) should result in \( 29 \).