Let's evaluate Tisha's work step by step to identify any mistakes.
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Starting with the original expression:
\[ 490 \div 72.9 - 2.3 \] -
In Step 1, Tisha rewrote it as:
\[ 490 \div 49 \cdot 9 - 2 \cdot 3 \]Here, Tisha attempted to transform \(72.9\) into \(49 \cdot 9\). This is correct because \(72.9 = 49 \cdot 1.5\), but let's evaluate separately.
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In Step 2, she then simplified \(490 \div 49 \cdot 9\). It's important to note that, according to the order of operations (PEMDAS/BODMAS), division and multiplication should be handled from left to right.
- So, first, we should evaluate \(490 \div 49\): \[ 490 \div 49 = 10 \]
- Next, multiply by 9: \[ 10 \cdot 9 = 90 \]
- Tisha then stated it was \(10.9\), which is incorrect.
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The expression now looks like: \[ 90 - 2 \cdot 3 \]
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In Step 3, she correctly writes \(90 - 2 \cdot 3\), but then evaluates \(2 \cdot 3\) without actually doing it in her Step 4:
- This should be: \[ 90 - 6 = 84 \]
- Tisha claims \(88.3\) in Step 4, which is incorrect.
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Finally, in Step 5, she states the answer is \(264\) for \(84\).
Given this analysis, Tisha made multiple mistakes, starting from how she handled the division and multiplication in Step 1, leading to incorrect results in subsequent steps. Specifically:
- She mishandled the construction of \(72.9\) and the changes to the operation.
- An error in interpreting calculations led her to derive the wrong numbers.
Therefore, the correct statement is:
No, Tisha made a mistake going from Step 1 to Step 2. Tisha should have multiplied 49 and 9 before dividing. The order of operations says to multiply before you divide.
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