Let's analyze Mackenzie's work to solve the problem \(1.35 \times 1.4\).
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Understanding the decimal multiplication: We can rewrite the problem without changing its value: \[ 1.35 = \frac{135}{100} \] \[ 1.4 = \frac{14}{10} \] Thus, we can write: \[ 1.35 \times 1.4 = \left(\frac{135}{100}\right) \times \left(\frac{14}{10}\right) \]
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Multiplying fractions: \[ = \frac{135 \times 14}{100 \times 10} = \frac{135 \times 14}{1000} \]
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Calculating \(135 \times 14\): To find the product \(135 \times 14\): \[ 135 \times 14 = 1890 \]
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Finding the final product: Now, place \(1890\) over \(1000\): \[ \frac{1890}{1000} = 1.890 \]
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Final conclusion: Thus, the final result of \(1.35 \times 1.4\) is: \[ 1.890 \]
Analyzing her steps: In the original work provided, it appears there were multiple representations of \(1.35\) and \(1.4\) using factors of \(10\) and \(100\). The organization and calculations may have switched between moving the factors around, but they need to demonstrate how to properly align the decimal point after multiplying.
The correct interpretation of the decimal places is to ultimately ensure that the result respects the placement of decimal points relative to the initial numbers.
In summary, Mackenzie ultimately performed the operations correctly, yielding \(1.890\) as the product of \(1.35 \times 1.4\).