To evaluate Bai's work, we need to verify both the division he completed and the multiplication he used to check his work.
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Division of Fractions: To divide fractions, we multiply by the reciprocal. Therefore: \[ \frac{7}{3} \div \frac{2}{9} = \frac{7}{3} \times \frac{9}{2} \] This simplifies to: \[ = \frac{7 \times 9}{3 \times 2} = \frac{63}{6} = \frac{21}{2} \]
So, the correct quotient of \(\frac{7}{3} \div \frac{2}{9}\) is \(\frac{21}{2}\).
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Checking the Work: Bai attempted to check his work using the equation: \[ \frac{21}{2} \times \frac{2}{9} \] This simplifies to: \[ = \frac{21 \times 2}{2 \times 9} = \frac{42}{18} = \frac{7}{3} \]
Here, he is verifying \(\frac{21}{2}\) was the correct quotient by multiplying it by \(\frac{2}{9}\), which simplifies correctly back to \(\frac{7}{3}\).
Now, examining Bai’s process:
- He found the correct quotient of \(\frac{7}{3} \div \frac{2}{9}\) resulted in \(\frac{21}{2}\).
- He checked his work correctly, as \( \frac{21}{2} \times \frac{2}{9} \) indeed equals \(\frac{7}{3}\).
Based on this assessment, the most accurate description of Bai’s work is:
Bai found the correct quotient and checked his work using multiplication correctly.
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