To calculate the quotient of \(10 \div \frac{3}{4}\), you can multiply by the reciprocal of \(\frac{3}{4}\).
The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\). So, you can rewrite the expression as:
\[ 10 \div \frac{3}{4} = 10 \times \frac{4}{3} \]
Now, calculate the multiplication:
\[ 10 \times \frac{4}{3} = \frac{10 \times 4}{3} = \frac{40}{3} \]
Thus, the quotient of \(10 \div \frac{3}{4}\) is \(\frac{40}{3}\), which can also be expressed as a mixed number:
\[ \frac{40}{3} = 13 \frac{1}{3} \]
Therefore, the final answer is:
\[ \frac{40}{3} \text{ or } 13 \frac{1}{3} \]
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