To divide by a fraction, you multiply by its reciprocal. Therefore, to calculate \( 10 \div \frac{3}{4} \), you can rewrite it as:
\[ 10 \times \frac{4}{3} \]
Now, perform the multiplication:
\[ 10 \times \frac{4}{3} = \frac{40}{3} \]
Thus, the quotient of \( 10 \div \frac{3}{4} \) is \( \frac{40}{3} \) or approximately \( 13.33 \) when expressed as a decimal.