1 1/3:q=1 1/5:3/4

To solve the proportion \( \frac{1 \frac{1}{3}}{q} = \frac{1 \frac{1}{5}}{\frac{3}{4}} \), we first need to convert the mixed numbers into improper fractions.

1. Convert \( 1 \frac{1}{3} \) to an improper fraction: \[ 1 \frac{1}{3} = \frac{3 \cdot 1 + 1}{3} = \frac{4}{3} \]

2. Convert \( 1 \frac{1}{5} \) to an improper fraction: \[ 1 \frac{1}{5} = \frac{5 \cdot 1 + 1}{5} = \frac{6}{5} \]

Next, substituting these fractions into the proportion gives us: \[ \frac{\frac{4}{3}}{q} = \frac{\frac{6}{5}}{\frac{3}{4}} \]

Now, simplify the right side: \[ \frac{\frac{6}{5}}{\frac{3}{4}} = \frac{6}{5} \times \frac{4}{3} = \frac{6 \cdot 4}{5 \cdot 3} = \frac{24}{15} = \frac{8}{5} \]

Now our equation is: \[ \frac{\frac{4}{3}}{q} = \frac{8}{5} \]

Next, we can cross-multiply to solve for \( q \): \[ 4 \cdot 5 = 8 \cdot 3q \] \[ 20 = 24q \] \[ q = \frac{20}{24} = \frac{5}{6} \]

Thus, the value of \( q \) is \( \frac{5}{6} \).