1 2/3 : 1 1/4

To simplify the ratio \( 1 \frac{2}{3} : 1 \frac{1}{4} \), we can first convert the mixed numbers into improper fractions.

1. Convert \( 1 \frac{2}{3} \): \[ 1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} \]

2. Convert \( 1 \frac{1}{4} \): \[ 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} \]

Now we can write the ratio: \[ \frac{5}{3} : \frac{5}{4} \]

To simplify this ratio, we can divide the two fractions: \[ \frac{5}{3} \div \frac{5}{4} = \frac{5}{3} \times \frac{4}{5} = \frac{4}{3} \]

Thus, the simplified ratio is: \[ 4 : 3 \]

So, the ratio \( 1 \frac{2}{3} : 1 \frac{1}{4} \) simplifies to \( 4 : 3 \).