3/16 : 4 1/8

To simplify the ratio \( \frac{3}{16} : 4 \frac{1}{8} \), we first need to convert the mixed number \( 4 \frac{1}{8} \) into an improper fraction.

1. Convert \( 4 \frac{1}{8} \) to an improper fraction: \[ 4 \frac{1}{8} = 4 \times 8 + 1 = 32 + 1 = 33 \] So, \( 4 \frac{1}{8} = \frac{33}{8} \).

2. Now we can rewrite the ratio: \[ \frac{3}{16} : \frac{33}{8} \]

3. To express this ratio as a single fraction, we can rewrite it in fraction form: \[ \frac{3}{16} \div \frac{33}{8} = \frac{3}{16} \times \frac{8}{33} \]

4. Multiply the fractions: \[ \frac{3 \times 8}{16 \times 33} = \frac{24}{528} \]

5. Simplify \( \frac{24}{528} \):

   • Find the greatest common divisor (GCD) of 24 and 528, which is 24.
   • Divide both the numerator and the denominator by 24: \[ \frac{24 \div 24}{528 \div 24} = \frac{1}{22} \]

Thus, the ratio \( \frac{3}{16} : 4 \frac{1}{8} \) simplifies to \( 1 : 22 \).