Add the fractions in the denominator

Convert 1/2 to 4/8 and add to 1/8 to get 5/8.

$\frac{1}{2}+\frac{1}{8}=\frac{5}{8}$

Replace division by multiplication of reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal.

$\frac{3}{4}\div\frac{5}{8}=\frac{3}{4}\times\frac{8}{5}$

Multiply numerators and denominators

Multiply across to obtain a single fraction.

$\frac{3\times8}{4\times5}=\frac{24}{20}$

Simplify the result

Reduce 24/20 to its lowest terms and convert to decimal.

$\frac{24}{20}=\frac{6}{5}=1.2$