From a sum of decimal fractions to a single fraction

Statement

Write as a single fraction in lowest terms: $\frac{7}{10} + \frac{2}{100} + \frac{5}{1000}.$

Solution

Bring everything to denominator $1000$: $\frac{700}{1000} + \frac{20}{1000} + \frac{5}{1000} = \frac{725}{1000}.$ Since $\gcd(725,1000)=25$: $\frac{725}{1000} = \boxed{\dfrac{29}{40}}.$