MathDB

Martin invented the following algorithm. Let two irreducible fractions

\frac{s_1}{t_1}

and

\frac{s_2}{t_2}

be given as inputs, with the numerators and denominators being positive integers. Divide

s_1

and

s_2

by their greatest common divisor

c

and obtain

a_1

and

a_2

, respectively. Similarily, divide

t_1

and

t_2

by their greatest common divisor

d

and obtain

b_1

and

b_2

, respectively. After that, form a new fraction \frac{a_1b_2 \plus{} a_2b_1}{t_1b_2}, reduce it, and multiply the numerator of the result by

c

. Martin claims that this algorithm always finds the sum of the original fractions as an irreducible fraction. Is his claim correct?

Problem Statement