We need to calculate the following sum:
[tex]\frac{8}{15}+\frac{7}{25}[/tex]The first step is to calculate the least common multiplier between the two denominators. This is done below:
[tex]\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}[/tex]We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:
[tex]\text{LCM}=3\cdot5\cdot5=75[/tex]Now we have to replace the denominators by 75 and calculate new numerators. The new numerators must be calculated as follows:
1 - Divide the LCM by the old denominator
2 - Multiply the result of 1 by the old numerator.
This is done below:
[tex]\begin{gathered} \frac{5\cdot8}{75}+\frac{3\cdot7}{75} \\ \frac{40}{75}+\frac{21}{75} \end{gathered}[/tex]Since both fractions have their denominators with the same value, we can just directly add them.
[tex]\frac{40+21}{75}=\frac{61}{75}[/tex]The fraction is already in its most reductable form, therefore the answer is 61/75.