Question

Perform the indicated operation numbers be sure to express your answer in reduced form

Answer 1

We need to calculate the following sum:

`(8)/(15)+(7)/(25)`

The first step is to calculate the least common multiplier between the two denominators. This is done below:

`\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}`

We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:

`\text{LCM}=3\cdot5\cdot5=75`

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:

`\begin{gathered} (5\cdot8)/(75)+(3\cdot7)/(75) \\ (40)/(75)+(21)/(75) \end{gathered}`

Since both fractions have their denominators with the same value, we can just directly add them.

`(40+21)/(75)=(61)/(75)`

The fraction is already in its most reductable form, therefore the answer is 61/75.