Question

How do you simplify `(6)/(7)+(5)/(2)`?

Answer 1

I found: `47/14`

Explanation:

Here you can add the two fractions BUT you must be careful becase you cannot add directly but you need to make their denominators equal first; if the denominators are equal you can add them directly adding the numerators.
Let us choose a common denominator:
A good one could be `14` that is small and common between `7` and `2`, and also is a multiple of both, making it easy to handle.
Let us do that:

`()/(14)+()/(14)=`

BUT what about the numerators?
We see that we "imposed" a new denominator but in order to mantain the fractions with the same original value we need to "manipulate" the numerator accordingly.

In the first fraction the old denominator `7` became `14`; this is the same as `7xx2=14`; so the old denominator was multiplyed by `2` and we do the same with the numerator:

In the second fraction the old denominator `2` became `14`; this is the same as `2xx7=14`; so the old denominator was multiplyed by `7` and we do the same with the numerator:

or:
`(6xxcolor(red)(2))/(14)+(5xxcolor(red)(7))/(14)=12/14+35/14=`

you can check that the two new fractions have exactly the same value of the original ones!
`6/7=12/14`
and
`5/2=35/14`

The good thing is that now the denominators are the same and we can add the two fractions as:
`(12+35)/14=47/14`