Question

Perform the indicated operations below and simplify ((a+b)/4) + ((2a-b)/5).

Answer 1

`((a+b))/(4) +((2a-b))/(5)=(13a)/(20) +(b)/(20)`

Explanation:

We have:

`((a+b))/(4) +((2a-b))/(5)`

We can use common denominator.

Observation:

If you have,
`(a)/(b) +(c)/(d)=((a*d)+(c*b))/(b*d)`

Then,

`((a+b))/(4) +((2a-b))/(5)=(5(a+b)+4(2a-b))/(4*5)`

Using distributive property:

Observation:

c(a+b)=ca+cb

`(5(a+b)+4(2a-b))/(4*5)=(5a+5b+8a-4b)/(20)=((5a+8a)+(5b-4b))/(20)`

Finally,

`((5a+8a)+(5b-4b))/(20) =(13a+b)/(20)=(13a)/(20) +(b)/(20)`

The answer then is:

`((a+b))/(4) +((2a-b))/(5)=(13a)/(20) +(b)/(20)`