+  

The denominators are not the same.  We must do "face-lifts" on
the fractions without changing their values to get them to
have the same denominator.

The LCD of 4 and 5 is 20.

Looking at the first fraction. To become 20, the denominator 
4 needs to be multiplied by 5.  But that would change the value
of , so instead we multiply by  which is just 
1, and multiplying by 1 won't change the value of , but
will just give it a face-lift, so we do that to the first fraction:

× + 

Looking at the second fraction. To become 20, the denominator 
5 needs to be multiplied by 4.  But that would change the value
of , so instead we multiply by  which is just 
1, and multiplying by 1 won't change the value of , but
will just give it a face-lift, so we do that to the second fraction:

× + ×

Now we multiply the numerators and denominators and get

 + 

That can be thought of as 

15 twentieths + 4 twentieths

and we know that 

15 twentieths + 4 twentieths = 19 twentieths

just as we would know that

15 pencils + 4 pencils = 19 pencils

So therefore,

 +  = .  So the whole process is:



 +  = × + × =  +  = .  

Edwin