+ 
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
