No, the answer is not $\displaystyle \frac{11}{2}$
To simplify
we need to find the
LOWEST COMMON DENOMINATOR of the two fractions. In other words, we need the two
BOTTOM NUMBERS of the fractions to be
THE SAME.
The easiest way to find a COMMON DENOMINATOR is to multiply the two DENOMINATORS (bottom numbers) together:
Aka. $\displaystyle 7*5=CD$
Therefore Common Denominator = 35
Therefore,
$\displaystyle \frac{110}{35}-\frac{77}{35}$
What I've done is place the original numerators (22 and 11) over the LOWEST COMMON DENOMINATOR. What we do to the bottom, we must do to the top (this keeps the ratio even).
In other words, to get from 7 (the denominator in the first fraction)) to 35 we needed to multiply it by 5! To get from 5 (the denominator in the second fraction) to 35 we needed to multiply it by 7!
What we do to the bottom, we do to the top!!
Keeping it short,
22*5 = 110 (New numerator for first fraction)
11*7 = 77
Now to simplify $\displaystyle \frac{110}{35}-\frac{77}{35}$!
Deal with the numerators only: 110-77 = 33 Place the new numerator over the new common denominator (35): 33/35
33/35 Can't be simplified any further, hence this is the answer!
Answer: $\displaystyle \frac{33}{35}$