Final answer:
The process of adding fractions with different denominators involves finding a common denominator and adjusting each fraction accordingly. The resulting fractions, with the same denominator, have their numerators added together. The final fraction is then simplified by reducing common factors.
Step-by-step explanation:
The question involves adding fractions with different denominators and simplifying the result. To achieve this, we find a common denominator, which is the product of the individual denominators. In this case, the common denominator for 22 and 23 is 22*23. We then adjust each fraction to have this common denominator by multiplying the numerator and denominator by the necessary factors. Now each fraction has the same denominator, we can add the numerators together directly.
Breaking it down for the fractions (21/22), (27/23), (2/1), and (27/22), we adjust them as follows: (21/22) becomes (21*23)/(22*23), (27/23) becomes (27*22)/(23*22), (2/1) becomes (2*22*23)/(1*22*23), and (27/22) remains as it is because it already has the common denominator of 22. By adding these adjusted numerators together, we get a new numerator, while the denominator stays as 22*23.
The next step is to simplify the resulting fraction if possible, by canceling out any common factors between the numerator and the denominator. This process brings us closer to the most reduced form of the fraction, which is our aim.