To add fractions with unlike denominators, you must first find a common denominator by multiplying each fraction's denominator by the other fraction's denominator. Then add the numerators and place the sum over the common denominator. When multiplying fractions, the new numerator is the product of the original numerators and the new denominator is the product of the original denominators, which can then be simplified if possible. The reciprocal of a fraction is formed by switching the original numerator and denominator.