Before you add two fractions, they must have the same denominator.  If they don’t, express one of the fractions in such a way that its denominator will be equal to that of the other fraction.  Once their denominators are equal, add the numerators.

(4 / 5) + (2 / 5) = (6 / 5)
(4 / 9) + (1 / 3) = (4 / 9) + (3 / 9) = (7 / 9)

Subtraction of fractions works in much the same way.  Make the denominators equal, and then subtract the numerators.

(4 / 5) - (2 / 5) = (2 / 5)
(4 / 9) - (1 / 3) = (4 / 9) - (3 / 9) = (1 / 9)

When you multiply fractions, you don’t need to equalize the denominators.  Just multiply the numerators and the denominators.

(4 / 5) x (2 / 5) = (8 / 25)
(4 / 9) x (1 / 3) = (4 / 27)

Dividing by a fraction is the same as multiplying by its reciprocal.  To perform division of fractions, switch the numerator and denominator of the fraction after the division sign, then multiply.

(4 / 5) / (2 / 5) = (4 / 5) x (5 / 2) = (20 / 10)
(4 / 9) / (1 / 3) = (4 / 9) x (3 / 1) = (12 / 9)

After you perform any of these operations, you’ve got to express the answer in lowest terms.  To reduce a fraction to lowest terms, divide the numerator and the denominator by their least common factor.

(1) Add.  (2 / 3) + (1 / 2)
(2) Subtract.  (7 / 8) - (4 / 5)
(3) Simplify.  (3 / 4) / (2 / 3) x (8 / 9)