The mnemonic for dividing fractions is "Invert the denominator and multiply".For example:
(1/2)/(1/4) is (1/2)*4 = 2. But think about what it means! ((1/2)/(1/4) means "How many fourths are in one half?" Think about a pie which you divided into 4 equal pieces. You served 2 two pies, i.e. you have 1/2 left. How many of the original 1/4 sized pieces are left?
To reduce fractions to lowest terms: find the largest factor common to both the numerator and denominator and divide it out. The way to find the great common factor is to factor the numerator and denominator, using the unique factorization theorem. For example: 15/18 = 5*3/(2*3*3) = 5/6.
