In general, the difference of two fractions is computed as a/b - c/d = (ad - bc)/(bd) Examples 5/7 - 2/3 = (5*3 - 7*2)/(7*3) = (15-14)/21 = 1/21 2/3 - 1/3 = (2*3 - 3*1)/(3*3) = (6 - 3)/9 = 3/9 = 1/3 (note that the formula above works even when the denominators are the same. The result needs to be reduced in this case.) 3/4 - 3/8 = (3*8 - 4*3)/(4*8) = (24 - 12)/32 = 12/32 = 3/8 (because the original denominators have a common factor, the result needs to be reduced by dividing numerator and denominator by that factor)
Usually, you are taught to choose a "least common denominator", find equivalents that have that denominator, then perform the subtraction. Examples 2/3 - 1/3 = (2 - 1)/3 = 1/3 (they already have a common denominator) 3/4 - 3/8 = 6/8 - 3/8 = (6 - 3)/8 = 3/8 (3/4 is rewritten as 6/8 to match the denominator of 3/8) 3/4 - 2/3 = 9/12 - 8/12 = (9 - 8)/12 = 1/2 (both are rewritten in terms of the least common denominator) The least common denominator is the least common multiple of the denominators. (This is the product of the denominators divided by their greatest common factor.)
Usually, you are taught to choose a "least common denominator", find equivalents that have that denominator, then perform the subtraction. Examples 2/3 - 1/3 = (2 - 1)/3 = 1/3 (they already have a common denominator) 3/4 - 3/8 = 6/8 - 3/8 = (6 - 3)/8 = 3/8 (3/4 is rewritten as 6/8 to match the denominator of 3/8) 3/4 - 2/3 = 9/12 - 8/12 = (9 - 8)/12 = 1/2 (both are rewritten in terms of the least common denominator) The least common denominator is the least common multiple of the denominators. (This is the product of the denominators divided by their greatest common factor.)
