Find the smallest multiple, also known as the least common multiple, or LCM, of all denominators in your subtraction equation. To find the LCM, find the lowest multiple of all numbers, excluding zero. List all of the multiples of the denominators. Circle the ones that are common to each list. The lowest number on all lists is the LCM. For example, if you were subtracting 3/4 - 1/3, you would list the multiples of both 3 and 4, the denominators. Multiples of 3 = 3,6,9,12,15. Multiples of 4 = 4, 8,12,16. 12 is common to both lists. It is also the lowest number that is common to both denominators. Your LCM for 3 and 4 is 12.
Change the denominator of both fractions to an equivalent fraction that has the LCM as the denominator. Determine the factor you need to multiply the denominator by to obtain the LCM. For instance, in the equation of 3/4 -1/3, you need to change the denominators to 12. For 3/4, the factor you need is 3, because 3 x 4 = 12. Multiply both the numerator and the denominator by that factor: 3/4 x 3/3 = 9/12. The equivalent fraction with the LCM as the denominator for 3/4 is 9/12. Change the other rational number to an equivalent fraction with the LCM as the new denominator. In this case, the factor you multiply both the numerator and denominator by is 4: 1/3 x 4/4 = 4/12.
Subtract the numerators. Now that you have common denominators in your equation, you can complete your equation. 3/4 - 1/3 rewritten as equivalent fractions with the LCM as the denominator is 9/12 - 4/12 = 5/12.