If the fractions don’t have the same denominators -- the number on the bottom -- they must be made to match. First, find a common denominator. For instance, consider the problem 7 1/5 – 4 2/3. Multiply the two denominators, 5 and 3, to get 15 -- this will be the new denominator for both numbers. Now the numerators -- the numbers on the top -- must be changed so that the values of the fractions remain the same. The numerators should be multiplied by the same numbers by which their corresponding denominators were multiplied to obtain the new denominators. For instance, in 7 1/5, the 5 is multiplied by 3 to produce 15, so multiply the numerator by 3 also, resulting in 7 3/15. In 4 2/3, the 3 was multiplied by 5 to obtain 15, so multiply the numerator by 5 as well, to get 4 10/15. The problem now becomes 7 3/15 – 4 10/15.
In the situation of 7 3/15 – 4 10/15, performing subtraction at this stage would result in subtracting 10 from 3, which would produce a negative numerator, rendering the problem a dead end. The way around this is to make the numerator of the first fraction larger by borrowing from its whole number. To do this, decrease the value of the whole number by 1, and add that 1 to the fraction. In the example, take 1 away from the whole number, 7, to get 6. Since 1 is the same as 15/15, adding 1 to 3/15 produces the improper fraction 18/15. Your new mixed number is 6 18/15.
The problem is now in a form that can be subtracted: 6 18/15 – 4 10/15. Subtract the whole numbers first: 6 – 4 = 2. Next, subtract the numerators of the fractions: 18 – 10 = 8. Do not subtract the fractions’ denominators -- they remain unchanged. The answer to the subtraction problem is then 2 8/15.
If the fraction isn’t already in lowest terms, put it in lowest terms. It isn’t necessary in this example, because 2 8/15 is already in its lowest terms. But suppose that, in a different problem, you had obtained an answer of 5 6/8. Leave the whole number alone and reduce the fraction portion by dividing both the numerator and the denominator by the greatest common factor. Here, the greatest common factor of 6 and 8 is two, so 6/8 becomes 3/4, for an answer of 5 3/4.