Fractions can not be added or subtracted unless there are similar denominators. The easy way to make the denominators the same is to multiply the numerators and denominators of each fraction by the denominators of the other fraction. For example, 2/3 + 1/4 = (4/4 X 2/3) + (3/3 X 1/4) = 8/12 + 3/12 = 11/12. Also 1/5 - 2/7 = (7/7 X 1/5) - (5/5 X 2/7) = 7/35 - 10/35 = -3/35.
Subtracting fractions can get confusing -- especially when the fractions have signs. The easy way to do it is to convert the subtraction problem to an addition problem by changing the sign of the second number. For example (3/4) - (-1/4) = (3/4) + (+1/4) = 3/4 + 1/4 = 4/4 = 1. Using plenty of parentheses during this process can help to keep things straight. (-3/7) - (-1/7) = (-3/7) + (+1/7) = 1/7 - 3/7 = -2/7.
If both the signs are the same -- after converting subtraction to addition -- the sign of the answer will be the same. The value will be the sum of the fractions without regard to signs. For example -5/9 - 7/7 = -(5/9 + 7/9) = -12/9 = -1 3/9 = -1 1/3. Also 2/19 + 5/19 = +(2/19 + 5'19) = 8/19. If the signs are different, the sign of the answer will be the sign of the largest fraction. Always subtract the small fraction from the large one. For example 3/11 - 4/11 = -(4/11 - 3/11) = -(1/11) = -1/11. Also -1/12 + 10/12 = +(10/12 - 1/12) = 9/12 = 3/4.
When combining mixed numbers, do the whole numbers and fractions separately and combine the answers. For example, (2 3/17) + (5 5/17) = (2 + 5) + (3/17 + 5/17) = 7 8/17. Sometimes you will need to combine a fraction and a whole number. The easy way to do this is to convert the whole number to a fraction and then combine. For example, 3/4 - 2 = 3/4 - 8/4 = -(8/4 - 3/4) = -5/4 = - 1 1/4.