Examine the problem 5/8 -- 3/8.
Subtract the numerators: 5 -- 3 = 2. Write the solution with the new numerator while keeping the same denominator, thus 2/8.
Reduce the fraction by finding the greatest common factor (GCF) of both the numerator and denominator. Both two and eight are evenly divisible by the factor two.
Divide both the numerator and the denominator by the GCF to reduce 2/8 to its lowest form: 2 ÷ 2 = 1 and 8 ÷ 2 = 4. Therefore, the difference of 5/8 and 3/8 is 1/4.
Examine the expression 8/9 -- 4/7. Since the denominators are different, they cannot subtract as before; i.e., you cannot subtract seven cats from a group of nine dogs. Instead, you must find equivalent fractions with the same denominator.
Find the least common multiple; i.e., the lowest number both nine and seven divide into evenly. In this case, the LCM is 63 (9 x 7 = 63 and 7 x 9 = 63).
Multiply the first numerator by seven since you multiplied the denominator by seven to find the LCM: 8 x 7 = 56, so 56/63 is the equivalent to 8/9.
Multiply the second numerator by nine, because you multiplied the denominator by nine to find the LCM. Since 4 x 9 = 36, 36/63 is the equivalent to 4/7. Now both fractions have like denominators.
Subtract the numerators and keep the denominator the same: 56/63 -- 36/63 = 20/63, which will not reduce.
Examine the problem 5 2/3 -- 4 1/3.
Subtract the fractional problem first: 2/3 -- 1/3 = 1/3.
Subtract the whole numbers: 5 -- 4 = 1. The solution is 1 1/3.
Examine the problem 8 3/4 -- 6 4/5.
Convert the fractions to their equivalent form by finding the LCM and multiplying the numerators by the factor. The LCM is 20, so multiply the first fraction by 5 and the second fraction by 4. 8 15/20 - 6 16/20.
Notice that the second fraction is larger than the first and therefore cannot be subtracted without borrowing. Borrow one from the whole number before the first fraction: 8 -- 1 = 7.
Add the borrowed one to the fraction 15/20. 15/20 + 1, or 15/20 + 1/1. Remember that 1/1 is the same as the whole number one. However, the denominators are different. The LCM of 20 and one equals 20, so rewrite the expression so it reads 15/20 + 20/20.
Add the numerators, 20 + 15 = 35, and place the total over the denominator: 35/20. The first fraction has been adjusted and now reads 7 35/20.
Take 7 35/20 -- 6 16/20. Subtract the numerators first and keep the denominator: 35 -- 16 = 19/20. Subtract the whole numbers, 7 -- 6 = 1. Therefore, 8 3/4 -- 6 4/5 = 1 19/20.