Convert the mixed fraction into an improper fraction. A mixed fraction is an integer (regular number) followed by a proper fraction. For example, a mixed fraction is 5 3/8. In this example, the "5" is the integer, the "3" is the numerator and the "8" is the denominator. To convert the mixed fraction into an improper fraction, simply multiply the denominator by the integer and add it to the numerator. The denominator stays the same. For the mixed fraction of 5 3/8, the improper fraction would be 43/8.
Find a common denominator. After both mixed fractions in the subtraction equation are converted to improper fractions, a common denominator must be found. In order to complete the subtraction equation with improper fractions, the denominators must both be the same. This can be achieved by choosing a number that both improper fractions are divisible by and multiplying the numerator and denominator by the number it takes to create the same denominator. For example, if the two improper fractions are 3/2 and 5/3, a number must be determined that is divisible by both 2 and 3. In this case it could be 6. Therefore, the denominators should both be 6 for each improper fraction. In this case 3/2 must be multiplied by 3, and 5/3 must be multiplied by 2. This will result in the two fractions being 9/6 and 10/6. The fractions are now ready to be subtracted.
Subtract the fraction. After the improper fractions have a common denominator, the numerators can be simply subtracted. If the improper fraction subtraction equation is 9/4 - 6/4, the numerators are subtracted (9-6). The result is 3/4.
Simplify the improper fraction. In any equation involving fractions, the result should always be simplified. In order to simplify a fraction, the numerator and denominator must be divided by a common divisible. For example, if the improper fraction is 10/6, a common divisible would be the number 2. Divide the numerator and denominator by 2, resulting in 5/3.
Convert the improper fraction back into a mixed number. An improper fraction can be converted into a mixed number by dividing the numerator by the denominator. The remainder of the division is the new numerator, and the denominator remains the same. For example, the improper fraction 39/8 would be converted to 4 7/8 (39 / 8 = 4, with a remainder of 7). The whole number is 4, the numerator is 7 and the denominator remains the same at 8.