Convert the mixed number to an improper fraction. Multiply the whole number by the denominator, add the numerator and place the result over the denominator. For example, to convert 4 5/6 to an improper fraction, multiply 4 by 6, yielding 24; add 5, yielding 29; and place the result over the denominator, yielding 29/6.
Change a whole number to a fraction by placing it over 1. For example, change the whole number 7 to a fraction by placing it over 1, yielding 7/1.
Multiply the fractions by multiplying the numerators and denominators separately. In the example, 29 x 7 = 203 and 6 x 1 = 6. The improper fraction answer is 203/6.
Divide the numerator by the denominator to reconvert to a mixed number. Dividing 203 by 6 yields 33, with a remainder of 5; 33 is the whole-number portion of the answer, and 5, placed atop the numerator, is the fractional portion, yielding a result of 33 5/6.
Convert the mixed number to an improper fraction. Multiply the whole number by the denominator, add the numerator and place the result over the denominator. To convert 3 3/4 to an improper fraction, multiply 3 by 4, yielding 12; add 3, yielding 15; and place the result over the denominator, yielding 15/4. To convert 3 1/3 to an improper fraction, multiply 3 by 3, yielding 9; add 1, yielding 10; and place the result over the denominator, yielding 10/3.
Write out the problem to perform the operation. Divide using cross-multiplication; to cross-multiply, change the second fraction (10/3) to its reciprocal (3/10), and change the operation from division to multiplication. The problem then becomes 15/4 x 3/10.
Reduce fractions before multiplying, if possible. In the example, 15 (in the numerator of the first fraction) and 10 (in the denominator of the second fraction) both can be divided by 5 -- reducing 15/4 to 3/4 and 3/10 to 3/2.
Multiply the reduced fractions by multiplying the numerators and the denominators. In the example, multiplying 3/4 by 3/2 yields 9/8.
Divide the numerator by the denominator to reconvert to a mixed number. Dividing 9 by 8 yields 1, with a remainder of 1; 1 is the whole-number portion of the answer, and 1, placed atop the numerator, is the fractional portion, yielding a result of 1 1/8.