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what is one difference between the steps for multiplying and dividing fractions?

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When you divide with fractions you use the following rule: dividing by a number is the same as multiplying by its reciprocal. After applying this rule you have a multiplication of fractions problem.
 
multiplication: (a/b) x (c/d) = ac/bd (don't forget to simplify or simplify before you multiply)
division: (a/b)/(c/d)=(a/b) x (d/c) = ad/bc (don't forget to simplify or simplify before you multiply)
 
(3/4) x (5/7) = (3*5)/(4*7) = 15/28
 
(4/9) x (15/16) = (4*15)/(9*16) = 60/144 = 5/12 or,
(4/9) x (15/16) = (1/3) x (5/4) = 5/12
In the above example divide 4 and 16 both by 4 and divide 9 and 15 both by 3.
 
(4/5)/(6/7) = (4/5) x (7/6) = 28/30 = 14/15
 
(8/15)/(12/25) = (8/15) x (25/12) = 200/180 = 10/9 = 1 and 1/9
(8/15)/(12/25) = (8/15) x (25/12) = (2/3) x (5/3) = 10/9 = 1 and 1/9

Comments

When you multiply with fractions you multiply the numerators together and you multiply the denominators together. The answer  is the product of the numerators over the product of the denominators. Simplify or reduce your answer to lowest terms and change any improper fractions to mixed numbers.
When you divide with fractions, the first fraction stays the same and the second fraction becomes its reciprocal-you "flip it upside down" or in other words you make the numerator the denominator and you make the denominator the numerator. For example the reciprocal of 4/5 is 5/4; the reciprocal of 3/8 is 8/3; the reciprocal of 1/7 is 7/1; the reciprocal of 9 is 1/9 because 9 is the same as 9/1.
After you change the second fraction to its reciprocal, you now multiply the fractions together.

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