Student understanding of dividing with fractions is usually regulated to something to the effect of, “You need to flip the fraction and you need to multiply.” As a teacher, I am usually excited if students can even recall that information. So why is this concept so difficult for students to understand and retain? Is it because they have no understanding of why they are flipping a fraction numerically?
Teaching division of fractions can be more meaningful to students when models are used before using an algorithm. Students need to be taught this concept using their previous understanding of multiplication and division. What does division mean? It tells you how many groups of a quantity there are in a whole amount. So phrasing these problems into those terms will help students conceptualize what they are doing with the fractions.
The following link provides a great description of how to teach division of fractions by having students draw and analyze a model of the problem.
http://www.doe.virginia.gov/testing/solsearch/sol/math/6/mess_6-4_6-6ab_1.pdf
Fraction strips can also be used to help students conceptualize what is happening numerically when you are dividing fractions. Check out this video from PBS: https://florida.pbslearningmedia.org/resource/mgbh.math.nf.divofrac/division-of-fractions-using-fraction-strips/#.WXpNVojyuM8
References:
Virginia Department of Education(2011). Modeling Division of Fractions. Retrieved from Virginia DOE website http://www.doe.virginia.gov/testing/solsearch/sol/math/6/mess_6-4_6-6ab_1.pdf
PBS Learning Media(2017). Division of Fractions: Using Fraction Strips. Retrieved from PBS & WGBH Educational Foundation websitehttps://florida.pbslearningmedia.org/resource/mgbh.math.nf.divofrac/division-of-fractions-using-fraction-strips/#.WXpPLYjyuM9