Division with Fractions 1 and 3/4 divided by 1/2

This is an example from Liping Ma's book:

Using Decimals
How much is 1.75 divided by .5?
1.75/.5 = 3.5


Using Fractions
1 and 3/4 divided by 1/2
1 and 3/4 = 7/4
7/4 divided by 1/2
How many half cups are in 7/4 cups?
1 half cup = 1/2
2 half cups = 2/2 = 1
3 half cups = 3/2
4 half cups = 4/2 = 2 -- this is too much

7/4 divided by 1/2
multiply 7/4 by the reciprocal of 1/2
7/4 x 2/1 = 14/4 = 7/2 = 3 and 1/2

Division with Fractions is "a topic at the summit of arithmetic". In the introduction, she asks a division with fractions question: 13/4 divided by 1/2 and offers three additional problem-solving methodologies (besides Keep, Change, Flip) -- Dividing Using Decimals, Applying the Distributive Law and You Don't Have to Multiply.