Word problem fractions

Question

A recipe calls for $3$ cans of condensed milk. Each can holds $\frac{1}{2}$ cups of condensed milk. If Alice wants to cut recipe in half, how much condensed milk will she need?

answer: $$ \frac31 \times \frac12 \times \frac12 $$

I did not understand the answer,if she want to cut the recipe in half ,why is not divided by 1/2 instead of multiplied by $\frac{1}{2}$?

Answer 1

The recipe calls for 3 cans, each holds $\frac12$ of a cup. So total recipe content is $3 \times \frac12 = \frac32$ of a cup.

You need another $\frac12$ of that since Alice is halving the recipe...

Answer 2

"Cutting in half" means "dividing by $2$", which is the same as "multiplying by $\frac12$".