1. I want you to explain not just that
𝑎
𝑏
⋅
𝑐
𝑑
=
𝑎𝑐
𝑏𝑑
, but why this is the correct definition of multiplication of
fractions. There are two models I have seen you propose so far for this, both are displayed below
illustrating why
1
2
⋅
2
3
=
2
6
, this example, and either one of these two models can be extended to an actual
explanation of the rule. This is what I am asking you to do here.
1/2 of 2/3
1/2
2/3 of 1/2
1/2
2/3
2/3
2/6
2/6
1/3
This model is interesting, finding2/3 of
1/2 naturally leads to 2/6, while taking
1/2 of 2/3 naturally leads to 1/3.
Of course 2/6 = 1/3, but it is interesting
how the models naturally lead to the
different forms.
This model is interesting, because it
is more symmetric and it resembles the usual
area model for multiplication. It simultaneously
represents 2/3 of 1/2 and 1/2 of 2/3 and in both
cases leads to 2/6.
