Explain why dividing by a fraction results in the same answer as multiplying by its reciprocal.

lets consider an example like

20 divided by 2/4 so we can rewrite as

2/4 * x = 20

so, 2 * x = 20*4

2 * x = 80

x=80/2

x=40

similarly, we can write the fraction as (20*4/2) - we can see that reciprocal of the fraction 2/4 is 4/2

x=20*4/2=80/2=40

so, we can say that dividing by a fraction results in the same answer as multiplying by its reciprocal.