Question

Multiplying a number by 4/5 then dividing by 2/5 is the same as multiplying by what number?

Answer 1

Number * 4/5 * reciprocal of 2/5 
number * 4/5 * 5/2 = number * 20/10 = number * 2

2

Answer 2

So say the number equals x.

Therefore, it would be:

x * 4/5 / 2/5

Division is basically multiplying by the second number flipped, like so:

x * 4/5 * 5/2

Then you could just multiply, saying

x * 20/10

or x * 2

So it's the same as multiplying by 2.