Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three?

Answer 1

The quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three because division is not commutative. In other words, changing the order of the numbers being divided will result in a different quotient.

To see why, let's calculate each quotient:

- Three divided by one-fifth is 3 ÷ (1/5) = 3 x 5 = 15.

- One-fifth divided by three is (1/5) ÷ 3 = (1/5) x (1/3) = 1/15.

So the first quotient is 15 and the second quotient is 1/15, which are clearly not the same.