To divide by a fraction, use the area model: the dividend is the area of a rectangle, the divisor is one side, and the missing side is the quotient.

So 2/3 ÷ 3/4 asks for the width of a rectangle of area 2/3 whose height is 3/4. The width is 8/9, because 3/4 of 8/9 is 2/3. That is the missing factor: the quotient times the divisor gives the dividend.

Rearranged, the quotient is the dividend times the reciprocal of the divisor: 2/3 × 4/3 = 8/9. That is why dividing by a fraction is the same as multiplying by its reciprocal.