To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Thus, 2/9 ÷ 2/8 is equivalent to 2/9 * 8/2, which simplifies to 16/18. To reduce this fraction to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 2. Therefore, 16/18 reduces to 8/9.