(a)
(i) As\(\frac{2}{3}\) × \(\frac{5}{10}\) = 10 / 30
Therefore, the number in the box, such that \(\frac{2}{3}\)× __ = \(\frac{10}{30}\) is \(\frac{5}{10}\)
(ii) The simplest form of \(\frac{5}{10}\) is \(\frac{1}{2}\).
(b)
(i) As \(\frac{3}{5}\) × \(\frac{8}{15}\) = \(\frac{24}{75}\).
Therefore, the number in the box, such that \(\frac{3}{5}\) × __= \(\frac{24}{75}\) is \(\frac{8}{15}\).
(ii) As \(\frac{8}{15}\) cannot be further simplified, therefore, its simplest form is \(\frac{8}{15}\).