4. Cheek whether the following pair of fraction are equavalent or not \( \begin{array}{ll}\text { (a) } \frac{3}{2} \text { and } \frac{5}{7} & \text { (b) } \frac{5}{7} \text { and } \frac{15}{35} \\ \text { (c) } \frac{4}{15} \text { and } \frac{8}{30} & \text { (d) } \frac{12}{18} \text { and } \frac{2}{3}\end{array} \)

To determine whether the pairs of fractions are equivalent, we'll cross-multiply or simplify them. In pair (a), \(\frac{3}{2}\) and \(\frac{5}{7}\) are not equivalent since \(3 \times 7 \neq 5 \times 2\). For pair (b), \(\frac{5}{7}\) and \(\frac{15}{35}\) are equivalent! This is because when you simplify \(\frac{15}{35}\) by dividing both the numerator and denominator by 5, you get \(\frac{3}{7}\), which is equal to \(\frac{5}{7}\) when simplified correctly. In pair (c), \(\frac{4}{15}\) and \(\frac{8}{30}\) are equivalent, since \(\frac{8}{30}\) simplifies to \(\frac{4}{15}\). For pair (d), \(\frac{12}{18}\) simplifies to \(\frac{2}{3}\), which means they are equivalent! So, the equivalent pairs are (b), (c), and (d), while (a) is not equivalent!