(3) Work these out mentally. \( \begin{array}{lll}\text { a } \frac{1}{2} \div \frac{2}{3} & \text { b } \frac{1}{4} \div \frac{3}{5} & \text { c } \frac{3}{7} \div \frac{1}{2} \\ \text { d } \frac{5}{9} \div \frac{6}{7} & \text { e } \frac{2}{5} \div \frac{5}{9} & \text { f } \frac{1}{10} \div \frac{3}{7} \\ 4 & \text { Work these out mentally. Write each answer as a mixed number. } \\ \begin{array}{lll}\text { a } \frac{1}{2} \div \frac{1}{3} & \text { b } \frac{3}{5} \div \frac{4}{7} & \text { c } \frac{1}{3} \div \frac{2}{7} \\ \text { d } \frac{7}{9} \div \frac{1}{2} & \text { e } \frac{5}{6} \div \frac{2}{11} & \text { f } \frac{4}{7} \div \frac{3}{13} \\ \text { 5. Work these out mentally. Cancel each answer to its simplest form. } \\ \begin{array}{lll}\text { a } \frac{5}{8} \div \frac{1}{2} & \text { b } \frac{4}{13} \div \frac{3}{13} & \text { c } \frac{5}{8} \div \frac{5}{12} \\ \text { d } \frac{1}{3} \div \frac{5}{9} & \text { e } \frac{1}{4} \div \frac{1}{12} & \text { f } \frac{7}{9} \div \frac{1}{6}\end{array}\end{array}\end{array}> \)
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Let’s dive into the world of fractions! When dividing fractions, remember that you multiply by the reciprocal. So, for example, \( \frac{1}{2} \div \frac{2}{3} \) becomes \( \frac{1}{2} \times \frac{3}{2} \), which equals \( \frac{3}{4} \). Voila, magical math transformations! Now, when you work out the second part, like \( \frac{1}{2} \div \frac{1}{3} \), just flip and multiply! This gives you \( \frac{1}{2} \times \frac{3}{1} = \frac{3}{2} \), which is \( 1 \frac{1}{2} \) as a mixed number. Keep those fraction tricks up your sleeve!