11. Which pairs of fractions are equivalent to \( \frac{2}{3} \) and \( \frac{5}{6} \) ? \begin{tabular}{l|c|c|}\hline\( \frac{12}{18} \) and \( \frac{15}{18} \) & \( \frac{8}{12} \) and \( \frac{11}{12} \) & \( \frac{16}{24} \) and \( \frac{20}{24} \)\end{tabular}
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To find fractions equivalent to \( \frac{2}{3} \) and \( \frac{5}{6} \), we can simplify or scale the fractions in the pairs given. - The fraction \( \frac{12}{18} \) simplifies to \( \frac{2}{3} \) (by dividing the numerator and denominator by 6), but \( \frac{15}{18} \) does not equal \( \frac{5}{6} \) (it simplifies to \( \frac{5}{6} \)), making this pair a match! - The second pair, \( \frac{8}{12} \) simplifies to \( \frac{2}{3} \), but \( \frac{11}{12} \) does not simplify to \( \frac{5}{6} \). - The last pair includes \( \frac{16}{24} \) which simplifies to \( \frac{2}{3} \), and \( \frac{20}{24} \) simplifies to \( \frac{5}{6} \). Therefore, the pairs \( \frac{12}{18} \) and \( \frac{15}{18} \), and \( \frac{16}{24} \) and \( \frac{20}{24} \) are equivalent to \( \frac{2}{3} \) and \( \frac{5}{6} \) respectively! These equivalent fractions showcase the beauty of mathematical relationships, and it's fascinating how many forms the same value can take!