Write the next 5 numbers in this pattern \( \frac{23}{24}, \frac{11}{12}, \frac{21}{24}, \frac{5}{6}, \frac{19}{24}, \frac{3}{4} \)

To find the next five numbers in the given pattern \( \frac{23}{24}, \frac{11}{12}, \frac{21}{24}, \frac{5}{6}, \frac{19}{24}, \frac{3}{4} \), let's first convert all fractions to have a common denominator for easier comparison. The common denominator for these fractions is 24. We can express each fraction as follows: 1. \( \frac{23}{24} \) remains \( \frac{23}{24} \) 2. \( \frac{11}{12} = \frac{11 \times 2}{12 \times 2} = \frac{22}{24} \) 3. \( \frac{21}{24} \) remains \( \frac{21}{24} \) 4. \( \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \) 5. \( \frac{19}{24} \) remains \( \frac{19}{24} \) 6. \( \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \) Now, we have the sequence in terms of a common denominator: - \( \frac{23}{24} \) - \( \frac{22}{24} \) - \( \frac{21}{24} \) - \( \frac{20}{24} \) - \( \frac{19}{24} \) - \( \frac{18}{24} \) From this, we can observe a pattern: the numerators are decreasing by 1 each time. Continuing this pattern, the next five numerators would be: 1. \( 17 \) 2. \( 16 \) 3. \( 15 \) 4. \( 14 \) 5. \( 13 \) Thus, the next five numbers in the sequence are: 1. \( \frac{17}{24} \) 2. \( \frac{16}{24} \) (which simplifies to \( \frac{2}{3} \)) 3. \( \frac{15}{24} \) (which simplifies to \( \frac{5}{8} \)) 4. \( \frac{14}{24} \) (which simplifies to \( \frac{7}{12} \)) 5. \( \frac{13}{24} \) So, the next five numbers in the pattern are: \[ \frac{17}{24}, \frac{2}{3}, \frac{5}{8}, \frac{7}{12}, \frac{13}{24} \]