Questions: 10 1/2 ÷ 9 2/6 =

△ Calculate \(10 \frac{1}{2} \div 9 \frac{2}{6}\). ○ Convert mixed numbers to improper fractions ☼ \(10 \frac{1}{2} = \frac{21}{2}\) and \(9 \frac{2}{6} = 9 \frac{1}{3} = \frac{28}{3}\). The mixed number \(10 \frac{1}{2}\) converts to \(\frac{21}{2}\) because \(10 \times 2 + 1 = 21\). Simplifying \(\frac{2}{6}\) to \(\frac{1}{3}\), \(9 \frac{1}{3}\) converts to \(\frac{28}{3}\) because \(9 \times 3 + 1 = 28\). ○ Perform division of fractions ☼ \(\frac{21}{2} \div \frac{28}{3} = \frac{21}{2} \times \frac{3}{28} = \frac{63}{56}\). Dividing by a fraction is equivalent to multiplying by its reciprocal. ○ Simplify the fraction ☼ \(\frac{63}{56} = \frac{9}{8}\). The GCD of 63 and 56 is 7, so \(\frac{63}{56}\) simplifies to \(\frac{9}{8}\) by dividing both numerator and denominator by 7. ○ Convert to a mixed number ☼ \(\frac{9}{8} = 1 \frac{1}{8}\). The improper fraction \(\frac{9}{8}\) converts to the mixed number \(1 \frac{1}{8}\). ✧ The final answer is \(1 \frac{1}{8}\). ☺ The final answer is \(10 \frac{1}{2} \div 9 \frac{2}{6} = 1 \frac{1}{8}\).