Questions: Fractions Mixed number division Divide. Write your answer as a fraction or a mixed number in simplest form. 1 2/3 ÷ 1 2/9

Solution Steps

Convert \(1\frac{2}{3}\) to an improper fraction: \[ 1\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3} \]

Convert \(1\frac{2}{9}\) to an improper fraction: \[ 1\frac{2}{9} = \frac{9 \times 1 + 2}{9} = \frac{11}{9} \]

Rewrite the division problem as multiplication by the reciprocal of the second fraction: \[ \frac{5}{3} \div \frac{11}{9} = \frac{5}{3} \times \frac{9}{11} \]

Multiply the numerators and denominators: \[ \frac{5}{3} \times \frac{9}{11} = \frac{5 \times 9}{3 \times 11} = \frac{45}{33} \]

Simplify \(\frac{45}{33}\) by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3: \[ \frac{45 \div 3}{33 \div 3} = \frac{15}{11} \]

Final Answer