Question

drag each tile to the correct box. place the complex fractions in order from least to greatest. \\(\frac{\frac{3}{4} + 1}{\frac{2}{5}}\\) \\(\frac{\frac{2}{3} + 1}{1 - \frac{3}{5}}\\) \\(\frac{\frac{4}{5}}{\frac{11}{9} - 1}\\) \\(\square < \square < \square\\)

Explanation:

Step1: Simplify first complex fraction

Simplify numerator: $\frac{3}{4} + 1=\frac{3}{4}+\frac{4}{4}=\frac{7}{4}$
Divide by denominator: $\frac{\frac{7}{4}}{\frac{2}{5}}=\frac{7}{4}\times\frac{5}{2}=\frac{35}{8} = 4.375$

Step2: Simplify second complex fraction

Simplify numerator: $\frac{2}{3}+1=\frac{2}{3}+\frac{3}{3}=\frac{5}{3}$
Simplify denominator: $1 - \frac{3}{5}=\frac{2}{5}$
Divide: $\frac{\frac{5}{3}}{\frac{2}{5}}=\frac{5}{3}\times\frac{5}{2}=\frac{25}{6}\approx4.1667$

Step3: Simplify third complex fraction

Simplify denominator: $\frac{11}{9}-1=\frac{11}{9}-\frac{9}{9}=\frac{2}{9}$
Divide: $\frac{\frac{4}{5}}{\frac{2}{9}}=\frac{4}{5}\times\frac{9}{2}=\frac{36}{10} = 3.6$

Answer:

$\boldsymbol{\frac{\frac{4}{5}}{\frac{11}{9}-1}}$ < $\boldsymbol{\frac{\frac{2}{3}+1}{1-\frac{3}{5}}}$ < $\boldsymbol{\frac{\frac{3}{4}+1}{\frac{2}{5}}}$