Simplify complex fractions worksheet with ten problems involving algebraic expressions and variables.

1) $\frac{11}{8} \cdot \frac{t^2}{1} \cdot \frac{4}{t^2} = \frac{11 \cdot 4}{8} = \frac{44}{8} = \frac{11}{2}$

2) $\frac{\frac{1}{s-1} \cdot \frac{5}{s+4}}{\frac{1}{8} + \frac{1}{6}} = \frac{\frac{5}{(s-1)(s+4)}}{\frac{6+8}{48}} = \frac{\frac{5}{(s-1)(s+4)}}{\frac{14}{48}} = \frac{5}{(s-1)(s+4)} \cdot \frac{48}{14} = \frac{240}{14(s-1)(s+4)} = \frac{120}{7(s-1)(s+4)}$

3) $\frac{\frac{11}{3} \cdot \frac{c}{6}}{c^2} = \frac{\frac{11c}{18}}{c^2} = \frac{11c}{18c^2} = \frac{11}{18c}$

4) $\frac{\frac{9}{8} \cdot \frac{9}{4}}{\frac{9}{8} + \frac{9}{4}} = \frac{\frac{81}{32}}{\frac{9+18}{8}} = \frac{\frac{81}{32}}{\frac{27}{8}} = \frac{81}{32} \cdot \frac{8}{27} = \frac{81 \cdot 8}{32 \cdot 27} = \frac{648}{864} = \frac{3}{4}$

5) $\frac{\frac{1}{4} \cdot \frac{d+6}{d^2} \cdot \frac{5}{4}}{\frac{11}{6} + \frac{5}{6}} = \frac{\frac{5(d+6)}{16d^2}}{\frac{16}{6}} = \frac{5(d+6)}{16d^2} \cdot \frac{6}{16} = \frac{30(d+6)}{256d^2} = \frac{15(d+6)}{128d^2}$

6) $\frac{\frac{11}{6} + \frac{5}{6}}{6} = \frac{\frac{16}{6}}{6} = \frac{16}{6} \cdot \frac{1}{6} = \frac{16}{36} = \frac{4}{9}$

7) $\frac{\frac{3}{2} \cdot \frac{3}{5}}{5} = \frac{\frac{9}{10}}{5} = \frac{9}{10} \cdot \frac{1}{5} = \frac{9}{50}$

8) $\frac{\frac{9}{4q} + \frac{7}{q}}{\frac{9}{4q} + \frac{7}{q}} = 1$

9) $\frac{8}{\frac{11}{8} + \frac{1}{8}} = \frac{8}{\frac{12}{8}} = 8 \cdot \frac{8}{12} = \frac{64}{12} = \frac{16}{3}$

10) $\frac{\frac{h^2}{8} + \frac{5}{8}}{\frac{11}{8} \cdot \frac{h+3}{9}} = \frac{\frac{h^2 + 5}{8}}{\frac{11(h+3)}{72}} = \frac{h^2 + 5}{8} \cdot \frac{72}{11(h+3)} = \frac{9(h^2 + 5)}{11(h+3)}$