1. $\frac{3}{4} - \frac{1}{6} \div \left(\frac{4}{5}\right)^2 = \frac{3}{4} - \frac{1}{6} \div \frac{16}{25} = \frac{3}{4} - \frac{1}{6} \times \frac{25}{16} = \frac{3}{4} - \frac{25}{96} = \frac{72}{96} - \frac{25}{96} = \frac{47}{96}$
2. $\left(\frac{5}{6}\right)^2 \times \left(\frac{1}{4} + \frac{7}{8}\right) = \frac{25}{36} \times \left(\frac{2}{8} + \frac{7}{8}\right) = \frac{25}{36} \times \frac{9}{8} = \frac{225}{288} = \frac{25}{32}$
3. $\frac{4}{9} + \frac{4}{5} \div \left(\frac{3}{5}\right)^2 = \frac{4}{9} + \frac{4}{5} \div \frac{9}{25} = \frac{4}{9} + \frac{4}{5} \times \frac{25}{9} = \frac{4}{9} + \frac{100}{45} = \frac{4}{9} + \frac{20}{9} = \frac{24}{9} = \frac{8}{3}$
4. $\frac{8}{9} \times \left[\frac{2}{9} + \left(\frac{1}{2}\right)^2\right] = \frac{8}{9} \times \left[\frac{2}{9} + \frac{1}{4}\right] = \frac{8}{9} \times \left[\frac{8}{36} + \frac{9}{36}\right] = \frac{8}{9} \times \frac{17}{36} = \frac{136}{324} = \frac{34}{81}$
5. $\left(\frac{5}{8}\right)^2 \div \left(\frac{2}{3} - \frac{1}{6}\right) = \frac{25}{64} \div \left(\frac{4}{6} - \frac{1}{6}\right) = \frac{25}{64} \div \frac{3}{6} = \frac{25}{64} \div \frac{1}{2} = \frac{25}{64} \times 2 = \frac{50}{64} = \frac{25}{32}$
6. $\left(\frac{1}{6} + \frac{1}{2}\right) \times \left(\frac{2}{3}\right)^3 = \left(\frac{1}{6} + \frac{3}{6}\right) \times \frac{8}{27} = \frac{4}{6} \times \frac{8}{27} = \frac{2}{3} \times \frac{8}{27} = \frac{16}{81}$
7. $\left(\frac{2}{3} + \frac{7}{8}\right) \times \left(\frac{1}{2}\right)^2 = \left(\frac{16}{24} + \frac{21}{24}\right) \times \frac{1}{4} = \frac{37}{24} \times \frac{1}{4} = \frac{37}{96}$
8. $\left(\frac{5}{6} - \frac{1}{6}\right)^3 \div \frac{1}{4} = \left(\frac{4}{6}\right)^3 \div \frac{1}{4} = \left(\frac{2}{3}\right)^3 \div \frac{1}{4} = \frac{8}{27} \div \frac{1}{4} = \frac{8}{27} \times 4 = \frac{32}{27}$
Parent Tip: Review the logic above to help your child master the concept of operations of fractions worksheet.
