42. Operations with fractions
Work out these operations and simplify the result.
a) $\displaystyle \left(\dfrac{3}{10} + \dfrac{1}{8}\right) : 2$
b) $\displaystyle 5 - \dfrac{1}{6} : \dfrac{4}{3}$
c) $\displaystyle \dfrac{2}{9} \cdot \left(1 - \dfrac{5}{4}\right)$
d) $\displaystyle -\dfrac{4}{11} : \dfrac{1}{3} - \dfrac{7}{3}$
e) $\displaystyle \dfrac{7}{9} \cdot \left(-\dfrac{3}{14}\right) + \dfrac{1}{6}$
f) $\displaystyle -4 + 3 \cdot \left(-\dfrac{5}{12}\right)$
43. Combined operations
Work out the operations and, if possible, simplify the result.
a) $\displaystyle \dfrac{2}{7} \cdot \left[3 - \left(\dfrac{2}{5} + \dfrac{1}{2}\right)\right] - \left(-\dfrac{2}{5}\right)$
b) $\displaystyle \left(\dfrac{1}{3}\right)^2 : \dfrac{4}{3} - \left(1 - \dfrac{5}{12}\right) \cdot \dfrac{3}{2}$
c) $\displaystyle \dfrac{2}{3} : \left(\dfrac{-1}{2}\right)^2 - \left(\dfrac{3}{5} - \dfrac{1}{6}\right)$
d) $\displaystyle -\dfrac{4}{9} + \dfrac{2}{3} \cdot \left(\dfrac{2}{7} - 1\right)^{-1}$
We did part 43 a) in class: it is in Exercises (13 Oct).