(a) Simplify : (frac{frac{1}{2} of frac{1}{4} div frac{1}{3}}{frac{1}{6} – frac{3}{4} + frac{1}{2}}).
(b) Given that (sqrt{x} = 10^{bar{1}.6741}), without using calculators, find the value of x.
Explanation
(a) (frac{frac{1}{2} of frac{1}{4} div frac{1}{3}}{frac{1}{6} – frac{3}{4} + frac{1}{2}})
Numerator – (frac{1}{2} times frac{1}{4} div frac{1}{3} = (frac{1}{2} times frac{1}{4}) div frac{1}{3})
(frac{1}{8} times 3 = frac{3}{8})
Denominator – (frac{1}{6} – frac{3}{4} + frac{1}{2} = frac{1}{6} – (frac{3}{4} – frac{1}{2}))
(frac{1}{6} – (frac{3 – 2}{4}) = frac{1}{6} – frac{1}{4})
(frac{2 – 3}{12} = frac{-1}{12})
(therefore frac{frac{1}{2} times frac{1}{4} div frac{1}{3}}{frac{1}{6} – frac{3}{4} + frac{1}{2}} = frac{3}{8} div frac{-1}{12})
(frac{3}{8} times -12 = frac{-9}{2})
= (-4.5)
(b) (sqrt{x} = 10^{bar{1}.6741}})
Squaring both sides, we have
(x = (10^{bar{1}.6741}})^{2})
(x = 10^{bar{1}.3482}) (checking antilogarithm)
(x = 0.2229)