Question

simplify and express the results as a rational numbers in its lowest form ​

Answer 1

GIVEN :-

$\to \sf \: \dfrac{0.4 \times 0.04 \times 0.005}{0.1 \times 10 \times 0.001} - \dfrac{1}{2} + \dfrac{1}{5}$

TO FIND :-

$\to \sf \: the \: value \: of \: \dfrac{0.4 \times 0.04 \times 0.005}{0.1 \times 10 \times 0.001} - \dfrac{1}{2} + \dfrac{1}{5}$

SOLUTION :-

$\to \sf \: \dfrac{0.4 \times 0.04 \times 0.005}{0.1 \times 10 \times 0.001} - \dfrac{1}{2} + \dfrac{1}{5} \\ \\ \\ \to \sf \dfrac{0.4}{0.1} \times \dfrac{0.04}{10} \times \dfrac{0.005}{0.001} - \dfrac{1}{2} + \dfrac{1}{5} \\ \\ \\ \to \sf \: \dfrac{0.4 \times 10}{0.1 \times 10} \times \dfrac{0.04 \times 100}{10 \times 100} \times \dfrac{0.005 \times 1000}{0.001 \times 1000} - \dfrac{1}{2} + \dfrac{1}{5} \\ \\ \\ \to \sf \: \dfrac{4}{1} \times \dfrac{4}{1000} \times \dfrac{5}{1} - \dfrac{1}{2} + \dfrac{1}{5} \\ \\ \\ \to \sf \: \dfrac{8 \cancel0}{100 \cancel0} - \dfrac{1}{2} + \dfrac{1}{5} \\ \\ \\ \to \sf \: \dfrac{8}{100} - \dfrac{1}{2} + \dfrac{1}{5}$

☯ Taking L.C.M = 100.

$\to \sf \: \dfrac{8}{100} + \dfrac{1 \times 20}{5 \times 20} - \dfrac{1 \times 50}{2 \times 50} \\ \\ \\ \to \sf \: \dfrac{8 + 20 - 50}{100} \\ \\ \\ \to \sf \: \dfrac{28 - 50}{100} \\ \\ \\ \to \sf \: \frac{ \cancel{ - 22}}{ \cancel{100}} \\ \\ \\ \to \boxed{ \red{ \bf\dfrac{ - 11}{50}}}$

Hence the required answer is-11/50