Question 44: Arrange the following numbers in ascending order: \(\frac{{ – 1}}{2};0,5;\frac{{ – 3}}{4}; – \sqrt 2 – \ frac{3}{4};\frac{4}{5}\)

We divide the given numbers into two groups: \( – \frac{1}{2}; – \frac{3}{4}; – \sqrt 2 – \frac{3}{4}\) and \( 0.5;\frac{4}{5}\)

Group 1: because \( \frac{3}{4} < \sqrt 2 + \frac{3}{4}\) Candlestick \(- \frac{3}{4} > – \left( {\sqrt 2 + \frac{3}{4}} \right) = – \sqrt 2 – \frac{3}{4}\)

Yes again \( \frac{1}{2} = \frac{2}{4} < \frac{3}{4} \Rightarrow - \frac{1}{2} > – \frac{3}{4}\ ) Candlestick \( – \sqrt 2 – \frac{3}{4} < - \frac{3}{4} < - \frac{1}{2}\)

Group 2:

\( 0.5 = \frac{1}{2} = \frac{5}{{10}} < \frac{8}{{10}} = \frac{4}{5} \Rightarrow 0.5 < \frac{4}{5}\)

So we have an increasing sequence of \( – \sqrt 2 – \frac{3}{4}; – \frac{3}{4}; – \frac{1}{2};0,5;\frac{4}{5}\)