Задаци које смо решили у видео лекцији:
1. Израчунати:
(а) $ - \frac{3}{5} + \frac{1}{5}=$
(б) $ - \frac{3}{{11}} + \left( { - \frac{1}{{11}}} \right)=$
(в) $\frac{3}{7} + \left( { - \frac{4}{7}} \right)=$
(г) $ - \frac{1}{3} + \left( { - \frac{1}{4}} \right)=$
(д) $ - 1\frac{1}{2} + 2\frac{1}{3}=$
(ђ) $ - 2\frac{3}{5} + \left( { - 3\frac{7}{{10}}} \right)=$
(е) $2\frac{3}{8} + \left( { - 3\frac{1}{6}} \right)=$
2. Израчунати:
(а) $ - \frac{2}{9} - \frac{1}{9}=$
(б) $ - \frac{3}{5} - \left( { - \frac{1}{5}} \right)=$
(в) $\frac{2}{7} - \left( { - \frac{2}{7}} \right)=$
(г) $ - \frac{3}{5} - \left( { - \frac{1}{2}} \right)=$
(д) $ - 2\frac{3}{4} - \left( { - 3\frac{1}{6}} \right) = $
(ђ) $ - 1\frac{5}{6} - 3\frac{2}{3} = $
(е) $2\frac{1}{5} - \left( { - 3\frac{1}{6}} \right) = $
3. Израчунати:
(a) $ - 2\frac{1}{2} - \left( { - 3\frac{1}{3}} \right) + \left( { - 3\frac{1}{4}} \right) = $
(б) $1\frac{2}{3} + \left( { - 1\frac{5}{6}} \right) - \left( { - 4\frac{1}{8}} \right) = $
1.
(а) $ - \frac{3}{5} + \frac{1}{5} = \frac{{ - 3 + 1}}{5} = \frac{{ - 2}}{5} = - \frac{2}{5}$
(б) $ - \frac{3}{{11}} + \left( { - \frac{1}{{11}}} \right) = \frac{{ - 3 + \left( { - 1} \right)}}{{11}} = \frac{{ - 4}}{{11}} = - \frac{4}{{11}}$
(в) $\frac{3}{7} + \left( { - \frac{4}{7}} \right) = \frac{{3 + \left( { - 4} \right)}}{7} = \frac{{ - 1}}{7} = - \frac{1}{7}$
(г) $ - \frac{1}{3} + \left( { - \frac{1}{4}} \right) = - \frac{4}{{12}} + \left( { - \frac{3}{{12}}} \right) = - \frac{7}{{12}}$
(д) $ - 1\frac{1}{2} + 2\frac{1}{3} = - 1\frac{3}{6} + 2\frac{2}{6} =$
$= 2\frac{2}{6} - 1\frac{3}{6} = 1\frac{8}{6} - 1\frac{3}{6} = \frac{5}{6}$
(ђ) $ - 2\frac{3}{5} + \left( { - 3\frac{7}{{10}}} \right) = - 2\frac{6}{{10}} + \left( { - 3\frac{7}{{10}}} \right) =$
$= - 5\frac{{13}}{{10}} = - 6\frac{3}{{10}}$
(е) $2\frac{3}{8} + \left( { - 3\frac{1}{6}} \right) = 2\frac{9}{{24}} + \left( { - 3\frac{4}{{24}}} \right) =$
$= - \left( {3\frac{4}{{24}} - 2\frac{9}{{24}}} \right) = - \frac{{19}}{{24}}$
2.
(а) $ - \frac{2}{9} - \frac{1}{9} = - \frac{3}{9} = - \frac{1}{3}$
(б) $- \frac{3}{5} - \left( { - \frac{1}{5}} \right) = - \frac{3}{5} + \frac{1}{5} = - \frac{2}{5}$
(в) $\frac{2}{7} - \left( { - \frac{2}{7}} \right) = \frac{2}{7} - \frac{2}{7} = \frac{4}{7}$
(г) $ - \frac{3}{5} - \left( { - \frac{1}{2}} \right) = - \frac{3}{5} + \frac{1}{2} = - \frac{6}{{10}} + \frac{5}{{10}} = - \frac{1}{{10}}$
(д) $ - 2\frac{3}{4} - \left( { - 3\frac{1}{6}} \right) = - 2\frac{3}{4} + \left( { + 3\frac{1}{6}} \right) = - 2\frac{9}{{12}} + 3\frac{2}{{12}} = \frac{5}{{12}} $
(ђ) $ - 1\frac{5}{6} - 3\frac{2}{3} = - 1\frac{5}{6} + \left( { - 3\frac{4}{6}} \right) = - 4\frac{9}{6} = - 4\frac{3}{2} = - 5\frac{1}{2} $
(е) $2\frac{1}{5} - \left( { - 3\frac{1}{6}} \right) = 2\frac{1}{5} + \left( { + 3\frac{1}{6}} \right) = 2\frac{6}{{30}} + 3\frac{5}{{30}} = 5\frac{{11}}{{30}}$
3.
(a)
\[\begin{gathered}
- 2\frac{1}{2} - \left( { - 3\frac{1}{3}} \right) + \left( { - 3\frac{1}{4}} \right) = - 2\frac{1}{2} + 3\frac{1}{3} - 3\frac{1}{4} = - 2\frac{6}{{12}} + 3\frac{4}{{12}} - 3\frac{3}{{12}} = \hfill \\
= \left( {3\frac{4}{{12}} - 2\frac{6}{{12}}} \right) - 3\frac{3}{{12}} = \left( {2\frac{{16}}{{12}} - 2\frac{6}{{12}}} \right) - 3\frac{3}{{12}} = \frac{{10}}{{12}} - 3\frac{3}{{12}} = \hfill \\
= - \left( {3\frac{3}{{12}} - \frac{{10}}{{12}}} \right) = - \left( {2\frac{{15}}{{12}} - \frac{{10}}{{12}}} \right) = - 2\frac{5}{{12}} \hfill \\
\end{gathered} \]
(б)
\[\begin{gathered}
1\frac{2}{3} + \left( { - 1\frac{5}{6}} \right) - \left( { - 4\frac{1}{8}} \right) = 1\frac{2}{3} - 1\frac{5}{6} + 4\frac{1}{8} = 1\frac{{16}}{{24}} - 1\frac{{20}}{{24}} + 4\frac{3}{{24}} = \hfill \\
= 5\frac{{19}}{{24}} - 1\frac{{20}}{{24}} = 4\frac{{43}}{{24}} - 1\frac{{20}}{{24}} = 3\frac{{23}}{{24}} \hfill \\
\end{gathered} \]
