Odpowiedź:
zadanie 2
a)
[tex]1 \frac{3}{5} - 2 \frac{1}{6} = \frac{8}{5} - \frac{13}{6} = \frac{48}{30} - \frac{65}{30} = \frac{ - 17}{30} = - \frac{17}{30} [/tex]
b)
[tex]3 \frac{3}{8} + 2 \frac{2}{5} = \frac{27}{8} + \frac{12}{5} = \frac{135}{40} + \frac{96}{40} = \frac{231}{40} = 5 \frac{31}{40} [/tex]
c)
[tex] \frac{1}{2} - ( - \frac{1}{6} - \frac{1}{3}) = \frac{1}{2} - ( - \frac{1}{6} - \frac{2}{6} ) = \frac{1}{2} + \frac{3}{6} = \frac{3}{6} + \frac{3}{6} = \frac{6}{6} = 1[/tex]
d)
[tex] \frac{7}{6} + ( - \frac{5}{4} - \frac{4}{3} ) = \frac{7}{6} + ( - \frac{15}{12} - \frac{16}{12} ) = \frac{7}{6} + ( - \frac{31}{12} ) = \frac{14}{12} - \frac{31}{12} = - \frac{17}{12} = - 1 \frac{5}{12} [/tex]
e)
[tex] - ( - 2 \frac{2}{3} ) + \frac{7}{15} = \frac{8}{3} + \frac{7}{15} = \frac{40}{15} + \frac{7}{15} = \frac{47}{15} = 3 \frac{2}{15} [/tex]
f)
[tex] - 1 \frac{9}{16} + \frac{11}{12} = - \frac{25}{16} + \frac{11}{12} = - \frac{75}{48} + \frac{44}{48} = - \frac{31}{48} [/tex]
g)
[tex]1 \frac{5}{8} - ( - 2 \frac{2}{3} + 0.25) = \frac{13}{8} - ( - \frac{8}{3} + \frac{1}{4} ) = \frac{13}{8} - ( - \frac{32}{12} + \frac{3}{12} ) = \frac{13}{8} - ( - \frac{35}{12} ) = \frac{13}{8} + \frac{35}{12} = \frac{39}{24} + \frac{70}{24} = \frac{109}{24} = 4 \frac{13}{24} [/tex]
h)
[tex]1 \frac{2}{5} - 3 \frac{7}{8} - 0.125 = \frac{12}{5} - \frac{31}{8} - \frac{1}{8} = \frac{12}{5} - \frac{32}{8} = \frac{96}{40} - \frac{160}{40} = - \frac{64}{40} = - 1 \frac{24}{40} = - 1 \frac{3}{5} [/tex]
i)
[tex] \frac{1}{2} - \frac{1}{3} - ( \frac{1}{4} - \frac{1}{5} ) = \frac{1}{2} - \frac{1}{3} - ( \frac{5}{20} - \frac{4}{20} ) = \frac{1}{2} - \frac{1}{3} - \frac{1}{20} = \frac{3}{6} - \frac{2}{6} - \frac{1}{20} = \frac{1}{6} - \frac{1}{20} = \frac{10}{60} - \frac{3}{60} = \frac{7}{60} [/tex]
[tex] - 1 \frac{2}{25} \times ( - 2 \frac{1}{12} ) = - \frac{27}{25} \times ( - \frac{25}{12} ) = \frac{9}{4} = 2 \frac{1}{4} [/tex]
[tex]4 \frac{1}{7} - 4 \frac{1}{2} \div ( - 5 \frac{1}{4} ) = \frac{29}{7} - \frac{9}{2} \div ( - \frac{21}{4} ) = \frac{29}{7} - \frac{9}{2} \times ( - \frac{4}{21} ) = \frac{29}{7} - \frac{6}{7} = \frac{23}{7} = 3 \frac{2}{7} [/tex]
[tex] - 2 \frac{1}{9} \times 1 \frac{16}{19} \div \frac{7}{5} = - \frac{19}{9} \times \frac{35}{19} \times \frac{5}{7} = - \frac{35}{9} \times \frac{5}{7} = - \frac{25}{9} = - 2 \frac{7}{9} [/tex]
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Verified answer
Odpowiedź:
zadanie 2
a)
[tex]1 \frac{3}{5} - 2 \frac{1}{6} = \frac{8}{5} - \frac{13}{6} = \frac{48}{30} - \frac{65}{30} = \frac{ - 17}{30} = - \frac{17}{30} [/tex]
b)
[tex]3 \frac{3}{8} + 2 \frac{2}{5} = \frac{27}{8} + \frac{12}{5} = \frac{135}{40} + \frac{96}{40} = \frac{231}{40} = 5 \frac{31}{40} [/tex]
c)
[tex] \frac{1}{2} - ( - \frac{1}{6} - \frac{1}{3}) = \frac{1}{2} - ( - \frac{1}{6} - \frac{2}{6} ) = \frac{1}{2} + \frac{3}{6} = \frac{3}{6} + \frac{3}{6} = \frac{6}{6} = 1[/tex]
d)
[tex] \frac{7}{6} + ( - \frac{5}{4} - \frac{4}{3} ) = \frac{7}{6} + ( - \frac{15}{12} - \frac{16}{12} ) = \frac{7}{6} + ( - \frac{31}{12} ) = \frac{14}{12} - \frac{31}{12} = - \frac{17}{12} = - 1 \frac{5}{12} [/tex]
e)
[tex] - ( - 2 \frac{2}{3} ) + \frac{7}{15} = \frac{8}{3} + \frac{7}{15} = \frac{40}{15} + \frac{7}{15} = \frac{47}{15} = 3 \frac{2}{15} [/tex]
f)
[tex] - 1 \frac{9}{16} + \frac{11}{12} = - \frac{25}{16} + \frac{11}{12} = - \frac{75}{48} + \frac{44}{48} = - \frac{31}{48} [/tex]
g)
[tex]1 \frac{5}{8} - ( - 2 \frac{2}{3} + 0.25) = \frac{13}{8} - ( - \frac{8}{3} + \frac{1}{4} ) = \frac{13}{8} - ( - \frac{32}{12} + \frac{3}{12} ) = \frac{13}{8} - ( - \frac{35}{12} ) = \frac{13}{8} + \frac{35}{12} = \frac{39}{24} + \frac{70}{24} = \frac{109}{24} = 4 \frac{13}{24} [/tex]
h)
[tex]1 \frac{2}{5} - 3 \frac{7}{8} - 0.125 = \frac{12}{5} - \frac{31}{8} - \frac{1}{8} = \frac{12}{5} - \frac{32}{8} = \frac{96}{40} - \frac{160}{40} = - \frac{64}{40} = - 1 \frac{24}{40} = - 1 \frac{3}{5} [/tex]
i)
[tex] \frac{1}{2} - \frac{1}{3} - ( \frac{1}{4} - \frac{1}{5} ) = \frac{1}{2} - \frac{1}{3} - ( \frac{5}{20} - \frac{4}{20} ) = \frac{1}{2} - \frac{1}{3} - \frac{1}{20} = \frac{3}{6} - \frac{2}{6} - \frac{1}{20} = \frac{1}{6} - \frac{1}{20} = \frac{10}{60} - \frac{3}{60} = \frac{7}{60} [/tex]
zadanie 2
a)
[tex] - 1 \frac{2}{25} \times ( - 2 \frac{1}{12} ) = - \frac{27}{25} \times ( - \frac{25}{12} ) = \frac{9}{4} = 2 \frac{1}{4} [/tex]
b)
[tex]4 \frac{1}{7} - 4 \frac{1}{2} \div ( - 5 \frac{1}{4} ) = \frac{29}{7} - \frac{9}{2} \div ( - \frac{21}{4} ) = \frac{29}{7} - \frac{9}{2} \times ( - \frac{4}{21} ) = \frac{29}{7} - \frac{6}{7} = \frac{23}{7} = 3 \frac{2}{7} [/tex]
c)
[tex] - 2 \frac{1}{9} \times 1 \frac{16}{19} \div \frac{7}{5} = - \frac{19}{9} \times \frac{35}{19} \times \frac{5}{7} = - \frac{35}{9} \times \frac{5}{7} = - \frac{25}{9} = - 2 \frac{7}{9} [/tex]