Oblicz. Pamiętaj o kolejności wykonywania działań.- Zadanie 11: Matematyka wokół nas 6. Zeszyt ćwiczeń cz. 2

Rozwiązanie

$1 \frac{5}{6} : 3 \frac{2}{3} \cdot 1 \frac{1}{7} =$

$= \frac{11}{6} : \frac{11}{3} \cdot \frac{8}{7} =$

$= \frac{11 ^{1}}{6} \cdot \frac{3}{11 _{1}} \cdot \frac{8}{7} =$

$= \frac{1}{6 _{2}} \cdot 3^{1} \cdot \frac{8}{7} =$

$= \frac{1}{2 _{1}} \cdot \frac{8 ^{4}}{7} =$

$= \frac{4}{7}$

$(\frac{1}{2})^{3} \cdot 2 \frac{2}{3} : 1 \frac{1}{6} =$

$= \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{8}{3} : \frac{7}{6} =$

$= \frac{1}{8} \cdot \frac{8}{3 _{1}} \cdot \frac{6 ^{2}}{7} =$

$= \frac{1}{8 _{1}} \cdot 8^{1} \cdot \frac{2}{7} = \frac{2}{7}$

$1 \frac{1}{4} \cdot 6 - 3 : 1 \frac{1}{5} =$

$= \frac{5}{4 _{2}} \cdot 6^{3} - 3^{1} \cdot \frac{5}{6 _{2}} =$

$= \frac{15}{2} - \frac{5}{2} = \frac{10}{2} = 5$

$(4 \frac{3}{8} - 1 \frac{2}{3}) : 3 \frac{3}{4} =$

$= (4 \frac{9}{24} - 1 \frac{16}{24}) : \frac{15}{4} =$

$= ((4 \frac{9}{24} + \frac{8}{24}) - (1 \frac{16}{24} + \frac{8}{24})) \cdot \frac{4}{15} =$

$= (4 \frac{17}{24} - 2) \cdot \frac{4}{15} =$

$= 2 \frac{17}{24} \cdot \frac{4}{15} =$

$= \frac{65 ^{13}}{24} \cdot \frac{4}{15 _{3}} =$

$= \frac{13}{24 _{6}} \cdot \frac{4 _{1}}{3} =$

$= \frac{13}{18}$

$2 \frac{1}{5} - 1 \frac{1}{6} : 2 \frac{1}{3} =$

$= 2 \frac{1}{5} - \frac{7}{6} : \frac{7}{3} =$

$= 2 \frac{1}{5} - \frac{7 _{1}}{6} \cdot \frac{3}{7 _{1}} =$

$= 2 \frac{1}{5} - \frac{3}{6} =$

$= 2 \frac{1}{5} - \frac{1}{2} =$

$= 2 \frac{2}{10} - \frac{5}{10} =$

$= 1 \frac{12}{10} - \frac{5}{10} =$

$= 1 \frac{7}{10}$

$[(\frac{3}{8} + \frac{1}{6}) : 3 \frac{1}{4}] - (\frac{1}{3})^{3} =$

$= [(\frac{9}{24} + \frac{4}{24}) : \frac{13}{4}] - \frac{1}{27} =$

$= [\frac{13 ^{1}}{24} \cdot \frac{4}{13 _{1}}] - \frac{1}{27} =$

$= \frac{4}{24} - \frac{1}{27} =$

$= \frac{1}{6} - \frac{1}{27} =$

$= \frac{9}{54} - \frac{2}{54} =$

$= \frac{7}{54}$

$\frac{5}{8} : 1 \frac{2}{3} + 1 \frac{4}{5} \cdot \frac{5}{6} - \frac{5}{9} \cdot (1 \frac{3}{4} - \frac{2}{5}) + 1 \frac{5}{6} =$

$= \frac{5}{8} : \frac{5}{3} + \frac{9}{5 _{1}} \cdot \frac{5 ^{1}}{6} - \frac{5}{9} \cdot (1 \frac{15}{20} - \frac{8}{20}) + 1 \frac{5}{6} =$

$= \frac{5 ^{1}}{8} \cdot \frac{3}{5 _{1}} + \frac{9}{6} - \frac{5}{9} \cdot 1 \frac{7}{20} + 1 \frac{5}{6} =$

$= \frac{3}{8} + \frac{3}{2} - \frac{5}{9 _{1}} \cdot \frac{27 ^{3}}{20} + 1 \frac{5}{6} =$

$= \frac{3}{8} + \frac{12}{8} - \frac{15}{20} + 1 \frac{5}{6} =$

$= \frac{15}{8} - \frac{3}{4} + 1 \frac{5}{6} =$

$= \frac{15}{8} - \frac{6}{8} + 1 \frac{5}{6} =$

$= \frac{9}{8} + 1 \frac{5}{6} =$

$= 1 \frac{1}{8} + 1 \frac{5}{6} =$

$= 1 \frac{6}{48} = 1 \frac{40}{48} =$

$= 2 \frac{46}{48} = 2 \frac{23}{24}$

$1 \frac{1}{3} \cdot 1 \frac{1}{4} - 1 \frac{1}{2} : 1 \frac{1}{5} + 1 \frac{1}{8} : (1 \frac{1}{8} - \frac{3}{4}) + 1 \frac{5}{6} =$

$= \frac{4 ^{1}}{3} \cdot \frac{5}{4 _{1}} - \frac{3}{2} : \frac{6}{5} + \frac{9}{8} : (\frac{9}{8} - \frac{6}{8}) + 1 \frac{5}{6} =$

$= \frac{5}{3} - \frac{3 ^{1}}{2} \cdot \frac{5}{6 _{2}} + \frac{9}{8} : \frac{3}{8} + 1 \frac{5}{6} =$

$= \frac{5}{3} - \frac{5}{4} + \frac{9}{8 _{1}} \cdot \frac{8 ^{1}}{3} + 1 \frac{5}{6} =$

$= \frac{5}{3} - \frac{5}{4} + 9^{3} \cdot \frac{1}{3 _{1}} + 1 \frac{5}{6} =$

$= 1 \frac{2}{3} - 1 \frac{1}{4} + 3 + 1 \frac{5}{6} =$

$= 1 \frac{8}{12} - 1 \frac{3}{12} + 3 + 1 \frac{10}{12} =$

$= 1 \frac{8}{12} + 3 + 1 \frac{10}{12} - 1 \frac{3}{12} =$

$= 5 \frac{18}{12} - 1 \frac{3}{12} =$

$= 4 \frac{15}{12} = 5 \frac{3}{12} = 5 \frac{1}{4}$

Łukasz Solarz

Nauczyciel matematyki

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