Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

1. \(+\left(\frac{-10}{-9}\right) +\left(\frac{4}{6}\right) +\left(\frac{-7}{4}\right)\)
2. \(+\left(\frac{-2}{3}\right) -\left(\frac{4}{5}\right) +\left(\frac{-10}{-3}\right)\)
3. \(+\left(\frac{8}{7}\right) -\left(\frac{2}{9}\right) +\left(\frac{-2}{6}\right)\)
4. \(-\left(\frac{9}{-2}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{-11}{10}\right)\)
5. \(-\left(\frac{-9}{8}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{4}{-9}\right)\)
6. \(-\left(\frac{6}{-5}\right) +\left(\frac{-2}{7}\right) -\left(\frac{7}{8}\right)\)
7. \(+\left(\frac{3}{8}\right) +\left(\frac{7}{9}\right) +\left(\frac{-4}{11}\right)\)
8. \(+\left(\frac{2}{9}\right) -\left(\frac{6}{2}\right) -\left(\frac{6}{-3}\right)\)
9. \(-\left(\frac{-5}{4}\right) -\left(\frac{-2}{2}\right) +\left(\frac{-6}{-4}\right)\)
10. \(-\left(\frac{-9}{-4}\right) -\left(\frac{9}{-9}\right) +\left(\frac{-7}{-2}\right)\)
11. \(+\left(\frac{-5}{-7}\right) +\left(\frac{10}{6}\right) -\left(\frac{6}{8}\right)\)
12. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-12}{6}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-9}\right) +\left(\frac{4}{6}\right) +\left(\frac{-7}{4}\right)\\= \frac{10}{9}+ \frac{4}{6}-\frac{7}{4}\\=\frac{10}{9}+\frac{2}{3}-\frac{7}{4}\\=\frac{40}{36}+\frac{24}{36}-\frac{63}{36}\\=\frac{40+24-63}{36}\\=\frac{1}{36}\)
2. \(+\left(\frac{-2}{3}\right) -\left(\frac{4}{5}\right) +\left(\frac{-10}{-3}\right)\\= \frac{-2}{3}- \frac{4}{5}+\frac{10}{3}\\=\frac{-10}{15}-\frac{12}{15}+\frac{50}{15}\\=\frac{-10-12+50}{15}\\=\frac{28}{15}\)
3. \(+\left(\frac{8}{7}\right) -\left(\frac{2}{9}\right) +\left(\frac{-2}{6}\right)\\= \frac{8}{7}- \frac{2}{9}-\frac{2}{6}\\=\frac{8}{7}-\frac{2}{9}-\frac{1}{3}\\=\frac{72}{63}-\frac{14}{63}-\frac{21}{63}\\=\frac{72-14-21}{63}\\=\frac{37}{63}\)
4. \(-\left(\frac{9}{-2}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{-11}{10}\right)\\= \frac{9}{2}- \frac{8}{9}-\frac{11}{10}\\=\frac{405}{90}-\frac{80}{90}-\frac{99}{90}\\=\frac{405-80-99}{90}\\=\frac{226}{90}\\=\frac{113}{45}\)
5. \(-\left(\frac{-9}{8}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{4}{-9}\right)\\= \frac{9}{8}+ \frac{3}{4}-\frac{4}{9}\\=\frac{81}{72}+\frac{54}{72}-\frac{32}{72}\\=\frac{81+54-32}{72}\\=\frac{103}{72}\)
6. \(-\left(\frac{6}{-5}\right) +\left(\frac{-2}{7}\right) -\left(\frac{7}{8}\right)\\= \frac{6}{5}- \frac{2}{7}-\frac{7}{8}\\=\frac{336}{280}-\frac{80}{280}-\frac{245}{280}\\=\frac{336-80-245}{280}\\=\frac{11}{280}\)
7. \(+\left(\frac{3}{8}\right) +\left(\frac{7}{9}\right) +\left(\frac{-4}{11}\right)\\= \frac{3}{8}+ \frac{7}{9}-\frac{4}{11}\\=\frac{297}{792}+\frac{616}{792}-\frac{288}{792}\\=\frac{297+616-288}{792}\\=\frac{625}{792}\)
8. \(+\left(\frac{2}{9}\right) -\left(\frac{6}{2}\right) -\left(\frac{6}{-3}\right)\\= \frac{2}{9}- \frac{6}{2}+\frac{6}{3}\\=\frac{2}{9}-\frac{3}{1}+\frac{2}{1}\\=\frac{2-3+2}{9}\\=\frac{1}{9}\)
9. \(-\left(\frac{-5}{4}\right) -\left(\frac{-2}{2}\right) +\left(\frac{-6}{-4}\right)\\= \frac{5}{4}+ \frac{2}{2}+\frac{6}{4}\\=\frac{5}{4}+\frac{1}{1}+\frac{3}{2}\\=\frac{5+1+3}{4}\\=\frac{9}{4}\)
10. \(-\left(\frac{-9}{-4}\right) -\left(\frac{9}{-9}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-9}{4}+ \frac{9}{9}+\frac{7}{2}\\=\frac{-9}{4}+\frac{1}{1}+\frac{7}{2}\\=\frac{-9+1+7}{4}\\=\frac{-1}{4}\)
11. \(+\left(\frac{-5}{-7}\right) +\left(\frac{10}{6}\right) -\left(\frac{6}{8}\right)\\= \frac{5}{7}+ \frac{10}{6}-\frac{6}{8}\\=\frac{5}{7}+\frac{5}{3}-\frac{3}{4}\\=\frac{60}{84}+\frac{140}{84}-\frac{63}{84}\\=\frac{60+140-63}{84}\\=\frac{137}{84}\)
12. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-12}{6}\right)\\= \frac{-9}{2}- \frac{10}{6}+\frac{12}{6}\\=\frac{-9}{2}-\frac{5}{3}+\frac{2}{1}\\=\frac{-27}{6}-\frac{10}{6}+\frac{12}{6}\\=\frac{-27-10+12}{6}\\=\frac{-25}{6}\)