Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-5}\right) -\left(\frac{-2}{4}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-4}{5}+ \frac{2}{4}-\frac{11}{6}\\=\frac{-4}{5}+\frac{1}{2}-\frac{11}{6}\\=\frac{-24}{30}+\frac{15}{30}-\frac{55}{30}\\=\frac{-24+15-55}{30}\\=\frac{-64}{30}\\=\frac{-32}{15}\)
2. \(-\left(\frac{-4}{-3}\right) -\left(\frac{4}{-6}\right) +\left(\frac{-4}{-3}\right)\\= \frac{-4}{3}+ \frac{4}{6}+\frac{4}{3}\\=\frac{-4}{3}+\frac{2}{3}+\frac{4}{3}\\=\frac{-4+2+4}{3}\\=\frac{2}{3}\)
3. \(+\left(\frac{3}{-7}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{11}{-2}\right)\\= \frac{-3}{7}+ \frac{7}{10}-\frac{11}{2}\\=\frac{-30}{70}+\frac{49}{70}-\frac{385}{70}\\=\frac{-30+49-385}{70}\\=\frac{-366}{70}\\=\frac{-183}{35}\)
4. \(+\left(\frac{3}{2}\right) +\left(\frac{-6}{6}\right) +\left(\frac{-5}{-11}\right)\\= \frac{3}{2}- \frac{6}{6}+\frac{5}{11}\\=\frac{3}{2}-\frac{1}{1}+\frac{5}{11}\\=\frac{33}{22}-\frac{22}{22}+\frac{10}{22}\\=\frac{33-22+10}{22}\\=\frac{21}{22}\)
5. \(-\left(\frac{4}{9}\right) -\left(\frac{8}{-2}\right) -\left(\frac{7}{-8}\right)\\= \frac{-4}{9}+ \frac{8}{2}+\frac{7}{8}\\=\frac{-4}{9}+\frac{4}{1}+\frac{7}{8}\\=\frac{-32}{72}+\frac{288}{72}+\frac{63}{72}\\=\frac{-32+288+63}{72}\\=\frac{319}{72}\)
6. \(-\left(\frac{-5}{-8}\right) -\left(\frac{-4}{4}\right) -\left(\frac{9}{-9}\right)\\= \frac{-5}{8}+ \frac{4}{4}+\frac{9}{9}\\=\frac{-5}{8}+\frac{1}{1}+\frac{1}{1}\\=\frac{-5+1+1}{8}\\=\frac{-3}{8}\)
7. \(+\left(\frac{5}{6}\right) -\left(\frac{6}{-4}\right) +\left(\frac{-6}{-11}\right)\\= \frac{5}{6}+ \frac{6}{4}+\frac{6}{11}\\=\frac{5}{6}+\frac{3}{2}+\frac{6}{11}\\=\frac{55}{66}+\frac{99}{66}+\frac{36}{66}\\=\frac{55+99+36}{66}\\=\frac{190}{66}\\=\frac{95}{33}\)
8. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-6}{7}\right) -\left(\frac{10}{-9}\right)\\= \frac{4}{3}- \frac{6}{7}+\frac{10}{9}\\=\frac{84}{63}-\frac{54}{63}+\frac{70}{63}\\=\frac{84-54+70}{63}\\=\frac{100}{63}\)
9. \(-\left(\frac{9}{7}\right) +\left(\frac{-5}{3}\right) -\left(\frac{-10}{-7}\right)\\= \frac{-9}{7}- \frac{5}{3}-\frac{10}{7}\\=\frac{-27}{21}-\frac{35}{21}-\frac{30}{21}\\=\frac{-27-35-30}{21}\\=\frac{-92}{21}\)
10. \(+\left(\frac{-9}{2}\right) -\left(\frac{9}{5}\right) -\left(\frac{-12}{6}\right)\\= \frac{-9}{2}- \frac{9}{5}+\frac{12}{6}\\=\frac{-9}{2}-\frac{9}{5}+\frac{2}{1}\\=\frac{-45}{10}-\frac{18}{10}+\frac{20}{10}\\=\frac{-45-18+20}{10}\\=\frac{-43}{10}\)
11. \(+\left(\frac{3}{-5}\right) -\left(\frac{2}{-10}\right) -\left(\frac{5}{7}\right)\\= \frac{-3}{5}+ \frac{2}{10}-\frac{5}{7}\\=\frac{-3}{5}+\frac{1}{5}-\frac{5}{7}\\=\frac{-21}{35}+\frac{7}{35}-\frac{25}{35}\\=\frac{-21+7-25}{35}\\=\frac{-39}{35}\)
12. \(+\left(\frac{6}{5}\right) -\left(\frac{5}{-9}\right) +\left(\frac{-4}{8}\right)\\= \frac{6}{5}+ \frac{5}{9}-\frac{4}{8}\\=\frac{6}{5}+\frac{5}{9}-\frac{1}{2}\\=\frac{108}{90}+\frac{50}{90}-\frac{45}{90}\\=\frac{108+50-45}{90}\\=\frac{113}{90}\)