Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-3}{8}\right) +\left(\frac{-2}{9}\right)\\= \frac{9}{4}+ \frac{3}{8}-\frac{2}{9}\\=\frac{162}{72}+\frac{27}{72}-\frac{16}{72}\\=\frac{162+27-16}{72}\\=\frac{173}{72}\)
2. \(-\left(\frac{9}{-2}\right) +\left(\frac{-6}{7}\right) +\left(\frac{-5}{-7}\right)\\= \frac{9}{2}- \frac{6}{7}+\frac{5}{7}\\=\frac{63}{14}-\frac{12}{14}+\frac{10}{14}\\=\frac{63-12+10}{14}\\=\frac{61}{14}\)
3. \(+\left(\frac{8}{3}\right) -\left(\frac{3}{-2}\right) -\left(\frac{11}{-8}\right)\\= \frac{8}{3}+ \frac{3}{2}+\frac{11}{8}\\=\frac{64}{24}+\frac{36}{24}+\frac{33}{24}\\=\frac{64+36+33}{24}\\=\frac{133}{24}\)
4. \(+\left(\frac{-7}{-4}\right) -\left(\frac{-2}{4}\right) +\left(\frac{-7}{-4}\right)\\= \frac{7}{4}+ \frac{2}{4}+\frac{7}{4}\\=\frac{7}{4}+\frac{1}{2}+\frac{7}{4}\\=\frac{7+1+7}{4}\\=\frac{15}{4}\)
5. \(+\left(\frac{10}{7}\right) -\left(\frac{4}{10}\right) +\left(\frac{-12}{-6}\right)\\= \frac{10}{7}- \frac{4}{10}+\frac{12}{6}\\=\frac{10}{7}-\frac{2}{5}+\frac{2}{1}\\=\frac{50}{35}-\frac{14}{35}+\frac{70}{35}\\=\frac{50-14+70}{35}\\=\frac{106}{35}\)
6. \(-\left(\frac{10}{-9}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{-6}{11}\right)\\= \frac{10}{9}- \frac{2}{3}-\frac{6}{11}\\=\frac{110}{99}-\frac{66}{99}-\frac{54}{99}\\=\frac{110-66-54}{99}\\=\frac{-10}{99}\)
7. \(-\left(\frac{-10}{7}\right) +\left(\frac{4}{-4}\right) +\left(\frac{-6}{12}\right)\\= \frac{10}{7}- \frac{4}{4}-\frac{6}{12}\\=\frac{10}{7}-\frac{1}{1}-\frac{1}{2}\\=\frac{20}{14}-\frac{14}{14}-\frac{7}{14}\\=\frac{20-14-7}{14}\\=\frac{-1}{14}\)
8. \(-\left(\frac{7}{8}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{4}{11}\right)\\= \frac{-7}{8}+ \frac{2}{9}-\frac{4}{11}\\=\frac{-693}{792}+\frac{176}{792}-\frac{288}{792}\\=\frac{-693+176-288}{792}\\=\frac{-805}{792}\)
9. \(+\left(\frac{-5}{2}\right) -\left(\frac{-8}{-4}\right) -\left(\frac{7}{-2}\right)\\= \frac{-5}{2}- \frac{8}{4}+\frac{7}{2}\\=\frac{-5}{2}-\frac{2}{1}+\frac{7}{2}\\=\frac{-5-2+7}{2}\\=\frac{0}{2}\\=\frac{0}{1}\)
10. \(+\left(\frac{4}{-3}\right) +\left(\frac{6}{4}\right) +\left(\frac{9}{9}\right)\\= \frac{-4}{3}+ \frac{6}{4}+\frac{9}{9}\\=\frac{-4}{3}+\frac{3}{2}+\frac{1}{1}\\=\frac{-8}{6}+\frac{9}{6}+\frac{6}{6}\\=\frac{-8+9+6}{6}\\=\frac{7}{6}\)
11. \(+\left(\frac{10}{3}\right) -\left(\frac{-2}{7}\right) +\left(\frac{-12}{-8}\right)\\= \frac{10}{3}+ \frac{2}{7}+\frac{12}{8}\\=\frac{10}{3}+\frac{2}{7}+\frac{3}{2}\\=\frac{140}{42}+\frac{12}{42}+\frac{63}{42}\\=\frac{140+12+63}{42}\\=\frac{215}{42}\)
12. \(-\left(\frac{10}{-7}\right) -\left(\frac{-7}{3}\right) -\left(\frac{11}{4}\right)\\= \frac{10}{7}+ \frac{7}{3}-\frac{11}{4}\\=\frac{120}{84}+\frac{196}{84}-\frac{231}{84}\\=\frac{120+196-231}{84}\\=\frac{85}{84}\)