Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-3}\right) +\left(\frac{9}{7}\right) +\left(\frac{-3}{-7}\right)\\= \frac{4}{3}+ \frac{9}{7}+\frac{3}{7}\\=\frac{28}{21}+\frac{27}{21}+\frac{9}{21}\\=\frac{28+27+9}{21}\\=\frac{64}{21}\)
2. \(+\left(\frac{-10}{-3}\right) +\left(\frac{8}{10}\right) +\left(\frac{3}{-3}\right)\\= \frac{10}{3}+ \frac{8}{10}-\frac{3}{3}\\=\frac{10}{3}+\frac{4}{5}-\frac{1}{1}\\=\frac{50}{15}+\frac{12}{15}-\frac{15}{15}\\=\frac{50+12-15}{15}\\=\frac{47}{15}\)
3. \(+\left(\frac{9}{2}\right) -\left(\frac{2}{-3}\right) +\left(\frac{-4}{-7}\right)\\= \frac{9}{2}+ \frac{2}{3}+\frac{4}{7}\\=\frac{189}{42}+\frac{28}{42}+\frac{24}{42}\\=\frac{189+28+24}{42}\\=\frac{241}{42}\)
4. \(+\left(\frac{-3}{7}\right) +\left(\frac{3}{9}\right) +\left(\frac{-5}{5}\right)\\= \frac{-3}{7}+ \frac{3}{9}-\frac{5}{5}\\=\frac{-3}{7}+\frac{1}{3}-\frac{1}{1}\\=\frac{-9}{21}+\frac{7}{21}-\frac{21}{21}\\=\frac{-9+7-21}{21}\\=\frac{-23}{21}\)
5. \(+\left(\frac{-4}{-5}\right) -\left(\frac{-7}{4}\right) +\left(\frac{-4}{-12}\right)\\= \frac{4}{5}+ \frac{7}{4}+\frac{4}{12}\\=\frac{4}{5}+\frac{7}{4}+\frac{1}{3}\\=\frac{48}{60}+\frac{105}{60}+\frac{20}{60}\\=\frac{48+105+20}{60}\\=\frac{173}{60}\)
6. \(+\left(\frac{2}{-5}\right) +\left(\frac{7}{8}\right) -\left(\frac{10}{-5}\right)\\= \frac{-2}{5}+ \frac{7}{8}+\frac{10}{5}\\=\frac{-2}{5}+\frac{7}{8}+\frac{2}{1}\\=\frac{-16}{40}+\frac{35}{40}+\frac{80}{40}\\=\frac{-16+35+80}{40}\\=\frac{99}{40}\)
7. \(+\left(\frac{-10}{-7}\right) +\left(\frac{6}{-9}\right) +\left(\frac{4}{-3}\right)\\= \frac{10}{7}- \frac{6}{9}-\frac{4}{3}\\=\frac{10}{7}-\frac{2}{3}-\frac{4}{3}\\=\frac{30}{21}-\frac{14}{21}-\frac{28}{21}\\=\frac{30-14-28}{21}\\=\frac{-12}{21}\\=\frac{-4}{7}\)
8. \(+\left(\frac{-6}{5}\right) -\left(\frac{-5}{2}\right) -\left(\frac{5}{-11}\right)\\= \frac{-6}{5}+ \frac{5}{2}+\frac{5}{11}\\=\frac{-132}{110}+\frac{275}{110}+\frac{50}{110}\\=\frac{-132+275+50}{110}\\=\frac{193}{110}\)
9. \(-\left(\frac{-9}{-5}\right) +\left(\frac{-2}{-2}\right) -\left(\frac{-9}{-11}\right)\\= \frac{-9}{5}+ \frac{2}{2}-\frac{9}{11}\\=\frac{-9}{5}+\frac{1}{1}-\frac{9}{11}\\=\frac{-99}{55}+\frac{55}{55}-\frac{45}{55}\\=\frac{-99+55-45}{55}\\=\frac{-89}{55}\)
10. \(+\left(\frac{5}{-9}\right) +\left(\frac{4}{-9}\right) -\left(\frac{11}{-3}\right)\\= \frac{-5}{9}- \frac{4}{9}+\frac{11}{3}\\=\frac{-5-4+11}{9}\\=\frac{2}{9}\)
11. \(+\left(\frac{-9}{-4}\right) +\left(\frac{4}{-9}\right) +\left(\frac{8}{-7}\right)\\= \frac{9}{4}- \frac{4}{9}-\frac{8}{7}\\=\frac{567}{252}-\frac{112}{252}-\frac{288}{252}\\=\frac{567-112-288}{252}\\=\frac{167}{252}\)
12. \(+\left(\frac{-4}{-9}\right) -\left(\frac{10}{3}\right) -\left(\frac{-7}{11}\right)\\= \frac{4}{9}- \frac{10}{3}+\frac{7}{11}\\=\frac{44}{99}-\frac{330}{99}+\frac{63}{99}\\=\frac{44-330+63}{99}\\=\frac{-223}{99}\)