Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{4}\right) +\left(\frac{10}{4}\right) -\left(\frac{-2}{4}\right)\\= \frac{-3}{4}+ \frac{10}{4}+\frac{2}{4}\\=\frac{-3}{4}+\frac{5}{2}+\frac{1}{2}\\=\frac{-3+5+1}{4}\\=\frac{3}{4}\)
2. \(+\left(\frac{-4}{5}\right) +\left(\frac{10}{-6}\right) +\left(\frac{-2}{-10}\right)\\= \frac{-4}{5}- \frac{10}{6}+\frac{2}{10}\\=\frac{-4}{5}-\frac{5}{3}+\frac{1}{5}\\=\frac{-12}{15}-\frac{25}{15}+\frac{3}{15}\\=\frac{-12-25+3}{15}\\=\frac{-34}{15}\)
3. \(-\left(\frac{7}{4}\right) -\left(\frac{-2}{7}\right) +\left(\frac{-3}{-10}\right)\\= \frac{-7}{4}+ \frac{2}{7}+\frac{3}{10}\\=\frac{-245}{140}+\frac{40}{140}+\frac{42}{140}\\=\frac{-245+40+42}{140}\\=\frac{-163}{140}\)
4. \(+\left(\frac{-6}{-5}\right) +\left(\frac{7}{-3}\right) -\left(\frac{-2}{-11}\right)\\= \frac{6}{5}- \frac{7}{3}-\frac{2}{11}\\=\frac{198}{165}-\frac{385}{165}-\frac{30}{165}\\=\frac{198-385-30}{165}\\=\frac{-217}{165}\)
5. \(-\left(\frac{4}{3}\right) -\left(\frac{7}{-5}\right) +\left(\frac{9}{-3}\right)\\= \frac{-4}{3}+ \frac{7}{5}-\frac{9}{3}\\=\frac{-4}{3}+\frac{7}{5}-\frac{3}{1}\\=\frac{-20}{15}+\frac{21}{15}-\frac{45}{15}\\=\frac{-20+21-45}{15}\\=\frac{-44}{15}\)
6. \(+\left(\frac{10}{7}\right) -\left(\frac{8}{5}\right) +\left(\frac{-3}{12}\right)\\= \frac{10}{7}- \frac{8}{5}-\frac{3}{12}\\=\frac{10}{7}-\frac{8}{5}-\frac{1}{4}\\=\frac{200}{140}-\frac{224}{140}-\frac{35}{140}\\=\frac{200-224-35}{140}\\=\frac{-59}{140}\)
7. \(+\left(\frac{-2}{-9}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-6}{2}\right)\\= \frac{2}{9}+ \frac{6}{3}+\frac{6}{2}\\=\frac{2}{9}+\frac{2}{1}+\frac{3}{1}\\=\frac{2+2+3}{9}\\=\frac{7}{9}\)
8. \(+\left(\frac{-4}{9}\right) -\left(\frac{8}{10}\right) -\left(\frac{5}{-7}\right)\\= \frac{-4}{9}- \frac{8}{10}+\frac{5}{7}\\=\frac{-4}{9}-\frac{4}{5}+\frac{5}{7}\\=\frac{-140}{315}-\frac{252}{315}+\frac{225}{315}\\=\frac{-140-252+225}{315}\\=\frac{-167}{315}\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{-9}{8}\right)\\= \frac{-10}{7}+ \frac{10}{8}-\frac{9}{8}\\=\frac{-10}{7}+\frac{5}{4}-\frac{9}{8}\\=\frac{-80}{56}+\frac{70}{56}-\frac{63}{56}\\=\frac{-80+70-63}{56}\\=\frac{-73}{56}\)
10. \(-\left(\frac{-7}{3}\right) -\left(\frac{9}{5}\right) +\left(\frac{-3}{12}\right)\\= \frac{7}{3}- \frac{9}{5}-\frac{3}{12}\\=\frac{7}{3}-\frac{9}{5}-\frac{1}{4}\\=\frac{140}{60}-\frac{108}{60}-\frac{15}{60}\\=\frac{140-108-15}{60}\\=\frac{17}{60}\)
11. \(+\left(\frac{6}{5}\right) +\left(\frac{-5}{8}\right) +\left(\frac{9}{-8}\right)\\= \frac{6}{5}- \frac{5}{8}-\frac{9}{8}\\=\frac{48}{40}-\frac{25}{40}-\frac{45}{40}\\=\frac{48-25-45}{40}\\=\frac{-22}{40}\\=\frac{-11}{20}\)
12. \(-\left(\frac{10}{-9}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{-5}{10}\right)\\= \frac{10}{9}- \frac{6}{2}-\frac{5}{10}\\=\frac{10}{9}-\frac{3}{1}-\frac{1}{2}\\=\frac{20}{18}-\frac{54}{18}-\frac{9}{18}\\=\frac{20-54-9}{18}\\=\frac{-43}{18}\)