Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{7}\right) +\left(\frac{9}{2}\right) +\left(\frac{-3}{5}\right)\\= \frac{6}{7}+ \frac{9}{2}-\frac{3}{5}\\=\frac{60}{70}+\frac{315}{70}-\frac{42}{70}\\=\frac{60+315-42}{70}\\=\frac{333}{70}\)
2. \(-\left(\frac{-5}{2}\right) -\left(\frac{2}{2}\right) +\left(\frac{-2}{-9}\right)\\= \frac{5}{2}- \frac{2}{2}+\frac{2}{9}\\=\frac{5}{2}-\frac{1}{1}+\frac{2}{9}\\=\frac{45}{18}-\frac{18}{18}+\frac{4}{18}\\=\frac{45-18+4}{18}\\=\frac{31}{18}\)
3. \(+\left(\frac{4}{-7}\right) +\left(\frac{-10}{7}\right) -\left(\frac{-7}{-8}\right)\\= \frac{-4}{7}- \frac{10}{7}-\frac{7}{8}\\=\frac{-32}{56}-\frac{80}{56}-\frac{49}{56}\\=\frac{-32-80-49}{56}\\=\frac{-161}{56}\\=\frac{-23}{8}\)
4. \(-\left(\frac{10}{3}\right) +\left(\frac{5}{-10}\right) +\left(\frac{-11}{-11}\right)\\= \frac{-10}{3}- \frac{5}{10}+\frac{11}{11}\\=\frac{-10}{3}-\frac{1}{2}+\frac{1}{1}\\=\frac{-20}{6}-\frac{3}{6}+\frac{6}{6}\\=\frac{-20-3+6}{6}\\=\frac{-17}{6}\)
5. \(-\left(\frac{-5}{-7}\right) -\left(\frac{4}{10}\right) +\left(\frac{11}{-10}\right)\\= \frac{-5}{7}- \frac{4}{10}-\frac{11}{10}\\=\frac{-5}{7}-\frac{2}{5}-\frac{11}{10}\\=\frac{-50}{70}-\frac{28}{70}-\frac{77}{70}\\=\frac{-50-28-77}{70}\\=\frac{-155}{70}\\=\frac{-31}{14}\)
6. \(+\left(\frac{-3}{8}\right) -\left(\frac{3}{-7}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-3}{8}+ \frac{3}{7}+\frac{10}{8}\\=\frac{-3}{8}+\frac{3}{7}+\frac{5}{4}\\=\frac{-21}{56}+\frac{24}{56}+\frac{70}{56}\\=\frac{-21+24+70}{56}\\=\frac{73}{56}\)
7. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-4}{9}\right) -\left(\frac{-12}{12}\right)\\= \frac{4}{3}+ \frac{4}{9}+\frac{12}{12}\\=\frac{4}{3}+\frac{4}{9}+\frac{1}{1}\\=\frac{12}{9}+\frac{4}{9}+\frac{9}{9}\\=\frac{12+4+9}{9}\\=\frac{25}{9}\)
8. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-8}{3}\right) -\left(\frac{4}{-12}\right)\\= \frac{-2}{7}- \frac{8}{3}+\frac{4}{12}\\=\frac{-2}{7}-\frac{8}{3}+\frac{1}{3}\\=\frac{-6}{21}-\frac{56}{21}+\frac{7}{21}\\=\frac{-6-56+7}{21}\\=\frac{-55}{21}\)
9. \(-\left(\frac{-9}{-7}\right) -\left(\frac{3}{-4}\right) -\left(\frac{-6}{-10}\right)\\= \frac{-9}{7}+ \frac{3}{4}-\frac{6}{10}\\=\frac{-9}{7}+\frac{3}{4}-\frac{3}{5}\\=\frac{-180}{140}+\frac{105}{140}-\frac{84}{140}\\=\frac{-180+105-84}{140}\\=\frac{-159}{140}\)
10. \(-\left(\frac{9}{-2}\right) +\left(\frac{10}{2}\right) +\left(\frac{-4}{-7}\right)\\= \frac{9}{2}+ \frac{10}{2}+\frac{4}{7}\\=\frac{9}{2}+\frac{5}{1}+\frac{4}{7}\\=\frac{63}{14}+\frac{70}{14}+\frac{8}{14}\\=\frac{63+70+8}{14}\\=\frac{141}{14}\)
11. \(+\left(\frac{7}{2}\right) +\left(\frac{-2}{3}\right) +\left(\frac{-8}{4}\right)\\= \frac{7}{2}- \frac{2}{3}-\frac{8}{4}\\=\frac{7}{2}-\frac{2}{3}-\frac{2}{1}\\=\frac{21}{6}-\frac{4}{6}-\frac{12}{6}\\=\frac{21-4-12}{6}\\=\frac{5}{6}\)
12. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{10}{4}\right)\\= \frac{6}{5}- \frac{2}{2}+\frac{10}{4}\\=\frac{6}{5}-\frac{1}{1}+\frac{5}{2}\\=\frac{12}{10}-\frac{10}{10}+\frac{25}{10}\\=\frac{12-10+25}{10}\\=\frac{27}{10}\)