Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-4}\right) +\left(\frac{-3}{8}\right) -\left(\frac{-11}{-11}\right)\\= \frac{7}{4}- \frac{3}{8}-\frac{11}{11}\\=\frac{7}{4}-\frac{3}{8}-\frac{1}{1}\\=\frac{14}{8}-\frac{3}{8}-\frac{8}{8}\\=\frac{14-3-8}{8}\\=\frac{3}{8}\)
2. \(-\left(\frac{4}{-3}\right) +\left(\frac{2}{-3}\right) -\left(\frac{12}{2}\right)\\= \frac{4}{3}- \frac{2}{3}-\frac{12}{2}\\=\frac{4}{3}-\frac{2}{3}-\frac{6}{1}\\=\frac{4-2-6}{3}\\=\frac{-4}{3}\)
3. \(-\left(\frac{-5}{6}\right) -\left(\frac{8}{6}\right) +\left(\frac{-12}{11}\right)\\= \frac{5}{6}- \frac{8}{6}-\frac{12}{11}\\=\frac{5}{6}-\frac{4}{3}-\frac{12}{11}\\=\frac{55}{66}-\frac{88}{66}-\frac{72}{66}\\=\frac{55-88-72}{66}\\=\frac{-105}{66}\\=\frac{-35}{22}\)
4. \(+\left(\frac{-7}{-2}\right) +\left(\frac{7}{4}\right) -\left(\frac{6}{9}\right)\\= \frac{7}{2}+ \frac{7}{4}-\frac{6}{9}\\=\frac{7}{2}+\frac{7}{4}-\frac{2}{3}\\=\frac{42}{12}+\frac{21}{12}-\frac{8}{12}\\=\frac{42+21-8}{12}\\=\frac{55}{12}\)
5. \(-\left(\frac{2}{3}\right) -\left(\frac{-3}{6}\right) +\left(\frac{-8}{2}\right)\\= \frac{-2}{3}+ \frac{3}{6}-\frac{8}{2}\\=\frac{-2}{3}+\frac{1}{2}-\frac{4}{1}\\=\frac{-4}{6}+\frac{3}{6}-\frac{24}{6}\\=\frac{-4+3-24}{6}\\=\frac{-25}{6}\)
6. \(+\left(\frac{-6}{5}\right) +\left(\frac{4}{8}\right) -\left(\frac{5}{9}\right)\\= \frac{-6}{5}+ \frac{4}{8}-\frac{5}{9}\\=\frac{-6}{5}+\frac{1}{2}-\frac{5}{9}\\=\frac{-108}{90}+\frac{45}{90}-\frac{50}{90}\\=\frac{-108+45-50}{90}\\=\frac{-113}{90}\)
7. \(+\left(\frac{-7}{4}\right) +\left(\frac{-4}{3}\right) +\left(\frac{-12}{10}\right)\\= \frac{-7}{4}- \frac{4}{3}-\frac{12}{10}\\=\frac{-7}{4}-\frac{4}{3}-\frac{6}{5}\\=\frac{-105}{60}-\frac{80}{60}-\frac{72}{60}\\=\frac{-105-80-72}{60}\\=\frac{-257}{60}\)
8. \(+\left(\frac{2}{7}\right) -\left(\frac{7}{-10}\right) -\left(\frac{8}{-3}\right)\\= \frac{2}{7}+ \frac{7}{10}+\frac{8}{3}\\=\frac{60}{210}+\frac{147}{210}+\frac{560}{210}\\=\frac{60+147+560}{210}\\=\frac{767}{210}\)
9. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{-5}{-3}\right)\\= \frac{2}{3}- \frac{4}{4}+\frac{5}{3}\\=\frac{2}{3}-\frac{1}{1}+\frac{5}{3}\\=\frac{2-1+5}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)
10. \(+\left(\frac{9}{-2}\right) -\left(\frac{-7}{4}\right) +\left(\frac{-8}{3}\right)\\= \frac{-9}{2}+ \frac{7}{4}-\frac{8}{3}\\=\frac{-54}{12}+\frac{21}{12}-\frac{32}{12}\\=\frac{-54+21-32}{12}\\=\frac{-65}{12}\)
11. \(-\left(\frac{10}{-7}\right) +\left(\frac{6}{10}\right) -\left(\frac{7}{10}\right)\\= \frac{10}{7}+ \frac{6}{10}-\frac{7}{10}\\=\frac{10}{7}+\frac{3}{5}-\frac{7}{10}\\=\frac{100}{70}+\frac{42}{70}-\frac{49}{70}\\=\frac{100+42-49}{70}\\=\frac{93}{70}\)
12. \(-\left(\frac{-7}{-8}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-3}{-5}\right)\\= \frac{-7}{8}+ \frac{7}{5}+\frac{3}{5}\\=\frac{-35}{40}+\frac{56}{40}+\frac{24}{40}\\=\frac{-35+56+24}{40}\\=\frac{45}{40}\\=\frac{9}{8}\)