Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-7}\right) +\left(\frac{-4}{-5}\right) -\left(\frac{-5}{11}\right)\\= \frac{9}{7}+ \frac{4}{5}+\frac{5}{11}\\=\frac{495}{385}+\frac{308}{385}+\frac{175}{385}\\=\frac{495+308+175}{385}\\=\frac{978}{385}\)
2. \(-\left(\frac{-6}{-5}\right) +\left(\frac{8}{-6}\right) +\left(\frac{3}{-11}\right)\\= \frac{-6}{5}- \frac{8}{6}-\frac{3}{11}\\=\frac{-6}{5}-\frac{4}{3}-\frac{3}{11}\\=\frac{-198}{165}-\frac{220}{165}-\frac{45}{165}\\=\frac{-198-220-45}{165}\\=\frac{-463}{165}\)
3. \(-\left(\frac{9}{-7}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{5}{-5}\right)\\= \frac{9}{7}+ \frac{7}{10}-\frac{5}{5}\\=\frac{9}{7}+\frac{7}{10}-\frac{1}{1}\\=\frac{90}{70}+\frac{49}{70}-\frac{70}{70}\\=\frac{90+49-70}{70}\\=\frac{69}{70}\)
4. \(-\left(\frac{-2}{-3}\right) +\left(\frac{5}{-9}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-2}{3}- \frac{5}{9}+\frac{6}{12}\\=\frac{-2}{3}-\frac{5}{9}+\frac{1}{2}\\=\frac{-12}{18}-\frac{10}{18}+\frac{9}{18}\\=\frac{-12-10+9}{18}\\=\frac{-13}{18}\)
5. \(-\left(\frac{-6}{-5}\right) +\left(\frac{10}{9}\right) -\left(\frac{-7}{11}\right)\\= \frac{-6}{5}+ \frac{10}{9}+\frac{7}{11}\\=\frac{-594}{495}+\frac{550}{495}+\frac{315}{495}\\=\frac{-594+550+315}{495}\\=\frac{271}{495}\)
6. \(+\left(\frac{4}{7}\right) +\left(\frac{6}{-9}\right) -\left(\frac{10}{-12}\right)\\= \frac{4}{7}- \frac{6}{9}+\frac{10}{12}\\=\frac{4}{7}-\frac{2}{3}+\frac{5}{6}\\=\frac{24}{42}-\frac{28}{42}+\frac{35}{42}\\=\frac{24-28+35}{42}\\=\frac{31}{42}\)
7. \(-\left(\frac{10}{-9}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{-11}{-4}\right)\\= \frac{10}{9}+ \frac{10}{8}+\frac{11}{4}\\=\frac{10}{9}+\frac{5}{4}+\frac{11}{4}\\=\frac{40}{36}+\frac{45}{36}+\frac{99}{36}\\=\frac{40+45+99}{36}\\=\frac{184}{36}\\=\frac{46}{9}\)
8. \(-\left(\frac{3}{-2}\right) -\left(\frac{7}{10}\right) -\left(\frac{2}{12}\right)\\= \frac{3}{2}- \frac{7}{10}-\frac{2}{12}\\=\frac{3}{2}-\frac{7}{10}-\frac{1}{6}\\=\frac{45}{30}-\frac{21}{30}-\frac{5}{30}\\=\frac{45-21-5}{30}\\=\frac{19}{30}\)
9. \(+\left(\frac{-9}{2}\right) +\left(\frac{-7}{3}\right) -\left(\frac{3}{9}\right)\\= \frac{-9}{2}- \frac{7}{3}-\frac{3}{9}\\=\frac{-9}{2}-\frac{7}{3}-\frac{1}{3}\\=\frac{-27}{6}-\frac{14}{6}-\frac{2}{6}\\=\frac{-27-14-2}{6}\\=\frac{-43}{6}\)
10. \(-\left(\frac{-7}{5}\right) +\left(\frac{8}{-4}\right) +\left(\frac{-3}{-2}\right)\\= \frac{7}{5}- \frac{8}{4}+\frac{3}{2}\\=\frac{7}{5}-\frac{2}{1}+\frac{3}{2}\\=\frac{14}{10}-\frac{20}{10}+\frac{15}{10}\\=\frac{14-20+15}{10}\\=\frac{9}{10}\)
11. \(+\left(\frac{-4}{9}\right) -\left(\frac{-9}{-2}\right) -\left(\frac{4}{-5}\right)\\= \frac{-4}{9}- \frac{9}{2}+\frac{4}{5}\\=\frac{-40}{90}-\frac{405}{90}+\frac{72}{90}\\=\frac{-40-405+72}{90}\\=\frac{-373}{90}\)
12. \(-\left(\frac{-7}{-2}\right) +\left(\frac{4}{5}\right) +\left(\frac{-7}{2}\right)\\= \frac{-7}{2}+ \frac{4}{5}-\frac{7}{2}\\=\frac{-35}{10}+\frac{8}{10}-\frac{35}{10}\\=\frac{-35+8-35}{10}\\=\frac{-62}{10}\\=\frac{-31}{5}\)