Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-3}\right) -\left(\frac{-3}{-4}\right) -\left(\frac{-3}{-10}\right)\\= \frac{4}{3}- \frac{3}{4}-\frac{3}{10}\\=\frac{80}{60}-\frac{45}{60}-\frac{18}{60}\\=\frac{80-45-18}{60}\\=\frac{17}{60}\)
2. \(+\left(\frac{-5}{-2}\right) +\left(\frac{6}{10}\right) -\left(\frac{-5}{-12}\right)\\= \frac{5}{2}+ \frac{6}{10}-\frac{5}{12}\\=\frac{5}{2}+\frac{3}{5}-\frac{5}{12}\\=\frac{150}{60}+\frac{36}{60}-\frac{25}{60}\\=\frac{150+36-25}{60}\\=\frac{161}{60}\)
3. \(-\left(\frac{2}{-3}\right) -\left(\frac{-3}{-2}\right) -\left(\frac{-7}{7}\right)\\= \frac{2}{3}- \frac{3}{2}+\frac{7}{7}\\=\frac{2}{3}-\frac{3}{2}+\frac{1}{1}\\=\frac{4}{6}-\frac{9}{6}+\frac{6}{6}\\=\frac{4-9+6}{6}\\=\frac{1}{6}\)
4. \(-\left(\frac{9}{5}\right) +\left(\frac{8}{2}\right) +\left(\frac{-3}{-5}\right)\\= \frac{-9}{5}+ \frac{8}{2}+\frac{3}{5}\\=\frac{-9}{5}+\frac{4}{1}+\frac{3}{5}\\=\frac{-9+4+3}{5}\\=\frac{-2}{5}\)
5. \(+\left(\frac{8}{7}\right) +\left(\frac{2}{-3}\right) -\left(\frac{11}{-9}\right)\\= \frac{8}{7}- \frac{2}{3}+\frac{11}{9}\\=\frac{72}{63}-\frac{42}{63}+\frac{77}{63}\\=\frac{72-42+77}{63}\\=\frac{107}{63}\)
6. \(+\left(\frac{-4}{-5}\right) -\left(\frac{10}{-4}\right) +\left(\frac{-9}{-11}\right)\\= \frac{4}{5}+ \frac{10}{4}+\frac{9}{11}\\=\frac{4}{5}+\frac{5}{2}+\frac{9}{11}\\=\frac{88}{110}+\frac{275}{110}+\frac{90}{110}\\=\frac{88+275+90}{110}\\=\frac{453}{110}\)
7. \(-\left(\frac{8}{7}\right) -\left(\frac{3}{-10}\right) -\left(\frac{-9}{10}\right)\\= \frac{-8}{7}+ \frac{3}{10}+\frac{9}{10}\\=\frac{-80}{70}+\frac{21}{70}+\frac{63}{70}\\=\frac{-80+21+63}{70}\\=\frac{4}{70}\\=\frac{2}{35}\)
8. \(+\left(\frac{-10}{3}\right) +\left(\frac{6}{5}\right) -\left(\frac{11}{-10}\right)\\= \frac{-10}{3}+ \frac{6}{5}+\frac{11}{10}\\=\frac{-100}{30}+\frac{36}{30}+\frac{33}{30}\\=\frac{-100+36+33}{30}\\=\frac{-31}{30}\)
9. \(+\left(\frac{-10}{3}\right) +\left(\frac{-10}{8}\right) +\left(\frac{-4}{3}\right)\\= \frac{-10}{3}- \frac{10}{8}-\frac{4}{3}\\=\frac{-10}{3}-\frac{5}{4}-\frac{4}{3}\\=\frac{-40}{12}-\frac{15}{12}-\frac{16}{12}\\=\frac{-40-15-16}{12}\\=\frac{-71}{12}\)
10. \(-\left(\frac{-4}{5}\right) -\left(\frac{-3}{4}\right) -\left(\frac{-2}{8}\right)\\= \frac{4}{5}+ \frac{3}{4}+\frac{2}{8}\\=\frac{4}{5}+\frac{3}{4}+\frac{1}{4}\\=\frac{16}{20}+\frac{15}{20}+\frac{5}{20}\\=\frac{16+15+5}{20}\\=\frac{36}{20}\\=\frac{9}{5}\)
11. \(+\left(\frac{9}{-4}\right) -\left(\frac{9}{-7}\right) -\left(\frac{-10}{-8}\right)\\= \frac{-9}{4}+ \frac{9}{7}-\frac{10}{8}\\=\frac{-9}{4}+\frac{9}{7}-\frac{5}{4}\\=\frac{-63}{28}+\frac{36}{28}-\frac{35}{28}\\=\frac{-63+36-35}{28}\\=\frac{-62}{28}\\=\frac{-31}{14}\)
12. \(+\left(\frac{2}{5}\right) -\left(\frac{7}{-3}\right) +\left(\frac{-7}{8}\right)\\= \frac{2}{5}+ \frac{7}{3}-\frac{7}{8}\\=\frac{48}{120}+\frac{280}{120}-\frac{105}{120}\\=\frac{48+280-105}{120}\\=\frac{223}{120}\)