Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-5}\right) -\left(\frac{-5}{-9}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-2}{5}- \frac{5}{9}-\frac{2}{3}\\=\frac{-18}{45}-\frac{25}{45}-\frac{30}{45}\\=\frac{-18-25-30}{45}\\=\frac{-73}{45}\)
2. \(-\left(\frac{-7}{3}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{7}{-8}\right)\\= \frac{7}{3}- \frac{4}{10}+\frac{7}{8}\\=\frac{7}{3}-\frac{2}{5}+\frac{7}{8}\\=\frac{280}{120}-\frac{48}{120}+\frac{105}{120}\\=\frac{280-48+105}{120}\\=\frac{337}{120}\)
3. \(-\left(\frac{10}{7}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-11}{7}\right)\\= \frac{-10}{7}+ \frac{5}{4}+\frac{11}{7}\\=\frac{-40}{28}+\frac{35}{28}+\frac{44}{28}\\=\frac{-40+35+44}{28}\\=\frac{39}{28}\)
4. \(+\left(\frac{-4}{7}\right) -\left(\frac{-7}{2}\right) -\left(\frac{6}{-2}\right)\\= \frac{-4}{7}+ \frac{7}{2}+\frac{6}{2}\\=\frac{-4}{7}+\frac{7}{2}+\frac{3}{1}\\=\frac{-8}{14}+\frac{49}{14}+\frac{42}{14}\\=\frac{-8+49+42}{14}\\=\frac{83}{14}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{4}{-8}\right)\\= \frac{-6}{5}+ \frac{5}{8}+\frac{4}{8}\\=\frac{-6}{5}+\frac{5}{8}+\frac{1}{2}\\=\frac{-48}{40}+\frac{25}{40}+\frac{20}{40}\\=\frac{-48+25+20}{40}\\=\frac{-3}{40}\)
6. \(+\left(\frac{-2}{-5}\right) -\left(\frac{9}{-3}\right) +\left(\frac{11}{6}\right)\\= \frac{2}{5}+ \frac{9}{3}+\frac{11}{6}\\=\frac{2}{5}+\frac{3}{1}+\frac{11}{6}\\=\frac{12}{30}+\frac{90}{30}+\frac{55}{30}\\=\frac{12+90+55}{30}\\=\frac{157}{30}\)
7. \(+\left(\frac{10}{-3}\right) +\left(\frac{-7}{2}\right) -\left(\frac{-11}{10}\right)\\= \frac{-10}{3}- \frac{7}{2}+\frac{11}{10}\\=\frac{-100}{30}-\frac{105}{30}+\frac{33}{30}\\=\frac{-100-105+33}{30}\\=\frac{-172}{30}\\=\frac{-86}{15}\)
8. \(+\left(\frac{7}{9}\right) -\left(\frac{-10}{-3}\right) +\left(\frac{6}{3}\right)\\= \frac{7}{9}- \frac{10}{3}+\frac{6}{3}\\=\frac{7}{9}-\frac{10}{3}+\frac{2}{1}\\=\frac{7-10+2}{9}\\=\frac{-1}{9}\)
9. \(+\left(\frac{-5}{-4}\right) -\left(\frac{-8}{8}\right) -\left(\frac{12}{-5}\right)\\= \frac{5}{4}+ \frac{8}{8}+\frac{12}{5}\\=\frac{5}{4}+\frac{1}{1}+\frac{12}{5}\\=\frac{25}{20}+\frac{20}{20}+\frac{48}{20}\\=\frac{25+20+48}{20}\\=\frac{93}{20}\)
10. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{3}{-5}\right)\\= \frac{2}{3}+ \frac{9}{9}+\frac{3}{5}\\=\frac{2}{3}+\frac{1}{1}+\frac{3}{5}\\=\frac{10}{15}+\frac{15}{15}+\frac{9}{15}\\=\frac{10+15+9}{15}\\=\frac{34}{15}\)
11. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-5}{-4}\right) -\left(\frac{-9}{-8}\right)\\= \frac{5}{6}+ \frac{5}{4}-\frac{9}{8}\\=\frac{20}{24}+\frac{30}{24}-\frac{27}{24}\\=\frac{20+30-27}{24}\\=\frac{23}{24}\)
12. \(+\left(\frac{5}{2}\right) -\left(\frac{-5}{6}\right) -\left(\frac{9}{2}\right)\\= \frac{5}{2}+ \frac{5}{6}-\frac{9}{2}\\=\frac{15}{6}+\frac{5}{6}-\frac{27}{6}\\=\frac{15+5-27}{6}\\=\frac{-7}{6}\)