Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{2}\right) +\left(\frac{-7}{10}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-3}{2}- \frac{7}{10}-\frac{2}{5}\\=\frac{-15}{10}-\frac{7}{10}-\frac{4}{10}\\=\frac{-15-7-4}{10}\\=\frac{-26}{10}\\=\frac{-13}{5}\)
2. \(+\left(\frac{-5}{-2}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-10}{-6}\right)\\= \frac{5}{2}+ \frac{6}{3}-\frac{10}{6}\\=\frac{5}{2}+\frac{2}{1}-\frac{5}{3}\\=\frac{15}{6}+\frac{12}{6}-\frac{10}{6}\\=\frac{15+12-10}{6}\\=\frac{17}{6}\)
3. \(+\left(\frac{10}{-7}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{-12}{5}\right)\\= \frac{-10}{7}+ \frac{5}{10}-\frac{12}{5}\\=\frac{-10}{7}+\frac{1}{2}-\frac{12}{5}\\=\frac{-100}{70}+\frac{35}{70}-\frac{168}{70}\\=\frac{-100+35-168}{70}\\=\frac{-233}{70}\)
4. \(-\left(\frac{5}{8}\right) -\left(\frac{9}{-5}\right) +\left(\frac{-6}{10}\right)\\= \frac{-5}{8}+ \frac{9}{5}-\frac{6}{10}\\=\frac{-5}{8}+\frac{9}{5}-\frac{3}{5}\\=\frac{-25}{40}+\frac{72}{40}-\frac{24}{40}\\=\frac{-25+72-24}{40}\\=\frac{23}{40}\)
5. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-8}{-3}\right) -\left(\frac{2}{5}\right)\\= \frac{6}{5}+ \frac{8}{3}-\frac{2}{5}\\=\frac{18}{15}+\frac{40}{15}-\frac{6}{15}\\=\frac{18+40-6}{15}\\=\frac{52}{15}\)
6. \(-\left(\frac{-3}{-7}\right) -\left(\frac{7}{-8}\right) -\left(\frac{5}{12}\right)\\= \frac{-3}{7}+ \frac{7}{8}-\frac{5}{12}\\=\frac{-72}{168}+\frac{147}{168}-\frac{70}{168}\\=\frac{-72+147-70}{168}\\=\frac{5}{168}\)
7. \(-\left(\frac{-10}{3}\right) +\left(\frac{9}{-5}\right) -\left(\frac{9}{-11}\right)\\= \frac{10}{3}- \frac{9}{5}+\frac{9}{11}\\=\frac{550}{165}-\frac{297}{165}+\frac{135}{165}\\=\frac{550-297+135}{165}\\=\frac{388}{165}\)
8. \(+\left(\frac{10}{-7}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-10}{-2}\right)\\= \frac{-10}{7}- \frac{4}{6}+\frac{10}{2}\\=\frac{-10}{7}-\frac{2}{3}+\frac{5}{1}\\=\frac{-30}{21}-\frac{14}{21}+\frac{105}{21}\\=\frac{-30-14+105}{21}\\=\frac{61}{21}\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{-6}{4}\right) -\left(\frac{10}{4}\right)\\= \frac{-10}{7}- \frac{6}{4}-\frac{10}{4}\\=\frac{-10}{7}-\frac{3}{2}-\frac{5}{2}\\=\frac{-20}{14}-\frac{21}{14}-\frac{35}{14}\\=\frac{-20-21-35}{14}\\=\frac{-76}{14}\\=\frac{-38}{7}\)
10. \(+\left(\frac{2}{9}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{2}{11}\right)\\= \frac{2}{9}+ \frac{8}{8}-\frac{2}{11}\\=\frac{2}{9}+\frac{1}{1}-\frac{2}{11}\\=\frac{22}{99}+\frac{99}{99}-\frac{18}{99}\\=\frac{22+99-18}{99}\\=\frac{103}{99}\)
11. \(-\left(\frac{7}{-4}\right) +\left(\frac{6}{6}\right) -\left(\frac{-10}{7}\right)\\= \frac{7}{4}+ \frac{6}{6}+\frac{10}{7}\\=\frac{7}{4}+\frac{1}{1}+\frac{10}{7}\\=\frac{49}{28}+\frac{28}{28}+\frac{40}{28}\\=\frac{49+28+40}{28}\\=\frac{117}{28}\)
12. \(+\left(\frac{-7}{-8}\right) +\left(\frac{-9}{-7}\right) -\left(\frac{-12}{-6}\right)\\= \frac{7}{8}+ \frac{9}{7}-\frac{12}{6}\\=\frac{7}{8}+\frac{9}{7}-\frac{2}{1}\\=\frac{49}{56}+\frac{72}{56}-\frac{112}{56}\\=\frac{49+72-112}{56}\\=\frac{9}{56}\)