Breuken haakjesregel (reeks 1)

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Bereken

1. \(+\left(\frac{-7}{-13}\right)+\left(\frac{-14}{-9}\right)\)
2. \(+\left(\frac{10}{-7}\right)+\left(\frac{-15}{13}\right)\)
3. \(+\left(\frac{8}{-7}\right)-\left(\frac{9}{-10}\right)\)
4. \(-\left(\frac{-14}{-9}\right)-\left(\frac{11}{-13}\right)\)
5. \(-\left(\frac{-4}{-3}\right)-\left(\frac{14}{-3}\right)\)
6. \(+\left(\frac{2}{3}\right)-\left(\frac{-6}{-5}\right)\)
7. \(-\left(\frac{-12}{11}\right)+\left(\frac{-13}{9}\right)\)
8. \(+\left(\frac{3}{5}\right)-\left(\frac{-11}{-14}\right)\)
9. \(-\left(\frac{2}{-3}\right)-\left(\frac{10}{-3}\right)\)
10. \(-\left(\frac{-2}{9}\right)-\left(\frac{-10}{-11}\right)\)
11. \(-\left(\frac{-15}{-4}\right)+\left(\frac{5}{-7}\right)\)
12. \(+\left(\frac{7}{4}\right)-\left(\frac{-13}{-8}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-13}\right)+\left(\frac{-14}{-9}\right)\\= \frac{7}{13}+\frac{14}{9}\\=\frac{63}{117}+\frac{182}{117}\\=\frac{63+182}{117}\\=\frac{245}{117}\)
2. \(+\left(\frac{10}{-7}\right)+\left(\frac{-15}{13}\right)\\= \frac{-10}{7}-\frac{15}{13}\\=\frac{-130}{91}-\frac{105}{91}\\=\frac{-130-105}{91}\\=\frac{-235}{91}\)
3. \(+\left(\frac{8}{-7}\right)-\left(\frac{9}{-10}\right)\\= \frac{-8}{7}+\frac{9}{10}\\=\frac{-80}{70}+\frac{63}{70}\\=\frac{-80+63}{70}\\=\frac{-17}{70}\)
4. \(-\left(\frac{-14}{-9}\right)-\left(\frac{11}{-13}\right)\\= \frac{-14}{9}+\frac{11}{13}\\=\frac{-182}{117}+\frac{99}{117}\\=\frac{-182+99}{117}\\=\frac{-83}{117}\)
5. \(-\left(\frac{-4}{-3}\right)-\left(\frac{14}{-3}\right)\\= \frac{-4}{3}+\frac{14}{3}\\=\frac{-4+14}{3}\\=\frac{10}{3}\)
6. \(+\left(\frac{2}{3}\right)-\left(\frac{-6}{-5}\right)\\= \frac{2}{3}-\frac{6}{5}\\=\frac{10}{15}-\frac{18}{15}\\=\frac{10-18}{15}\\=\frac{-8}{15}\)
7. \(-\left(\frac{-12}{11}\right)+\left(\frac{-13}{9}\right)\\= \frac{12}{11}-\frac{13}{9}\\=\frac{108}{99}-\frac{143}{99}\\=\frac{108-143}{99}\\=\frac{-35}{99}\)
8. \(+\left(\frac{3}{5}\right)-\left(\frac{-11}{-14}\right)\\= \frac{3}{5}-\frac{11}{14}\\=\frac{42}{70}-\frac{55}{70}\\=\frac{42-55}{70}\\=\frac{-13}{70}\)
9. \(-\left(\frac{2}{-3}\right)-\left(\frac{10}{-3}\right)\\= \frac{2}{3}+\frac{10}{3}\\=\frac{2+10}{3}\\=\frac{12}{3}\\=\frac{4}{1}\)
10. \(-\left(\frac{-2}{9}\right)-\left(\frac{-10}{-11}\right)\\= \frac{2}{9}-\frac{10}{11}\\=\frac{22}{99}-\frac{90}{99}\\=\frac{22-90}{99}\\=\frac{-68}{99}\)
11. \(-\left(\frac{-15}{-4}\right)+\left(\frac{5}{-7}\right)\\= \frac{-15}{4}-\frac{5}{7}\\=\frac{-105}{28}-\frac{20}{28}\\=\frac{-105-20}{28}\\=\frac{-125}{28}\)
12. \(+\left(\frac{7}{4}\right)-\left(\frac{-13}{-8}\right)\\= \frac{7}{4}-\frac{13}{8}\\=\frac{14}{8}-\frac{13}{8}\\=\frac{14-13}{8}\\=\frac{1}{8}\)