Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-9}\right)+\left(\frac{-13}{-3}\right)\\= \frac{5}{9}+\frac{13}{3}\\=\frac{5+13}{9}\\=\frac{18}{9}\\=\frac{2}{1}\)
2. \(+\left(\frac{-11}{6}\right)-\left(\frac{7}{2}\right)\\= \frac{-11}{6}-\frac{7}{2}\\=\frac{-11-7}{6}\\=\frac{-18}{6}\\=\frac{-3}{1}\)
3. \(+\left(\frac{-7}{10}\right)-\left(\frac{-10}{7}\right)\\= \frac{-7}{10}+\frac{10}{7}\\=\frac{-49}{70}+\frac{100}{70}\\=\frac{-49+100}{70}\\=\frac{51}{70}\)
4. \(+\left(\frac{5}{-3}\right)+\left(\frac{14}{3}\right)\\= \frac{-5}{3}+\frac{14}{3}\\=\frac{-5+14}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
5. \(+\left(\frac{4}{13}\right)+\left(\frac{-4}{13}\right)\\= \frac{4}{13}-\frac{4}{13}\\=\frac{4-4}{13}\\=\frac{0}{13}\\=\frac{0}{1}\)
6. \(-\left(\frac{3}{-7}\right)-\left(\frac{9}{2}\right)\\= \frac{3}{7}-\frac{9}{2}\\=\frac{6}{14}-\frac{63}{14}\\=\frac{6-63}{14}\\=\frac{-57}{14}\)
7. \(+\left(\frac{3}{10}\right)-\left(\frac{12}{11}\right)\\= \frac{3}{10}-\frac{12}{11}\\=\frac{33}{110}-\frac{120}{110}\\=\frac{33-120}{110}\\=\frac{-87}{110}\)
8. \(+\left(\frac{15}{4}\right)-\left(\frac{10}{3}\right)\\= \frac{15}{4}-\frac{10}{3}\\=\frac{45}{12}-\frac{40}{12}\\=\frac{45-40}{12}\\=\frac{5}{12}\)
9. \(-\left(\frac{-11}{12}\right)-\left(\frac{-2}{-7}\right)\\= \frac{11}{12}-\frac{2}{7}\\=\frac{77}{84}-\frac{24}{84}\\=\frac{77-24}{84}\\=\frac{53}{84}\)
10. \(+\left(\frac{6}{-7}\right)+\left(\frac{12}{11}\right)\\= \frac{-6}{7}+\frac{12}{11}\\=\frac{-66}{77}+\frac{84}{77}\\=\frac{-66+84}{77}\\=\frac{18}{77}\)
11. \(+\left(\frac{5}{-13}\right)-\left(\frac{8}{-9}\right)\\= \frac{-5}{13}+\frac{8}{9}\\=\frac{-45}{117}+\frac{104}{117}\\=\frac{-45+104}{117}\\=\frac{59}{117}\)
12. \(+\left(\frac{8}{-3}\right)-\left(\frac{-13}{-4}\right)\\= \frac{-8}{3}-\frac{13}{4}\\=\frac{-32}{12}-\frac{39}{12}\\=\frac{-32-39}{12}\\=\frac{-71}{12}\)