Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-13}\right)+\left(\frac{12}{5}\right)\\= \frac{3}{13}+\frac{12}{5}\\=\frac{15}{65}+\frac{156}{65}\\=\frac{15+156}{65}\\=\frac{171}{65}\)
2. \(-\left(\frac{-7}{2}\right)+\left(\frac{13}{14}\right)\\= \frac{7}{2}+\frac{13}{14}\\=\frac{49}{14}+\frac{13}{14}\\=\frac{49+13}{14}\\=\frac{62}{14}\\=\frac{31}{7}\)
3. \(+\left(\frac{3}{-10}\right)+\left(\frac{2}{11}\right)\\= \frac{-3}{10}+\frac{2}{11}\\=\frac{-33}{110}+\frac{20}{110}\\=\frac{-33+20}{110}\\=\frac{-13}{110}\)
4. \(+\left(\frac{-2}{-3}\right)-\left(\frac{10}{7}\right)\\= \frac{2}{3}-\frac{10}{7}\\=\frac{14}{21}-\frac{30}{21}\\=\frac{14-30}{21}\\=\frac{-16}{21}\)
5. \(+\left(\frac{4}{3}\right)-\left(\frac{13}{2}\right)\\= \frac{4}{3}-\frac{13}{2}\\=\frac{8}{6}-\frac{39}{6}\\=\frac{8-39}{6}\\=\frac{-31}{6}\)
6. \(-\left(\frac{-7}{-13}\right)-\left(\frac{4}{9}\right)\\= \frac{-7}{13}-\frac{4}{9}\\=\frac{-63}{117}-\frac{52}{117}\\=\frac{-63-52}{117}\\=\frac{-115}{117}\)
7. \(+\left(\frac{-4}{-9}\right)-\left(\frac{-13}{-10}\right)\\= \frac{4}{9}-\frac{13}{10}\\=\frac{40}{90}-\frac{117}{90}\\=\frac{40-117}{90}\\=\frac{-77}{90}\)
8. \(-\left(\frac{-13}{10}\right)-\left(\frac{10}{7}\right)\\= \frac{13}{10}-\frac{10}{7}\\=\frac{91}{70}-\frac{100}{70}\\=\frac{91-100}{70}\\=\frac{-9}{70}\)
9. \(+\left(\frac{13}{-4}\right)-\left(\frac{-3}{-13}\right)\\= \frac{-13}{4}-\frac{3}{13}\\=\frac{-169}{52}-\frac{12}{52}\\=\frac{-169-12}{52}\\=\frac{-181}{52}\)
10. \(+\left(\frac{12}{-11}\right)-\left(\frac{-9}{5}\right)\\= \frac{-12}{11}+\frac{9}{5}\\=\frac{-60}{55}+\frac{99}{55}\\=\frac{-60+99}{55}\\=\frac{39}{55}\)
11. \(+\left(\frac{8}{9}\right)-\left(\frac{15}{13}\right)\\= \frac{8}{9}-\frac{15}{13}\\=\frac{104}{117}-\frac{135}{117}\\=\frac{104-135}{117}\\=\frac{-31}{117}\)
12. \(+\left(\frac{-8}{7}\right)-\left(\frac{4}{11}\right)\\= \frac{-8}{7}-\frac{4}{11}\\=\frac{-88}{77}-\frac{28}{77}\\=\frac{-88-28}{77}\\=\frac{-116}{77}\)