Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{11}\right)-\left(\frac{-6}{7}\right)\\= \frac{6}{11}+\frac{6}{7}\\=\frac{42}{77}+\frac{66}{77}\\=\frac{42+66}{77}\\=\frac{108}{77}\)
2. \(+\left(\frac{10}{7}\right)-\left(\frac{-13}{14}\right)\\= \frac{10}{7}+\frac{13}{14}\\=\frac{20}{14}+\frac{13}{14}\\=\frac{20+13}{14}\\=\frac{33}{14}\)
3. \(+\left(\frac{7}{-3}\right)-\left(\frac{4}{5}\right)\\= \frac{-7}{3}-\frac{4}{5}\\=\frac{-35}{15}-\frac{12}{15}\\=\frac{-35-12}{15}\\=\frac{-47}{15}\)
4. \(+\left(\frac{6}{5}\right)-\left(\frac{12}{5}\right)\\= \frac{6}{5}-\frac{12}{5}\\=\frac{6-12}{5}\\=\frac{-6}{5}\)
5. \(-\left(\frac{-9}{8}\right)+\left(\frac{13}{6}\right)\\= \frac{9}{8}+\frac{13}{6}\\=\frac{27}{24}+\frac{52}{24}\\=\frac{27+52}{24}\\=\frac{79}{24}\)
6. \(+\left(\frac{10}{-9}\right)+\left(\frac{-12}{7}\right)\\= \frac{-10}{9}-\frac{12}{7}\\=\frac{-70}{63}-\frac{108}{63}\\=\frac{-70-108}{63}\\=\frac{-178}{63}\)
7. \(-\left(\frac{-12}{13}\right)+\left(\frac{5}{6}\right)\\= \frac{12}{13}+\frac{5}{6}\\=\frac{72}{78}+\frac{65}{78}\\=\frac{72+65}{78}\\=\frac{137}{78}\)
8. \(+\left(\frac{-8}{-5}\right)-\left(\frac{6}{-5}\right)\\= \frac{8}{5}+\frac{6}{5}\\=\frac{8+6}{5}\\=\frac{14}{5}\)
9. \(+\left(\frac{9}{10}\right)-\left(\frac{15}{-7}\right)\\= \frac{9}{10}+\frac{15}{7}\\=\frac{63}{70}+\frac{150}{70}\\=\frac{63+150}{70}\\=\frac{213}{70}\)
10. \(+\left(\frac{-2}{-5}\right)+\left(\frac{-3}{-10}\right)\\= \frac{2}{5}+\frac{3}{10}\\=\frac{4}{10}+\frac{3}{10}\\=\frac{4+3}{10}\\=\frac{7}{10}\)
11. \(+\left(\frac{-12}{-7}\right)-\left(\frac{-5}{6}\right)\\= \frac{12}{7}+\frac{5}{6}\\=\frac{72}{42}+\frac{35}{42}\\=\frac{72+35}{42}\\=\frac{107}{42}\)
12. \(-\left(\frac{-2}{7}\right)+\left(\frac{-10}{-3}\right)\\= \frac{2}{7}+\frac{10}{3}\\=\frac{6}{21}+\frac{70}{21}\\=\frac{6+70}{21}\\=\frac{76}{21}\)