Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{7}\right)+\left(\frac{-7}{10}\right)\\= \frac{10}{7}-\frac{7}{10}\\=\frac{100}{70}-\frac{49}{70}\\=\frac{100-49}{70}\\=\frac{51}{70}\)
2. \(+\left(\frac{-11}{7}\right)-\left(\frac{13}{-10}\right)\\= \frac{-11}{7}+\frac{13}{10}\\=\frac{-110}{70}+\frac{91}{70}\\=\frac{-110+91}{70}\\=\frac{-19}{70}\)
3. \(+\left(\frac{15}{11}\right)-\left(\frac{4}{11}\right)\\= \frac{15}{11}-\frac{4}{11}\\=\frac{15-4}{11}\\=\frac{11}{11}\\=\frac{1}{1}\)
4. \(+\left(\frac{-5}{-7}\right)-\left(\frac{-9}{10}\right)\\= \frac{5}{7}+\frac{9}{10}\\=\frac{50}{70}+\frac{63}{70}\\=\frac{50+63}{70}\\=\frac{113}{70}\)
5. \(+\left(\frac{-11}{13}\right)+\left(\frac{-7}{-2}\right)\\= \frac{-11}{13}+\frac{7}{2}\\=\frac{-22}{26}+\frac{91}{26}\\=\frac{-22+91}{26}\\=\frac{69}{26}\)
6. \(+\left(\frac{5}{-2}\right)-\left(\frac{12}{5}\right)\\= \frac{-5}{2}-\frac{12}{5}\\=\frac{-25}{10}-\frac{24}{10}\\=\frac{-25-24}{10}\\=\frac{-49}{10}\)
7. \(-\left(\frac{5}{2}\right)-\left(\frac{7}{-6}\right)\\= \frac{-5}{2}+\frac{7}{6}\\=\frac{-15}{6}+\frac{7}{6}\\=\frac{-15+7}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
8. \(-\left(\frac{3}{-2}\right)+\left(\frac{-15}{2}\right)\\= \frac{3}{2}-\frac{15}{2}\\=\frac{3-15}{2}\\=\frac{-12}{2}\\=\frac{-6}{1}\)
9. \(+\left(\frac{4}{13}\right)-\left(\frac{12}{11}\right)\\= \frac{4}{13}-\frac{12}{11}\\=\frac{44}{143}-\frac{156}{143}\\=\frac{44-156}{143}\\=\frac{-112}{143}\)
10. \(+\left(\frac{5}{-7}\right)+\left(\frac{8}{3}\right)\\= \frac{-5}{7}+\frac{8}{3}\\=\frac{-15}{21}+\frac{56}{21}\\=\frac{-15+56}{21}\\=\frac{41}{21}\)
11. \(+\left(\frac{8}{-13}\right)+\left(\frac{8}{3}\right)\\= \frac{-8}{13}+\frac{8}{3}\\=\frac{-24}{39}+\frac{104}{39}\\=\frac{-24+104}{39}\\=\frac{80}{39}\)
12. \(+\left(\frac{7}{-9}\right)-\left(\frac{11}{14}\right)\\= \frac{-7}{9}-\frac{11}{14}\\=\frac{-98}{126}-\frac{99}{126}\\=\frac{-98-99}{126}\\=\frac{-197}{126}\)