Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-15}{7}\right)+\left(\frac{13}{3}\right)\\= \frac{-15}{7}+\frac{13}{3}\\=\frac{-45}{21}+\frac{91}{21}\\=\frac{-45+91}{21}\\=\frac{46}{21}\)
2. \(-\left(\frac{-5}{3}\right)-\left(\frac{10}{-3}\right)\\= \frac{5}{3}+\frac{10}{3}\\=\frac{5+10}{3}\\=\frac{15}{3}\\=\frac{5}{1}\)
3. \(+\left(\frac{4}{9}\right)-\left(\frac{-7}{-8}\right)\\= \frac{4}{9}-\frac{7}{8}\\=\frac{32}{72}-\frac{63}{72}\\=\frac{32-63}{72}\\=\frac{-31}{72}\)
4. \(-\left(\frac{-13}{4}\right)-\left(\frac{-5}{14}\right)\\= \frac{13}{4}+\frac{5}{14}\\=\frac{91}{28}+\frac{10}{28}\\=\frac{91+10}{28}\\=\frac{101}{28}\)
5. \(-\left(\frac{-6}{-5}\right)-\left(\frac{-2}{-5}\right)\\= \frac{-6}{5}-\frac{2}{5}\\=\frac{-6-2}{5}\\=\frac{-8}{5}\)
6. \(+\left(\frac{-10}{-3}\right)+\left(\frac{-2}{-13}\right)\\= \frac{10}{3}+\frac{2}{13}\\=\frac{130}{39}+\frac{6}{39}\\=\frac{130+6}{39}\\=\frac{136}{39}\)
7. \(-\left(\frac{10}{-3}\right)-\left(\frac{15}{-2}\right)\\= \frac{10}{3}+\frac{15}{2}\\=\frac{20}{6}+\frac{45}{6}\\=\frac{20+45}{6}\\=\frac{65}{6}\)
8. \(+\left(\frac{-5}{8}\right)-\left(\frac{9}{2}\right)\\= \frac{-5}{8}-\frac{9}{2}\\=\frac{-5-9}{8}\\=\frac{-14}{8}\\=\frac{-7}{4}\)
9. \(-\left(\frac{-11}{-14}\right)+\left(\frac{-15}{-7}\right)\\= \frac{-11}{14}+\frac{15}{7}\\=\frac{-11+15}{14}\\=\frac{4}{14}\\=\frac{2}{7}\)
10. \(+\left(\frac{-3}{10}\right)+\left(\frac{-11}{-2}\right)\\= \frac{-3}{10}+\frac{11}{2}\\=\frac{-3+11}{10}\\=\frac{8}{10}\\=\frac{4}{5}\)
11. \(+\left(\frac{-14}{9}\right)-\left(\frac{-5}{3}\right)\\= \frac{-14}{9}+\frac{5}{3}\\=\frac{-14+5}{9}\\=\frac{-9}{9}\\=\frac{-1}{1}\)
12. \(+\left(\frac{-2}{7}\right)-\left(\frac{-15}{-4}\right)\\= \frac{-2}{7}-\frac{15}{4}\\=\frac{-8}{28}-\frac{105}{28}\\=\frac{-8-105}{28}\\=\frac{-113}{28}\)