Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{10}\right)-\left(\frac{10}{-13}\right)\\= \frac{-9}{10}+\frac{10}{13}\\=\frac{-117}{130}+\frac{100}{130}\\=\frac{-117+100}{130}\\=\frac{-17}{130}\)
2. \(+\left(\frac{-15}{4}\right)+\left(\frac{6}{-11}\right)\\= \frac{-15}{4}-\frac{6}{11}\\=\frac{-165}{44}-\frac{24}{44}\\=\frac{-165-24}{44}\\=\frac{-189}{44}\)
3. \(+\left(\frac{9}{10}\right)+\left(\frac{-10}{11}\right)\\= \frac{9}{10}-\frac{10}{11}\\=\frac{99}{110}-\frac{100}{110}\\=\frac{99-100}{110}\\=\frac{-1}{110}\)
4. \(+\left(\frac{11}{13}\right)-\left(\frac{-5}{-11}\right)\\= \frac{11}{13}-\frac{5}{11}\\=\frac{121}{143}-\frac{65}{143}\\=\frac{121-65}{143}\\=\frac{56}{143}\)
5. \(+\left(\frac{8}{-3}\right)-\left(\frac{-8}{-7}\right)\\= \frac{-8}{3}-\frac{8}{7}\\=\frac{-56}{21}-\frac{24}{21}\\=\frac{-56-24}{21}\\=\frac{-80}{21}\)
6. \(-\left(\frac{-5}{-11}\right)-\left(\frac{-11}{7}\right)\\= \frac{-5}{11}+\frac{11}{7}\\=\frac{-35}{77}+\frac{121}{77}\\=\frac{-35+121}{77}\\=\frac{86}{77}\)
7. \(-\left(\frac{-9}{4}\right)-\left(\frac{9}{7}\right)\\= \frac{9}{4}-\frac{9}{7}\\=\frac{63}{28}-\frac{36}{28}\\=\frac{63-36}{28}\\=\frac{27}{28}\)
8. \(-\left(\frac{11}{13}\right)-\left(\frac{-9}{-7}\right)\\= \frac{-11}{13}-\frac{9}{7}\\=\frac{-77}{91}-\frac{117}{91}\\=\frac{-77-117}{91}\\=\frac{-194}{91}\)
9. \(+\left(\frac{-7}{-11}\right)+\left(\frac{2}{-13}\right)\\= \frac{7}{11}-\frac{2}{13}\\=\frac{91}{143}-\frac{22}{143}\\=\frac{91-22}{143}\\=\frac{69}{143}\)
10. \(+\left(\frac{-5}{6}\right)-\left(\frac{-13}{-10}\right)\\= \frac{-5}{6}-\frac{13}{10}\\=\frac{-25}{30}-\frac{39}{30}\\=\frac{-25-39}{30}\\=\frac{-64}{30}\\=\frac{-32}{15}\)
11. \(+\left(\frac{13}{11}\right)+\left(\frac{-5}{-9}\right)\\= \frac{13}{11}+\frac{5}{9}\\=\frac{117}{99}+\frac{55}{99}\\=\frac{117+55}{99}\\=\frac{172}{99}\)
12. \(+\left(\frac{12}{11}\right)-\left(\frac{13}{-4}\right)\\= \frac{12}{11}+\frac{13}{4}\\=\frac{48}{44}+\frac{143}{44}\\=\frac{48+143}{44}\\=\frac{191}{44}\)