Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{9}\right)-\left(\frac{-15}{11}\right)\\= \frac{-4}{9}+\frac{15}{11}\\=\frac{-44}{99}+\frac{135}{99}\\=\frac{-44+135}{99}\\=\frac{91}{99}\)
2. \(+\left(\frac{12}{-11}\right)-\left(\frac{-9}{-10}\right)\\= \frac{-12}{11}-\frac{9}{10}\\=\frac{-120}{110}-\frac{99}{110}\\=\frac{-120-99}{110}\\=\frac{-219}{110}\)
3. \(-\left(\frac{-13}{9}\right)-\left(\frac{-4}{-13}\right)\\= \frac{13}{9}-\frac{4}{13}\\=\frac{169}{117}-\frac{36}{117}\\=\frac{169-36}{117}\\=\frac{133}{117}\)
4. \(-\left(\frac{-10}{7}\right)+\left(\frac{4}{7}\right)\\= \frac{10}{7}+\frac{4}{7}\\=\frac{10+4}{7}\\=\frac{14}{7}\\=\frac{2}{1}\)
5. \(-\left(\frac{-12}{-5}\right)-\left(\frac{-14}{-9}\right)\\= \frac{-12}{5}-\frac{14}{9}\\=\frac{-108}{45}-\frac{70}{45}\\=\frac{-108-70}{45}\\=\frac{-178}{45}\)
6. \(-\left(\frac{15}{-7}\right)-\left(\frac{-6}{-5}\right)\\= \frac{15}{7}-\frac{6}{5}\\=\frac{75}{35}-\frac{42}{35}\\=\frac{75-42}{35}\\=\frac{33}{35}\)
7. \(+\left(\frac{-3}{2}\right)-\left(\frac{10}{-11}\right)\\= \frac{-3}{2}+\frac{10}{11}\\=\frac{-33}{22}+\frac{20}{22}\\=\frac{-33+20}{22}\\=\frac{-13}{22}\)
8. \(+\left(\frac{-15}{2}\right)-\left(\frac{4}{-13}\right)\\= \frac{-15}{2}+\frac{4}{13}\\=\frac{-195}{26}+\frac{8}{26}\\=\frac{-195+8}{26}\\=\frac{-187}{26}\)
9. \(-\left(\frac{10}{3}\right)-\left(\frac{-7}{10}\right)\\= \frac{-10}{3}+\frac{7}{10}\\=\frac{-100}{30}+\frac{21}{30}\\=\frac{-100+21}{30}\\=\frac{-79}{30}\)
10. \(-\left(\frac{-13}{8}\right)+\left(\frac{14}{9}\right)\\= \frac{13}{8}+\frac{14}{9}\\=\frac{117}{72}+\frac{112}{72}\\=\frac{117+112}{72}\\=\frac{229}{72}\)
11. \(-\left(\frac{12}{5}\right)-\left(\frac{-10}{-3}\right)\\= \frac{-12}{5}-\frac{10}{3}\\=\frac{-36}{15}-\frac{50}{15}\\=\frac{-36-50}{15}\\=\frac{-86}{15}\)
12. \(-\left(\frac{11}{7}\right)-\left(\frac{-10}{3}\right)\\= \frac{-11}{7}+\frac{10}{3}\\=\frac{-33}{21}+\frac{70}{21}\\=\frac{-33+70}{21}\\=\frac{37}{21}\)