Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{11}{10}\right)+\left(\frac{13}{11}\right)\\= \frac{11}{10}+\frac{13}{11}\\=\frac{121}{110}+\frac{130}{110}\\=\frac{121+130}{110}\\=\frac{251}{110}\)
2. \(-\left(\frac{-5}{12}\right)-\left(\frac{5}{2}\right)\\= \frac{5}{12}-\frac{5}{2}\\=\frac{5-5}{12}\\=\frac{0}{12}\\=\frac{0}{1}\)
3. \(+\left(\frac{4}{11}\right)+\left(\frac{7}{12}\right)\\= \frac{4}{11}+\frac{7}{12}\\=\frac{48}{132}+\frac{77}{132}\\=\frac{48+77}{132}\\=\frac{125}{132}\)
4. \(-\left(\frac{10}{7}\right)-\left(\frac{7}{4}\right)\\= \frac{-10}{7}-\frac{7}{4}\\=\frac{-40}{28}-\frac{49}{28}\\=\frac{-40-49}{28}\\=\frac{-89}{28}\)
5. \(-\left(\frac{7}{12}\right)-\left(\frac{-13}{-7}\right)\\= \frac{-7}{12}-\frac{13}{7}\\=\frac{-49}{84}-\frac{156}{84}\\=\frac{-49-156}{84}\\=\frac{-205}{84}\)
6. \(-\left(\frac{11}{4}\right)+\left(\frac{11}{10}\right)\\= \frac{-11}{4}+\frac{11}{10}\\=\frac{-55}{20}+\frac{22}{20}\\=\frac{-55+22}{20}\\=\frac{-33}{20}\)
7. \(+\left(\frac{15}{-4}\right)-\left(\frac{-5}{11}\right)\\= \frac{-15}{4}+\frac{5}{11}\\=\frac{-165}{44}+\frac{20}{44}\\=\frac{-165+20}{44}\\=\frac{-145}{44}\)
8. \(+\left(\frac{-4}{-3}\right)-\left(\frac{-11}{-5}\right)\\= \frac{4}{3}-\frac{11}{5}\\=\frac{20}{15}-\frac{33}{15}\\=\frac{20-33}{15}\\=\frac{-13}{15}\)
9. \(-\left(\frac{9}{-4}\right)-\left(\frac{7}{-9}\right)\\= \frac{9}{4}+\frac{7}{9}\\=\frac{81}{36}+\frac{28}{36}\\=\frac{81+28}{36}\\=\frac{109}{36}\)
10. \(+\left(\frac{-15}{7}\right)+\left(\frac{-3}{-8}\right)\\= \frac{-15}{7}+\frac{3}{8}\\=\frac{-120}{56}+\frac{21}{56}\\=\frac{-120+21}{56}\\=\frac{-99}{56}\)
11. \(-\left(\frac{2}{11}\right)-\left(\frac{-4}{-11}\right)\\= \frac{-2}{11}-\frac{4}{11}\\=\frac{-2-4}{11}\\=\frac{-6}{11}\)
12. \(+\left(\frac{3}{5}\right)+\left(\frac{-9}{4}\right)\\= \frac{3}{5}-\frac{9}{4}\\=\frac{12}{20}-\frac{45}{20}\\=\frac{12-45}{20}\\=\frac{-33}{20}\)