Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-2}\right)+\left(\frac{3}{10}\right)\\= \frac{5}{2}+\frac{3}{10}\\=\frac{25}{10}+\frac{3}{10}\\=\frac{25+3}{10}\\=\frac{28}{10}\\=\frac{14}{5}\)
2. \(+\left(\frac{-2}{9}\right)+\left(\frac{14}{9}\right)\\= \frac{-2}{9}+\frac{14}{9}\\=\frac{-2+14}{9}\\=\frac{12}{9}\\=\frac{4}{3}\)
3. \(-\left(\frac{-9}{10}\right)-\left(\frac{-12}{-13}\right)\\= \frac{9}{10}-\frac{12}{13}\\=\frac{117}{130}-\frac{120}{130}\\=\frac{117-120}{130}\\=\frac{-3}{130}\)
4. \(+\left(\frac{-15}{-14}\right)+\left(\frac{-4}{-3}\right)\\= \frac{15}{14}+\frac{4}{3}\\=\frac{45}{42}+\frac{56}{42}\\=\frac{45+56}{42}\\=\frac{101}{42}\)
5. \(+\left(\frac{4}{-7}\right)+\left(\frac{-12}{-7}\right)\\= \frac{-4}{7}+\frac{12}{7}\\=\frac{-4+12}{7}\\=\frac{8}{7}\)
6. \(-\left(\frac{-5}{7}\right)-\left(\frac{5}{-11}\right)\\= \frac{5}{7}+\frac{5}{11}\\=\frac{55}{77}+\frac{35}{77}\\=\frac{55+35}{77}\\=\frac{90}{77}\)
7. \(+\left(\frac{-14}{-11}\right)+\left(\frac{-4}{13}\right)\\= \frac{14}{11}-\frac{4}{13}\\=\frac{182}{143}-\frac{44}{143}\\=\frac{182-44}{143}\\=\frac{138}{143}\)
8. \(+\left(\frac{4}{3}\right)+\left(\frac{-5}{3}\right)\\= \frac{4}{3}-\frac{5}{3}\\=\frac{4-5}{3}\\=\frac{-1}{3}\)
9. \(-\left(\frac{-14}{-9}\right)-\left(\frac{7}{10}\right)\\= \frac{-14}{9}-\frac{7}{10}\\=\frac{-140}{90}-\frac{63}{90}\\=\frac{-140-63}{90}\\=\frac{-203}{90}\)
10. \(+\left(\frac{-10}{-3}\right)+\left(\frac{15}{-4}\right)\\= \frac{10}{3}-\frac{15}{4}\\=\frac{40}{12}-\frac{45}{12}\\=\frac{40-45}{12}\\=\frac{-5}{12}\)
11. \(-\left(\frac{15}{-7}\right)-\left(\frac{-13}{11}\right)\\= \frac{15}{7}+\frac{13}{11}\\=\frac{165}{77}+\frac{91}{77}\\=\frac{165+91}{77}\\=\frac{256}{77}\)
12. \(-\left(\frac{12}{5}\right)-\left(\frac{14}{5}\right)\\= \frac{-12}{5}-\frac{14}{5}\\=\frac{-12-14}{5}\\=\frac{-26}{5}\)