Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-5}\right)-\left(\frac{10}{-7}\right)\\= \frac{9}{5}+\frac{10}{7}\\=\frac{63}{35}+\frac{50}{35}\\=\frac{63+50}{35}\\=\frac{113}{35}\)
2. \(-\left(\frac{15}{-2}\right)-\left(\frac{6}{5}\right)\\= \frac{15}{2}-\frac{6}{5}\\=\frac{75}{10}-\frac{12}{10}\\=\frac{75-12}{10}\\=\frac{63}{10}\)
3. \(+\left(\frac{-9}{-7}\right)+\left(\frac{9}{-2}\right)\\= \frac{9}{7}-\frac{9}{2}\\=\frac{18}{14}-\frac{63}{14}\\=\frac{18-63}{14}\\=\frac{-45}{14}\)
4. \(-\left(\frac{-14}{-13}\right)+\left(\frac{13}{3}\right)\\= \frac{-14}{13}+\frac{13}{3}\\=\frac{-42}{39}+\frac{169}{39}\\=\frac{-42+169}{39}\\=\frac{127}{39}\)
5. \(+\left(\frac{-12}{11}\right)-\left(\frac{10}{-11}\right)\\= \frac{-12}{11}+\frac{10}{11}\\=\frac{-12+10}{11}\\=\frac{-2}{11}\)
6. \(-\left(\frac{13}{-11}\right)+\left(\frac{14}{9}\right)\\= \frac{13}{11}+\frac{14}{9}\\=\frac{117}{99}+\frac{154}{99}\\=\frac{117+154}{99}\\=\frac{271}{99}\)
7. \(+\left(\frac{9}{-7}\right)+\left(\frac{2}{3}\right)\\= \frac{-9}{7}+\frac{2}{3}\\=\frac{-27}{21}+\frac{14}{21}\\=\frac{-27+14}{21}\\=\frac{-13}{21}\)
8. \(-\left(\frac{8}{-7}\right)-\left(\frac{-5}{-13}\right)\\= \frac{8}{7}-\frac{5}{13}\\=\frac{104}{91}-\frac{35}{91}\\=\frac{104-35}{91}\\=\frac{69}{91}\)
9. \(-\left(\frac{15}{7}\right)-\left(\frac{5}{4}\right)\\= \frac{-15}{7}-\frac{5}{4}\\=\frac{-60}{28}-\frac{35}{28}\\=\frac{-60-35}{28}\\=\frac{-95}{28}\)
10. \(+\left(\frac{10}{3}\right)+\left(\frac{-13}{-9}\right)\\= \frac{10}{3}+\frac{13}{9}\\=\frac{30}{9}+\frac{13}{9}\\=\frac{30+13}{9}\\=\frac{43}{9}\)
11. \(-\left(\frac{7}{-13}\right)+\left(\frac{-12}{-11}\right)\\= \frac{7}{13}+\frac{12}{11}\\=\frac{77}{143}+\frac{156}{143}\\=\frac{77+156}{143}\\=\frac{233}{143}\)
12. \(+\left(\frac{-4}{3}\right)-\left(\frac{10}{-3}\right)\\= \frac{-4}{3}+\frac{10}{3}\\=\frac{-4+10}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)