Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{3}\right) +\left(\frac{5}{7}\right) -\left(\frac{4}{9}\right)\\= \frac{-4}{3}+ \frac{5}{7}-\frac{4}{9}\\=\frac{-84}{63}+\frac{45}{63}-\frac{28}{63}\\=\frac{-84+45-28}{63}\\=\frac{-67}{63}\)
2. \(-\left(\frac{-10}{3}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{3}{-10}\right)\\= \frac{10}{3}+ \frac{3}{5}-\frac{3}{10}\\=\frac{100}{30}+\frac{18}{30}-\frac{9}{30}\\=\frac{100+18-9}{30}\\=\frac{109}{30}\)
3. \(-\left(\frac{2}{-9}\right) -\left(\frac{7}{9}\right) +\left(\frac{-6}{-11}\right)\\= \frac{2}{9}- \frac{7}{9}+\frac{6}{11}\\=\frac{22}{99}-\frac{77}{99}+\frac{54}{99}\\=\frac{22-77+54}{99}\\=\frac{-1}{99}\)
4. \(+\left(\frac{-6}{-5}\right) +\left(\frac{5}{-2}\right) +\left(\frac{-5}{5}\right)\\= \frac{6}{5}- \frac{5}{2}-\frac{5}{5}\\=\frac{6}{5}-\frac{5}{2}-\frac{1}{1}\\=\frac{12}{10}-\frac{25}{10}-\frac{10}{10}\\=\frac{12-25-10}{10}\\=\frac{-23}{10}\)
5. \(+\left(\frac{4}{9}\right) +\left(\frac{9}{6}\right) -\left(\frac{-10}{-10}\right)\\= \frac{4}{9}+ \frac{9}{6}-\frac{10}{10}\\=\frac{4}{9}+\frac{3}{2}-\frac{1}{1}\\=\frac{8}{18}+\frac{27}{18}-\frac{18}{18}\\=\frac{8+27-18}{18}\\=\frac{17}{18}\)
6. \(+\left(\frac{4}{7}\right) +\left(\frac{-6}{7}\right) +\left(\frac{-2}{-2}\right)\\= \frac{4}{7}- \frac{6}{7}+\frac{2}{2}\\=\frac{4}{7}-\frac{6}{7}+\frac{1}{1}\\=\frac{4-6+1}{7}\\=\frac{-1}{7}\)
7. \(-\left(\frac{3}{-2}\right) +\left(\frac{-2}{9}\right) -\left(\frac{-10}{-11}\right)\\= \frac{3}{2}- \frac{2}{9}-\frac{10}{11}\\=\frac{297}{198}-\frac{44}{198}-\frac{180}{198}\\=\frac{297-44-180}{198}\\=\frac{73}{198}\)
8. \(-\left(\frac{-8}{-7}\right) +\left(\frac{3}{-5}\right) +\left(\frac{-3}{5}\right)\\= \frac{-8}{7}- \frac{3}{5}-\frac{3}{5}\\=\frac{-40}{35}-\frac{21}{35}-\frac{21}{35}\\=\frac{-40-21-21}{35}\\=\frac{-82}{35}\)
9. \(+\left(\frac{-3}{-5}\right) +\left(\frac{7}{-6}\right) -\left(\frac{-10}{9}\right)\\= \frac{3}{5}- \frac{7}{6}+\frac{10}{9}\\=\frac{54}{90}-\frac{105}{90}+\frac{100}{90}\\=\frac{54-105+100}{90}\\=\frac{49}{90}\)
10. \(-\left(\frac{-8}{3}\right) +\left(\frac{-9}{4}\right) +\left(\frac{-9}{-10}\right)\\= \frac{8}{3}- \frac{9}{4}+\frac{9}{10}\\=\frac{160}{60}-\frac{135}{60}+\frac{54}{60}\\=\frac{160-135+54}{60}\\=\frac{79}{60}\)
11. \(-\left(\frac{-9}{7}\right) +\left(\frac{5}{2}\right) -\left(\frac{7}{-12}\right)\\= \frac{9}{7}+ \frac{5}{2}+\frac{7}{12}\\=\frac{108}{84}+\frac{210}{84}+\frac{49}{84}\\=\frac{108+210+49}{84}\\=\frac{367}{84}\)
12. \(+\left(\frac{-2}{3}\right) -\left(\frac{7}{4}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-2}{3}- \frac{7}{4}-\frac{5}{9}\\=\frac{-24}{36}-\frac{63}{36}-\frac{20}{36}\\=\frac{-24-63-20}{36}\\=\frac{-107}{36}\)