Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{-2}\right) -\left(\frac{-2}{4}\right) +\left(\frac{6}{7}\right)\\= \frac{-7}{2}+ \frac{2}{4}+\frac{6}{7}\\=\frac{-7}{2}+\frac{1}{2}+\frac{6}{7}\\=\frac{-49}{14}+\frac{7}{14}+\frac{12}{14}\\=\frac{-49+7+12}{14}\\=\frac{-30}{14}\\=\frac{-15}{7}\)
2. \(+\left(\frac{-8}{3}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-9}{-6}\right)\\= \frac{-8}{3}- \frac{7}{8}+\frac{9}{6}\\=\frac{-8}{3}-\frac{7}{8}+\frac{3}{2}\\=\frac{-64}{24}-\frac{21}{24}+\frac{36}{24}\\=\frac{-64-21+36}{24}\\=\frac{-49}{24}\)
3. \(+\left(\frac{4}{-7}\right) -\left(\frac{-8}{2}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-4}{7}+ \frac{8}{2}+\frac{8}{10}\\=\frac{-4}{7}+\frac{4}{1}+\frac{4}{5}\\=\frac{-20}{35}+\frac{140}{35}+\frac{28}{35}\\=\frac{-20+140+28}{35}\\=\frac{148}{35}\)
4. \(-\left(\frac{6}{5}\right) +\left(\frac{6}{8}\right) -\left(\frac{5}{3}\right)\\= \frac{-6}{5}+ \frac{6}{8}-\frac{5}{3}\\=\frac{-6}{5}+\frac{3}{4}-\frac{5}{3}\\=\frac{-72}{60}+\frac{45}{60}-\frac{100}{60}\\=\frac{-72+45-100}{60}\\=\frac{-127}{60}\)
5. \(-\left(\frac{-9}{-2}\right) +\left(\frac{6}{-6}\right) -\left(\frac{-7}{-5}\right)\\= \frac{-9}{2}- \frac{6}{6}-\frac{7}{5}\\=\frac{-9}{2}-\frac{1}{1}-\frac{7}{5}\\=\frac{-45}{10}-\frac{10}{10}-\frac{14}{10}\\=\frac{-45-10-14}{10}\\=\frac{-69}{10}\)
6. \(-\left(\frac{6}{5}\right) -\left(\frac{6}{-4}\right) +\left(\frac{5}{3}\right)\\= \frac{-6}{5}+ \frac{6}{4}+\frac{5}{3}\\=\frac{-6}{5}+\frac{3}{2}+\frac{5}{3}\\=\frac{-36}{30}+\frac{45}{30}+\frac{50}{30}\\=\frac{-36+45+50}{30}\\=\frac{59}{30}\)
7. \(-\left(\frac{-2}{3}\right) -\left(\frac{9}{7}\right) +\left(\frac{-9}{5}\right)\\= \frac{2}{3}- \frac{9}{7}-\frac{9}{5}\\=\frac{70}{105}-\frac{135}{105}-\frac{189}{105}\\=\frac{70-135-189}{105}\\=\frac{-254}{105}\)
8. \(-\left(\frac{10}{9}\right) -\left(\frac{-9}{3}\right) -\left(\frac{-11}{-11}\right)\\= \frac{-10}{9}+ \frac{9}{3}-\frac{11}{11}\\=\frac{-10}{9}+\frac{3}{1}-\frac{1}{1}\\=\frac{-10+3-1}{9}\\=\frac{-8}{9}\)
9. \(+\left(\frac{-8}{7}\right) +\left(\frac{7}{3}\right) -\left(\frac{-5}{8}\right)\\= \frac{-8}{7}+ \frac{7}{3}+\frac{5}{8}\\=\frac{-192}{168}+\frac{392}{168}+\frac{105}{168}\\=\frac{-192+392+105}{168}\\=\frac{305}{168}\)
10. \(-\left(\frac{8}{5}\right) -\left(\frac{8}{-7}\right) +\left(\frac{-3}{7}\right)\\= \frac{-8}{5}+ \frac{8}{7}-\frac{3}{7}\\=\frac{-56}{35}+\frac{40}{35}-\frac{15}{35}\\=\frac{-56+40-15}{35}\\=\frac{-31}{35}\)
11. \(+\left(\frac{8}{7}\right) -\left(\frac{8}{9}\right) +\left(\frac{-8}{-9}\right)\\= \frac{8}{7}- \frac{8}{9}+\frac{8}{9}\\=\frac{72}{63}-\frac{56}{63}+\frac{56}{63}\\=\frac{72-56+56}{63}\\=\frac{72}{63}\\=\frac{8}{7}\)
12. \(-\left(\frac{10}{-9}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{7}{-4}\right)\\= \frac{10}{9}- \frac{5}{2}-\frac{7}{4}\\=\frac{40}{36}-\frac{90}{36}-\frac{63}{36}\\=\frac{40-90-63}{36}\\=\frac{-113}{36}\)