Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-8}\right) +\left(\frac{8}{-4}\right) -\left(\frac{9}{-7}\right)\\= \frac{9}{8}- \frac{8}{4}+\frac{9}{7}\\=\frac{9}{8}-\frac{2}{1}+\frac{9}{7}\\=\frac{63}{56}-\frac{112}{56}+\frac{72}{56}\\=\frac{63-112+72}{56}\\=\frac{23}{56}\)
2. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{5}\right) -\left(\frac{8}{-5}\right)\\= \frac{6}{5}- \frac{4}{5}+\frac{8}{5}\\=\frac{6-4+8}{5}\\=\frac{10}{5}\\=\frac{2}{1}\)
3. \(+\left(\frac{-6}{5}\right) +\left(\frac{4}{-8}\right) -\left(\frac{3}{-8}\right)\\= \frac{-6}{5}- \frac{4}{8}+\frac{3}{8}\\=\frac{-6}{5}-\frac{1}{2}+\frac{3}{8}\\=\frac{-48}{40}-\frac{20}{40}+\frac{15}{40}\\=\frac{-48-20+15}{40}\\=\frac{-53}{40}\)
4. \(-\left(\frac{-7}{8}\right) -\left(\frac{-6}{7}\right) +\left(\frac{9}{7}\right)\\= \frac{7}{8}+ \frac{6}{7}+\frac{9}{7}\\=\frac{49}{56}+\frac{48}{56}+\frac{72}{56}\\=\frac{49+48+72}{56}\\=\frac{169}{56}\)
5. \(-\left(\frac{-8}{9}\right) -\left(\frac{-9}{5}\right) +\left(\frac{2}{-8}\right)\\= \frac{8}{9}+ \frac{9}{5}-\frac{2}{8}\\=\frac{8}{9}+\frac{9}{5}-\frac{1}{4}\\=\frac{160}{180}+\frac{324}{180}-\frac{45}{180}\\=\frac{160+324-45}{180}\\=\frac{439}{180}\)
6. \(-\left(\frac{-10}{7}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{-3}{11}\right)\\= \frac{10}{7}+ \frac{2}{2}-\frac{3}{11}\\=\frac{10}{7}+\frac{1}{1}-\frac{3}{11}\\=\frac{110}{77}+\frac{77}{77}-\frac{21}{77}\\=\frac{110+77-21}{77}\\=\frac{166}{77}\)
7. \(+\left(\frac{-4}{-9}\right) +\left(\frac{2}{10}\right) -\left(\frac{-2}{11}\right)\\= \frac{4}{9}+ \frac{2}{10}+\frac{2}{11}\\=\frac{4}{9}+\frac{1}{5}+\frac{2}{11}\\=\frac{220}{495}+\frac{99}{495}+\frac{90}{495}\\=\frac{220+99+90}{495}\\=\frac{409}{495}\)
8. \(-\left(\frac{-8}{7}\right) -\left(\frac{5}{-2}\right) -\left(\frac{3}{5}\right)\\= \frac{8}{7}+ \frac{5}{2}-\frac{3}{5}\\=\frac{80}{70}+\frac{175}{70}-\frac{42}{70}\\=\frac{80+175-42}{70}\\=\frac{213}{70}\)
9. \(+\left(\frac{5}{7}\right) -\left(\frac{-10}{10}\right) -\left(\frac{-8}{5}\right)\\= \frac{5}{7}+ \frac{10}{10}+\frac{8}{5}\\=\frac{5}{7}+\frac{1}{1}+\frac{8}{5}\\=\frac{25}{35}+\frac{35}{35}+\frac{56}{35}\\=\frac{25+35+56}{35}\\=\frac{116}{35}\)
10. \(-\left(\frac{8}{-9}\right) -\left(\frac{-2}{7}\right) -\left(\frac{-2}{8}\right)\\= \frac{8}{9}+ \frac{2}{7}+\frac{2}{8}\\=\frac{8}{9}+\frac{2}{7}+\frac{1}{4}\\=\frac{224}{252}+\frac{72}{252}+\frac{63}{252}\\=\frac{224+72+63}{252}\\=\frac{359}{252}\)
11. \(+\left(\frac{-9}{2}\right) +\left(\frac{9}{10}\right) +\left(\frac{-5}{-6}\right)\\= \frac{-9}{2}+ \frac{9}{10}+\frac{5}{6}\\=\frac{-135}{30}+\frac{27}{30}+\frac{25}{30}\\=\frac{-135+27+25}{30}\\=\frac{-83}{30}\)
12. \(+\left(\frac{-5}{-7}\right) +\left(\frac{-4}{8}\right) -\left(\frac{9}{-12}\right)\\= \frac{5}{7}- \frac{4}{8}+\frac{9}{12}\\=\frac{5}{7}-\frac{1}{2}+\frac{3}{4}\\=\frac{20}{28}-\frac{14}{28}+\frac{21}{28}\\=\frac{20-14+21}{28}\\=\frac{27}{28}\)