Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-2}\right) +\left(\frac{10}{-3}\right) +\left(\frac{-7}{-5}\right)\\= \frac{-9}{2}- \frac{10}{3}+\frac{7}{5}\\=\frac{-135}{30}-\frac{100}{30}+\frac{42}{30}\\=\frac{-135-100+42}{30}\\=\frac{-193}{30}\)
2. \(-\left(\frac{-6}{5}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-2}{7}\right)\\= \frac{6}{5}+ \frac{5}{4}-\frac{2}{7}\\=\frac{168}{140}+\frac{175}{140}-\frac{40}{140}\\=\frac{168+175-40}{140}\\=\frac{303}{140}\)
3. \(+\left(\frac{10}{-7}\right) -\left(\frac{-5}{-8}\right) +\left(\frac{4}{-11}\right)\\= \frac{-10}{7}- \frac{5}{8}-\frac{4}{11}\\=\frac{-880}{616}-\frac{385}{616}-\frac{224}{616}\\=\frac{-880-385-224}{616}\\=\frac{-1489}{616}\)
4. \(-\left(\frac{-10}{9}\right) +\left(\frac{8}{8}\right) +\left(\frac{-9}{-10}\right)\\= \frac{10}{9}+ \frac{8}{8}+\frac{9}{10}\\=\frac{10}{9}+\frac{1}{1}+\frac{9}{10}\\=\frac{100}{90}+\frac{90}{90}+\frac{81}{90}\\=\frac{100+90+81}{90}\\=\frac{271}{90}\)
5. \(+\left(\frac{8}{-5}\right) -\left(\frac{-4}{-7}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-8}{5}- \frac{4}{7}-\frac{5}{9}\\=\frac{-504}{315}-\frac{180}{315}-\frac{175}{315}\\=\frac{-504-180-175}{315}\\=\frac{-859}{315}\)
6. \(-\left(\frac{-5}{4}\right) +\left(\frac{10}{5}\right) -\left(\frac{4}{7}\right)\\= \frac{5}{4}+ \frac{10}{5}-\frac{4}{7}\\=\frac{5}{4}+\frac{2}{1}-\frac{4}{7}\\=\frac{35}{28}+\frac{56}{28}-\frac{16}{28}\\=\frac{35+56-16}{28}\\=\frac{75}{28}\)
7. \(-\left(\frac{-9}{4}\right) -\left(\frac{-7}{-10}\right) -\left(\frac{12}{5}\right)\\= \frac{9}{4}- \frac{7}{10}-\frac{12}{5}\\=\frac{45}{20}-\frac{14}{20}-\frac{48}{20}\\=\frac{45-14-48}{20}\\=\frac{-17}{20}\)
8. \(+\left(\frac{-6}{7}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{-11}{-10}\right)\\= \frac{-6}{7}- \frac{6}{10}+\frac{11}{10}\\=\frac{-6}{7}-\frac{3}{5}+\frac{11}{10}\\=\frac{-60}{70}-\frac{42}{70}+\frac{77}{70}\\=\frac{-60-42+77}{70}\\=\frac{-25}{70}\\=\frac{-5}{14}\)
9. \(-\left(\frac{-2}{5}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{3}{6}\right)\\= \frac{2}{5}+ \frac{10}{8}+\frac{3}{6}\\=\frac{2}{5}+\frac{5}{4}+\frac{1}{2}\\=\frac{8}{20}+\frac{25}{20}+\frac{10}{20}\\=\frac{8+25+10}{20}\\=\frac{43}{20}\)
10. \(+\left(\frac{3}{-5}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{8}{12}\right)\\= \frac{-3}{5}+ \frac{6}{6}-\frac{8}{12}\\=\frac{-3}{5}+\frac{1}{1}-\frac{2}{3}\\=\frac{-9}{15}+\frac{15}{15}-\frac{10}{15}\\=\frac{-9+15-10}{15}\\=\frac{-4}{15}\)
11. \(-\left(\frac{3}{5}\right) +\left(\frac{2}{-7}\right) +\left(\frac{8}{4}\right)\\= \frac{-3}{5}- \frac{2}{7}+\frac{8}{4}\\=\frac{-3}{5}-\frac{2}{7}+\frac{2}{1}\\=\frac{-21}{35}-\frac{10}{35}+\frac{70}{35}\\=\frac{-21-10+70}{35}\\=\frac{39}{35}\)
12. \(+\left(\frac{2}{-7}\right) -\left(\frac{-2}{4}\right) +\left(\frac{-8}{-5}\right)\\= \frac{-2}{7}+ \frac{2}{4}+\frac{8}{5}\\=\frac{-2}{7}+\frac{1}{2}+\frac{8}{5}\\=\frac{-20}{70}+\frac{35}{70}+\frac{112}{70}\\=\frac{-20+35+112}{70}\\=\frac{127}{70}\)