Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{7}\right) -\left(\frac{2}{9}\right) +\left(\frac{4}{3}\right)\\= \frac{-4}{7}- \frac{2}{9}+\frac{4}{3}\\=\frac{-36}{63}-\frac{14}{63}+\frac{84}{63}\\=\frac{-36-14+84}{63}\\=\frac{34}{63}\)
2. \(-\left(\frac{5}{-4}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{10}{-2}\right)\\= \frac{5}{4}+ \frac{6}{10}-\frac{10}{2}\\=\frac{5}{4}+\frac{3}{5}-\frac{5}{1}\\=\frac{25}{20}+\frac{12}{20}-\frac{100}{20}\\=\frac{25+12-100}{20}\\=\frac{-63}{20}\)
3. \(+\left(\frac{10}{-7}\right) +\left(\frac{7}{-6}\right) +\left(\frac{5}{-6}\right)\\= \frac{-10}{7}- \frac{7}{6}-\frac{5}{6}\\=\frac{-60}{42}-\frac{49}{42}-\frac{35}{42}\\=\frac{-60-49-35}{42}\\=\frac{-144}{42}\\=\frac{-24}{7}\)
4. \(+\left(\frac{-10}{7}\right) +\left(\frac{2}{7}\right) +\left(\frac{-10}{3}\right)\\= \frac{-10}{7}+ \frac{2}{7}-\frac{10}{3}\\=\frac{-30}{21}+\frac{6}{21}-\frac{70}{21}\\=\frac{-30+6-70}{21}\\=\frac{-94}{21}\)
5. \(-\left(\frac{9}{-8}\right) +\left(\frac{3}{9}\right) -\left(\frac{-12}{-9}\right)\\= \frac{9}{8}+ \frac{3}{9}-\frac{12}{9}\\=\frac{9}{8}+\frac{1}{3}-\frac{4}{3}\\=\frac{27}{24}+\frac{8}{24}-\frac{32}{24}\\=\frac{27+8-32}{24}\\=\frac{3}{24}\\=\frac{1}{8}\)
6. \(-\left(\frac{8}{3}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{11}{-3}\right)\\= \frac{-8}{3}+ \frac{5}{9}+\frac{11}{3}\\=\frac{-24}{9}+\frac{5}{9}+\frac{33}{9}\\=\frac{-24+5+33}{9}\\=\frac{14}{9}\)
7. \(-\left(\frac{7}{4}\right) -\left(\frac{-5}{8}\right) +\left(\frac{7}{11}\right)\\= \frac{-7}{4}+ \frac{5}{8}+\frac{7}{11}\\=\frac{-154}{88}+\frac{55}{88}+\frac{56}{88}\\=\frac{-154+55+56}{88}\\=\frac{-43}{88}\)
8. \(-\left(\frac{3}{-7}\right) -\left(\frac{3}{-6}\right) -\left(\frac{5}{12}\right)\\= \frac{3}{7}+ \frac{3}{6}-\frac{5}{12}\\=\frac{3}{7}+\frac{1}{2}-\frac{5}{12}\\=\frac{36}{84}+\frac{42}{84}-\frac{35}{84}\\=\frac{36+42-35}{84}\\=\frac{43}{84}\)
9. \(+\left(\frac{-4}{-3}\right) -\left(\frac{5}{-9}\right) +\left(\frac{-7}{-7}\right)\\= \frac{4}{3}+ \frac{5}{9}+\frac{7}{7}\\=\frac{4}{3}+\frac{5}{9}+\frac{1}{1}\\=\frac{12}{9}+\frac{5}{9}+\frac{9}{9}\\=\frac{12+5+9}{9}\\=\frac{26}{9}\)
10. \(+\left(\frac{3}{-7}\right) +\left(\frac{3}{10}\right) +\left(\frac{5}{8}\right)\\= \frac{-3}{7}+ \frac{3}{10}+\frac{5}{8}\\=\frac{-120}{280}+\frac{84}{280}+\frac{175}{280}\\=\frac{-120+84+175}{280}\\=\frac{139}{280}\)
11. \(+\left(\frac{3}{4}\right) -\left(\frac{-8}{-10}\right) -\left(\frac{-7}{-5}\right)\\= \frac{3}{4}- \frac{8}{10}-\frac{7}{5}\\=\frac{3}{4}-\frac{4}{5}-\frac{7}{5}\\=\frac{15}{20}-\frac{16}{20}-\frac{28}{20}\\=\frac{15-16-28}{20}\\=\frac{-29}{20}\)
12. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-5}{7}\right) -\left(\frac{5}{-4}\right)\\= \frac{-7}{2}- \frac{5}{7}+\frac{5}{4}\\=\frac{-98}{28}-\frac{20}{28}+\frac{35}{28}\\=\frac{-98-20+35}{28}\\=\frac{-83}{28}\)