Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{-5}\right) +\left(\frac{9}{7}\right) -\left(\frac{-4}{-8}\right)\\= \frac{4}{5}+ \frac{9}{7}-\frac{4}{8}\\=\frac{4}{5}+\frac{9}{7}-\frac{1}{2}\\=\frac{56}{70}+\frac{90}{70}-\frac{35}{70}\\=\frac{56+90-35}{70}\\=\frac{111}{70}\)
2. \(+\left(\frac{10}{7}\right) +\left(\frac{-3}{-7}\right) +\left(\frac{-3}{10}\right)\\= \frac{10}{7}+ \frac{3}{7}-\frac{3}{10}\\=\frac{100}{70}+\frac{30}{70}-\frac{21}{70}\\=\frac{100+30-21}{70}\\=\frac{109}{70}\)
3. \(+\left(\frac{7}{-2}\right) +\left(\frac{-8}{-4}\right) +\left(\frac{10}{-11}\right)\\= \frac{-7}{2}+ \frac{8}{4}-\frac{10}{11}\\=\frac{-7}{2}+\frac{2}{1}-\frac{10}{11}\\=\frac{-77}{22}+\frac{44}{22}-\frac{20}{22}\\=\frac{-77+44-20}{22}\\=\frac{-53}{22}\)
4. \(+\left(\frac{-6}{5}\right) +\left(\frac{-5}{-10}\right) -\left(\frac{-10}{2}\right)\\= \frac{-6}{5}+ \frac{5}{10}+\frac{10}{2}\\=\frac{-6}{5}+\frac{1}{2}+\frac{5}{1}\\=\frac{-12}{10}+\frac{5}{10}+\frac{50}{10}\\=\frac{-12+5+50}{10}\\=\frac{43}{10}\)
5. \(-\left(\frac{-3}{2}\right) +\left(\frac{9}{7}\right) +\left(\frac{8}{-6}\right)\\= \frac{3}{2}+ \frac{9}{7}-\frac{8}{6}\\=\frac{3}{2}+\frac{9}{7}-\frac{4}{3}\\=\frac{63}{42}+\frac{54}{42}-\frac{56}{42}\\=\frac{63+54-56}{42}\\=\frac{61}{42}\)
6. \(+\left(\frac{3}{7}\right) +\left(\frac{4}{-2}\right) +\left(\frac{-3}{-12}\right)\\= \frac{3}{7}- \frac{4}{2}+\frac{3}{12}\\=\frac{3}{7}-\frac{2}{1}+\frac{1}{4}\\=\frac{12}{28}-\frac{56}{28}+\frac{7}{28}\\=\frac{12-56+7}{28}\\=\frac{-37}{28}\)
7. \(+\left(\frac{-8}{9}\right) +\left(\frac{9}{-8}\right) -\left(\frac{2}{2}\right)\\= \frac{-8}{9}- \frac{9}{8}-\frac{2}{2}\\=\frac{-8}{9}-\frac{9}{8}-\frac{1}{1}\\=\frac{-64}{72}-\frac{81}{72}-\frac{72}{72}\\=\frac{-64-81-72}{72}\\=\frac{-217}{72}\)
8. \(-\left(\frac{-7}{-8}\right) -\left(\frac{6}{-6}\right) -\left(\frac{-10}{4}\right)\\= \frac{-7}{8}+ \frac{6}{6}+\frac{10}{4}\\=\frac{-7}{8}+\frac{1}{1}+\frac{5}{2}\\=\frac{-7+1+5}{8}\\=\frac{-1}{8}\)
9. \(+\left(\frac{4}{-9}\right) +\left(\frac{-2}{3}\right) +\left(\frac{-10}{-7}\right)\\= \frac{-4}{9}- \frac{2}{3}+\frac{10}{7}\\=\frac{-28}{63}-\frac{42}{63}+\frac{90}{63}\\=\frac{-28-42+90}{63}\\=\frac{20}{63}\)
10. \(+\left(\frac{-10}{3}\right) -\left(\frac{-10}{7}\right) -\left(\frac{8}{-9}\right)\\= \frac{-10}{3}+ \frac{10}{7}+\frac{8}{9}\\=\frac{-210}{63}+\frac{90}{63}+\frac{56}{63}\\=\frac{-210+90+56}{63}\\=\frac{-64}{63}\)
11. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-4}{3}+ \frac{7}{5}+\frac{5}{12}\\=\frac{-80}{60}+\frac{84}{60}+\frac{25}{60}\\=\frac{-80+84+25}{60}\\=\frac{29}{60}\)
12. \(-\left(\frac{-6}{-5}\right) -\left(\frac{2}{-5}\right) -\left(\frac{3}{10}\right)\\= \frac{-6}{5}+ \frac{2}{5}-\frac{3}{10}\\=\frac{-12}{10}+\frac{4}{10}-\frac{3}{10}\\=\frac{-12+4-3}{10}\\=\frac{-11}{10}\)