Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{7}{2}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{12}{-10}\right)\\= \frac{-7}{2}- \frac{2}{6}-\frac{12}{10}\\=\frac{-7}{2}-\frac{1}{3}-\frac{6}{5}\\=\frac{-105}{30}-\frac{10}{30}-\frac{36}{30}\\=\frac{-105-10-36}{30}\\=\frac{-151}{30}\)
2. \(-\left(\frac{4}{-3}\right) -\left(\frac{-7}{9}\right) -\left(\frac{-11}{-6}\right)\\= \frac{4}{3}+ \frac{7}{9}-\frac{11}{6}\\=\frac{24}{18}+\frac{14}{18}-\frac{33}{18}\\=\frac{24+14-33}{18}\\=\frac{5}{18}\)
3. \(+\left(\frac{4}{7}\right) -\left(\frac{-4}{10}\right) -\left(\frac{-3}{-6}\right)\\= \frac{4}{7}+ \frac{4}{10}-\frac{3}{6}\\=\frac{4}{7}+\frac{2}{5}-\frac{1}{2}\\=\frac{40}{70}+\frac{28}{70}-\frac{35}{70}\\=\frac{40+28-35}{70}\\=\frac{33}{70}\)
4. \(+\left(\frac{-10}{3}\right) -\left(\frac{3}{-9}\right) -\left(\frac{12}{10}\right)\\= \frac{-10}{3}+ \frac{3}{9}-\frac{12}{10}\\=\frac{-10}{3}+\frac{1}{3}-\frac{6}{5}\\=\frac{-50}{15}+\frac{5}{15}-\frac{18}{15}\\=\frac{-50+5-18}{15}\\=\frac{-63}{15}\\=\frac{-21}{5}\)
5. \(-\left(\frac{4}{-3}\right) +\left(\frac{5}{3}\right) +\left(\frac{-3}{8}\right)\\= \frac{4}{3}+ \frac{5}{3}-\frac{3}{8}\\=\frac{32}{24}+\frac{40}{24}-\frac{9}{24}\\=\frac{32+40-9}{24}\\=\frac{63}{24}\\=\frac{21}{8}\)
6. \(-\left(\frac{3}{2}\right) +\left(\frac{6}{-9}\right) -\left(\frac{8}{-4}\right)\\= \frac{-3}{2}- \frac{6}{9}+\frac{8}{4}\\=\frac{-3}{2}-\frac{2}{3}+\frac{2}{1}\\=\frac{-9}{6}-\frac{4}{6}+\frac{12}{6}\\=\frac{-9-4+12}{6}\\=\frac{-1}{6}\)
7. \(-\left(\frac{-4}{-3}\right) -\left(\frac{9}{9}\right) +\left(\frac{2}{-9}\right)\\= \frac{-4}{3}- \frac{9}{9}-\frac{2}{9}\\=\frac{-4}{3}-\frac{1}{1}-\frac{2}{9}\\=\frac{-12}{9}-\frac{9}{9}-\frac{2}{9}\\=\frac{-12-9-2}{9}\\=\frac{-23}{9}\)
8. \(+\left(\frac{3}{-2}\right) +\left(\frac{3}{-10}\right) -\left(\frac{-5}{6}\right)\\= \frac{-3}{2}- \frac{3}{10}+\frac{5}{6}\\=\frac{-45}{30}-\frac{9}{30}+\frac{25}{30}\\=\frac{-45-9+25}{30}\\=\frac{-29}{30}\)
9. \(-\left(\frac{3}{-4}\right) +\left(\frac{-9}{7}\right) -\left(\frac{7}{9}\right)\\= \frac{3}{4}- \frac{9}{7}-\frac{7}{9}\\=\frac{189}{252}-\frac{324}{252}-\frac{196}{252}\\=\frac{189-324-196}{252}\\=\frac{-331}{252}\)
10. \(+\left(\frac{-5}{6}\right) -\left(\frac{-5}{-9}\right) +\left(\frac{5}{8}\right)\\= \frac{-5}{6}- \frac{5}{9}+\frac{5}{8}\\=\frac{-60}{72}-\frac{40}{72}+\frac{45}{72}\\=\frac{-60-40+45}{72}\\=\frac{-55}{72}\)
11. \(-\left(\frac{10}{-7}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{2}{8}\right)\\= \frac{10}{7}+ \frac{9}{8}+\frac{2}{8}\\=\frac{10}{7}+\frac{9}{8}+\frac{1}{4}\\=\frac{80}{56}+\frac{63}{56}+\frac{14}{56}\\=\frac{80+63+14}{56}\\=\frac{157}{56}\)
12. \(-\left(\frac{10}{-3}\right) -\left(\frac{6}{-7}\right) +\left(\frac{4}{-10}\right)\\= \frac{10}{3}+ \frac{6}{7}-\frac{4}{10}\\=\frac{10}{3}+\frac{6}{7}-\frac{2}{5}\\=\frac{350}{105}+\frac{90}{105}-\frac{42}{105}\\=\frac{350+90-42}{105}\\=\frac{398}{105}\)