Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{8}\right) -\left(\frac{-2}{6}\right) -\left(\frac{9}{-7}\right)\\= \frac{-7}{8}+ \frac{2}{6}+\frac{9}{7}\\=\frac{-7}{8}+\frac{1}{3}+\frac{9}{7}\\=\frac{-147}{168}+\frac{56}{168}+\frac{216}{168}\\=\frac{-147+56+216}{168}\\=\frac{125}{168}\)
2. \(-\left(\frac{8}{-7}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-2}{-2}\right)\\= \frac{8}{7}+ \frac{8}{10}-\frac{2}{2}\\=\frac{8}{7}+\frac{4}{5}-\frac{1}{1}\\=\frac{40}{35}+\frac{28}{35}-\frac{35}{35}\\=\frac{40+28-35}{35}\\=\frac{33}{35}\)
3. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-5}{7}\right) +\left(\frac{5}{-3}\right)\\= \frac{-6}{5}- \frac{5}{7}-\frac{5}{3}\\=\frac{-126}{105}-\frac{75}{105}-\frac{175}{105}\\=\frac{-126-75-175}{105}\\=\frac{-376}{105}\)
4. \(-\left(\frac{4}{-5}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-12}{-11}\right)\\= \frac{4}{5}+ \frac{7}{4}+\frac{12}{11}\\=\frac{176}{220}+\frac{385}{220}+\frac{240}{220}\\=\frac{176+385+240}{220}\\=\frac{801}{220}\)
5. \(-\left(\frac{-7}{-8}\right) +\left(\frac{9}{-10}\right) +\left(\frac{-11}{-5}\right)\\= \frac{-7}{8}- \frac{9}{10}+\frac{11}{5}\\=\frac{-35}{40}-\frac{36}{40}+\frac{88}{40}\\=\frac{-35-36+88}{40}\\=\frac{17}{40}\)
6. \(+\left(\frac{-5}{2}\right) +\left(\frac{8}{-10}\right) +\left(\frac{-4}{-11}\right)\\= \frac{-5}{2}- \frac{8}{10}+\frac{4}{11}\\=\frac{-5}{2}-\frac{4}{5}+\frac{4}{11}\\=\frac{-275}{110}-\frac{88}{110}+\frac{40}{110}\\=\frac{-275-88+40}{110}\\=\frac{-323}{110}\)
7. \(+\left(\frac{5}{-3}\right) -\left(\frac{4}{-8}\right) -\left(\frac{-8}{4}\right)\\= \frac{-5}{3}+ \frac{4}{8}+\frac{8}{4}\\=\frac{-5}{3}+\frac{1}{2}+\frac{2}{1}\\=\frac{-10}{6}+\frac{3}{6}+\frac{12}{6}\\=\frac{-10+3+12}{6}\\=\frac{5}{6}\)
8. \(+\left(\frac{-2}{-5}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{5}{-10}\right)\\= \frac{2}{5}- \frac{6}{7}-\frac{5}{10}\\=\frac{2}{5}-\frac{6}{7}-\frac{1}{2}\\=\frac{28}{70}-\frac{60}{70}-\frac{35}{70}\\=\frac{28-60-35}{70}\\=\frac{-67}{70}\)
9. \(-\left(\frac{3}{2}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{-10}{-3}\right)\\= \frac{-3}{2}+ \frac{4}{9}+\frac{10}{3}\\=\frac{-27}{18}+\frac{8}{18}+\frac{60}{18}\\=\frac{-27+8+60}{18}\\=\frac{41}{18}\)
10. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-10}{-9}\right) -\left(\frac{12}{12}\right)\\= \frac{-6}{5}- \frac{10}{9}-\frac{12}{12}\\=\frac{-6}{5}-\frac{10}{9}-\frac{1}{1}\\=\frac{-54}{45}-\frac{50}{45}-\frac{45}{45}\\=\frac{-54-50-45}{45}\\=\frac{-149}{45}\)
11. \(-\left(\frac{6}{-5}\right) +\left(\frac{5}{-3}\right) -\left(\frac{6}{12}\right)\\= \frac{6}{5}- \frac{5}{3}-\frac{6}{12}\\=\frac{6}{5}-\frac{5}{3}-\frac{1}{2}\\=\frac{36}{30}-\frac{50}{30}-\frac{15}{30}\\=\frac{36-50-15}{30}\\=\frac{-29}{30}\)
12. \(-\left(\frac{-9}{5}\right) -\left(\frac{4}{10}\right) +\left(\frac{-3}{9}\right)\\= \frac{9}{5}- \frac{4}{10}-\frac{3}{9}\\=\frac{9}{5}-\frac{2}{5}-\frac{1}{3}\\=\frac{27}{15}-\frac{6}{15}-\frac{5}{15}\\=\frac{27-6-5}{15}\\=\frac{16}{15}\)