Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{3}{7}\right) -\left(\frac{4}{-8}\right) -\left(\frac{10}{-10}\right)\\= \frac{-3}{7}+ \frac{4}{8}+\frac{10}{10}\\=\frac{-3}{7}+\frac{1}{2}+\frac{1}{1}\\=\frac{-6}{14}+\frac{7}{14}+\frac{14}{14}\\=\frac{-6+7+14}{14}\\=\frac{15}{14}\)
2. \(-\left(\frac{3}{-8}\right) -\left(\frac{-2}{2}\right) -\left(\frac{-12}{7}\right)\\= \frac{3}{8}+ \frac{2}{2}+\frac{12}{7}\\=\frac{3}{8}+\frac{1}{1}+\frac{12}{7}\\=\frac{21}{56}+\frac{56}{56}+\frac{96}{56}\\=\frac{21+56+96}{56}\\=\frac{173}{56}\)
3. \(-\left(\frac{5}{-6}\right) +\left(\frac{2}{6}\right) -\left(\frac{-8}{8}\right)\\= \frac{5}{6}+ \frac{2}{6}+\frac{8}{8}\\=\frac{5}{6}+\frac{1}{3}+\frac{1}{1}\\=\frac{5+1+1}{6}\\=\frac{7}{6}\)
4. \(-\left(\frac{-2}{-3}\right) -\left(\frac{4}{-8}\right) +\left(\frac{12}{-4}\right)\\= \frac{-2}{3}+ \frac{4}{8}-\frac{12}{4}\\=\frac{-2}{3}+\frac{1}{2}-\frac{3}{1}\\=\frac{-4}{6}+\frac{3}{6}-\frac{18}{6}\\=\frac{-4+3-18}{6}\\=\frac{-19}{6}\)
5. \(+\left(\frac{7}{-2}\right) +\left(\frac{-6}{7}\right) -\left(\frac{-3}{8}\right)\\= \frac{-7}{2}- \frac{6}{7}+\frac{3}{8}\\=\frac{-196}{56}-\frac{48}{56}+\frac{21}{56}\\=\frac{-196-48+21}{56}\\=\frac{-223}{56}\)
6. \(+\left(\frac{6}{-5}\right) -\left(\frac{-4}{10}\right) -\left(\frac{2}{8}\right)\\= \frac{-6}{5}+ \frac{4}{10}-\frac{2}{8}\\=\frac{-6}{5}+\frac{2}{5}-\frac{1}{4}\\=\frac{-24}{20}+\frac{8}{20}-\frac{5}{20}\\=\frac{-24+8-5}{20}\\=\frac{-21}{20}\)
7. \(-\left(\frac{-3}{-7}\right) -\left(\frac{6}{-10}\right) -\left(\frac{7}{4}\right)\\= \frac{-3}{7}+ \frac{6}{10}-\frac{7}{4}\\=\frac{-3}{7}+\frac{3}{5}-\frac{7}{4}\\=\frac{-60}{140}+\frac{84}{140}-\frac{245}{140}\\=\frac{-60+84-245}{140}\\=\frac{-221}{140}\)
8. \(-\left(\frac{2}{9}\right) +\left(\frac{10}{4}\right) -\left(\frac{-3}{-4}\right)\\= \frac{-2}{9}+ \frac{10}{4}-\frac{3}{4}\\=\frac{-2}{9}+\frac{5}{2}-\frac{3}{4}\\=\frac{-8}{36}+\frac{90}{36}-\frac{27}{36}\\=\frac{-8+90-27}{36}\\=\frac{55}{36}\)
9. \(-\left(\frac{-10}{3}\right) +\left(\frac{10}{8}\right) +\left(\frac{8}{-2}\right)\\= \frac{10}{3}+ \frac{10}{8}-\frac{8}{2}\\=\frac{10}{3}+\frac{5}{4}-\frac{4}{1}\\=\frac{40}{12}+\frac{15}{12}-\frac{48}{12}\\=\frac{40+15-48}{12}\\=\frac{7}{12}\)
10. \(-\left(\frac{5}{6}\right) -\left(\frac{-8}{10}\right) +\left(\frac{-2}{-9}\right)\\= \frac{-5}{6}+ \frac{8}{10}+\frac{2}{9}\\=\frac{-5}{6}+\frac{4}{5}+\frac{2}{9}\\=\frac{-75}{90}+\frac{72}{90}+\frac{20}{90}\\=\frac{-75+72+20}{90}\\=\frac{17}{90}\)
11. \(+\left(\frac{8}{-9}\right) +\left(\frac{7}{-2}\right) -\left(\frac{-9}{-11}\right)\\= \frac{-8}{9}- \frac{7}{2}-\frac{9}{11}\\=\frac{-176}{198}-\frac{693}{198}-\frac{162}{198}\\=\frac{-176-693-162}{198}\\=\frac{-1031}{198}\)
12. \(-\left(\frac{-5}{-2}\right) +\left(\frac{10}{7}\right) +\left(\frac{11}{10}\right)\\= \frac{-5}{2}+ \frac{10}{7}+\frac{11}{10}\\=\frac{-175}{70}+\frac{100}{70}+\frac{77}{70}\\=\frac{-175+100+77}{70}\\=\frac{2}{70}\\=\frac{1}{35}\)