Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{7}{-8}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-7}{8}+ \frac{2}{7}+\frac{5}{12}\\=\frac{-147}{168}+\frac{48}{168}+\frac{70}{168}\\=\frac{-147+48+70}{168}\\=\frac{-29}{168}\)
2. \(+\left(\frac{-7}{-3}\right) +\left(\frac{10}{-2}\right) +\left(\frac{-3}{12}\right)\\= \frac{7}{3}- \frac{10}{2}-\frac{3}{12}\\=\frac{7}{3}-\frac{5}{1}-\frac{1}{4}\\=\frac{28}{12}-\frac{60}{12}-\frac{3}{12}\\=\frac{28-60-3}{12}\\=\frac{-35}{12}\)
3. \(+\left(\frac{-3}{4}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{-6}{-11}\right)\\= \frac{-3}{4}- \frac{9}{9}-\frac{6}{11}\\=\frac{-3}{4}-\frac{1}{1}-\frac{6}{11}\\=\frac{-33}{44}-\frac{44}{44}-\frac{24}{44}\\=\frac{-33-44-24}{44}\\=\frac{-101}{44}\)
4. \(-\left(\frac{10}{-9}\right) -\left(\frac{2}{8}\right) -\left(\frac{10}{9}\right)\\= \frac{10}{9}- \frac{2}{8}-\frac{10}{9}\\=\frac{10}{9}-\frac{1}{4}-\frac{10}{9}\\=\frac{40}{36}-\frac{9}{36}-\frac{40}{36}\\=\frac{40-9-40}{36}\\=\frac{-9}{36}\\=\frac{-1}{4}\)
5. \(-\left(\frac{8}{-7}\right) +\left(\frac{-7}{2}\right) +\left(\frac{8}{-9}\right)\\= \frac{8}{7}- \frac{7}{2}-\frac{8}{9}\\=\frac{144}{126}-\frac{441}{126}-\frac{112}{126}\\=\frac{144-441-112}{126}\\=\frac{-409}{126}\)
6. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-7}{6}\right) -\left(\frac{-3}{-2}\right)\\= \frac{6}{5}+ \frac{7}{6}-\frac{3}{2}\\=\frac{36}{30}+\frac{35}{30}-\frac{45}{30}\\=\frac{36+35-45}{30}\\=\frac{26}{30}\\=\frac{13}{15}\)
7. \(-\left(\frac{-8}{3}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{-6}{12}\right)\\= \frac{8}{3}+ \frac{2}{9}+\frac{6}{12}\\=\frac{8}{3}+\frac{2}{9}+\frac{1}{2}\\=\frac{48}{18}+\frac{4}{18}+\frac{9}{18}\\=\frac{48+4+9}{18}\\=\frac{61}{18}\)
8. \(-\left(\frac{9}{-2}\right) -\left(\frac{-9}{7}\right) -\left(\frac{9}{10}\right)\\= \frac{9}{2}+ \frac{9}{7}-\frac{9}{10}\\=\frac{315}{70}+\frac{90}{70}-\frac{63}{70}\\=\frac{315+90-63}{70}\\=\frac{342}{70}\\=\frac{171}{35}\)
9. \(-\left(\frac{10}{-9}\right) -\left(\frac{5}{7}\right) -\left(\frac{-3}{9}\right)\\= \frac{10}{9}- \frac{5}{7}+\frac{3}{9}\\=\frac{10}{9}-\frac{5}{7}+\frac{1}{3}\\=\frac{70}{63}-\frac{45}{63}+\frac{21}{63}\\=\frac{70-45+21}{63}\\=\frac{46}{63}\)
10. \(+\left(\frac{-8}{7}\right) -\left(\frac{-6}{-10}\right) -\left(\frac{12}{8}\right)\\= \frac{-8}{7}- \frac{6}{10}-\frac{12}{8}\\=\frac{-8}{7}-\frac{3}{5}-\frac{3}{2}\\=\frac{-80}{70}-\frac{42}{70}-\frac{105}{70}\\=\frac{-80-42-105}{70}\\=\frac{-227}{70}\)
11. \(+\left(\frac{-7}{9}\right) +\left(\frac{3}{8}\right) -\left(\frac{-5}{-5}\right)\\= \frac{-7}{9}+ \frac{3}{8}-\frac{5}{5}\\=\frac{-7}{9}+\frac{3}{8}-\frac{1}{1}\\=\frac{-56}{72}+\frac{27}{72}-\frac{72}{72}\\=\frac{-56+27-72}{72}\\=\frac{-101}{72}\)
12. \(-\left(\frac{7}{8}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{-12}{-7}\right)\\= \frac{-7}{8}- \frac{9}{6}-\frac{12}{7}\\=\frac{-7}{8}-\frac{3}{2}-\frac{12}{7}\\=\frac{-49}{56}-\frac{84}{56}-\frac{96}{56}\\=\frac{-49-84-96}{56}\\=\frac{-229}{56}\)