Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{7}{6}\right)\\= \frac{5}{6}+ \frac{7}{5}+\frac{7}{6}\\=\frac{25}{30}+\frac{42}{30}+\frac{35}{30}\\=\frac{25+42+35}{30}\\=\frac{102}{30}\\=\frac{17}{5}\)
2. \(-\left(\frac{2}{-5}\right) +\left(\frac{10}{7}\right) +\left(\frac{-12}{8}\right)\\= \frac{2}{5}+ \frac{10}{7}-\frac{12}{8}\\=\frac{2}{5}+\frac{10}{7}-\frac{3}{2}\\=\frac{28}{70}+\frac{100}{70}-\frac{105}{70}\\=\frac{28+100-105}{70}\\=\frac{23}{70}\)
3. \(+\left(\frac{7}{9}\right) -\left(\frac{-3}{-10}\right) -\left(\frac{10}{-3}\right)\\= \frac{7}{9}- \frac{3}{10}+\frac{10}{3}\\=\frac{70}{90}-\frac{27}{90}+\frac{300}{90}\\=\frac{70-27+300}{90}\\=\frac{343}{90}\)
4. \(+\left(\frac{-7}{2}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-10}{-12}\right)\\= \frac{-7}{2}+ \frac{8}{8}+\frac{10}{12}\\=\frac{-7}{2}+\frac{1}{1}+\frac{5}{6}\\=\frac{-21}{6}+\frac{6}{6}+\frac{5}{6}\\=\frac{-21+6+5}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
5. \(+\left(\frac{-9}{2}\right) +\left(\frac{7}{-10}\right) +\left(\frac{7}{7}\right)\\= \frac{-9}{2}- \frac{7}{10}+\frac{7}{7}\\=\frac{-9}{2}-\frac{7}{10}+\frac{1}{1}\\=\frac{-45}{10}-\frac{7}{10}+\frac{10}{10}\\=\frac{-45-7+10}{10}\\=\frac{-42}{10}\\=\frac{-21}{5}\)
6. \(+\left(\frac{10}{-3}\right) +\left(\frac{8}{-5}\right) +\left(\frac{8}{-3}\right)\\= \frac{-10}{3}- \frac{8}{5}-\frac{8}{3}\\=\frac{-50}{15}-\frac{24}{15}-\frac{40}{15}\\=\frac{-50-24-40}{15}\\=\frac{-114}{15}\\=\frac{-38}{5}\)
7. \(-\left(\frac{-4}{3}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-11}{10}\right)\\= \frac{4}{3}- \frac{9}{3}-\frac{11}{10}\\=\frac{4}{3}-\frac{3}{1}-\frac{11}{10}\\=\frac{40}{30}-\frac{90}{30}-\frac{33}{30}\\=\frac{40-90-33}{30}\\=\frac{-83}{30}\)
8. \(-\left(\frac{8}{-7}\right) -\left(\frac{-5}{-9}\right) +\left(\frac{6}{-8}\right)\\= \frac{8}{7}- \frac{5}{9}-\frac{6}{8}\\=\frac{8}{7}-\frac{5}{9}-\frac{3}{4}\\=\frac{288}{252}-\frac{140}{252}-\frac{189}{252}\\=\frac{288-140-189}{252}\\=\frac{-41}{252}\)
9. \(+\left(\frac{9}{-7}\right) -\left(\frac{-8}{4}\right) +\left(\frac{8}{-10}\right)\\= \frac{-9}{7}+ \frac{8}{4}-\frac{8}{10}\\=\frac{-9}{7}+\frac{2}{1}-\frac{4}{5}\\=\frac{-45}{35}+\frac{70}{35}-\frac{28}{35}\\=\frac{-45+70-28}{35}\\=\frac{-3}{35}\)
10. \(+\left(\frac{-8}{7}\right) -\left(\frac{-6}{3}\right) +\left(\frac{-8}{4}\right)\\= \frac{-8}{7}+ \frac{6}{3}-\frac{8}{4}\\=\frac{-8}{7}+\frac{2}{1}-\frac{2}{1}\\=\frac{-8+2-2}{7}\\=\frac{-8}{7}\)
11. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{-9}{8}\right)\\= \frac{-2}{3}- \frac{2}{5}+\frac{9}{8}\\=\frac{-80}{120}-\frac{48}{120}+\frac{135}{120}\\=\frac{-80-48+135}{120}\\=\frac{7}{120}\)
12. \(-\left(\frac{-9}{2}\right) +\left(\frac{5}{-6}\right) -\left(\frac{-3}{-9}\right)\\= \frac{9}{2}- \frac{5}{6}-\frac{3}{9}\\=\frac{9}{2}-\frac{5}{6}-\frac{1}{3}\\=\frac{27}{6}-\frac{5}{6}-\frac{2}{6}\\=\frac{27-5-2}{6}\\=\frac{20}{6}\\=\frac{10}{3}\)