Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{7}\right) -\left(\frac{-4}{-7}\right) -\left(\frac{11}{-4}\right)\\= \frac{2}{7}- \frac{4}{7}+\frac{11}{4}\\=\frac{8}{28}-\frac{16}{28}+\frac{77}{28}\\=\frac{8-16+77}{28}\\=\frac{69}{28}\)
2. \(+\left(\frac{4}{-5}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{8}{10}\right)\\= \frac{-4}{5}- \frac{5}{6}+\frac{8}{10}\\=\frac{-4}{5}-\frac{5}{6}+\frac{4}{5}\\=\frac{-24}{30}-\frac{25}{30}+\frac{24}{30}\\=\frac{-24-25+24}{30}\\=\frac{-25}{30}\\=\frac{-5}{6}\)
3. \(-\left(\frac{7}{8}\right) +\left(\frac{-9}{9}\right) +\left(\frac{-6}{2}\right)\\= \frac{-7}{8}- \frac{9}{9}-\frac{6}{2}\\=\frac{-7}{8}-\frac{1}{1}-\frac{3}{1}\\=\frac{-7-1-3}{8}\\=\frac{-11}{8}\)
4. \(-\left(\frac{9}{8}\right) +\left(\frac{4}{4}\right) -\left(\frac{-11}{-3}\right)\\= \frac{-9}{8}+ \frac{4}{4}-\frac{11}{3}\\=\frac{-9}{8}+\frac{1}{1}-\frac{11}{3}\\=\frac{-27}{24}+\frac{24}{24}-\frac{88}{24}\\=\frac{-27+24-88}{24}\\=\frac{-91}{24}\)
5. \(+\left(\frac{9}{8}\right) +\left(\frac{-5}{-6}\right) -\left(\frac{12}{-3}\right)\\= \frac{9}{8}+ \frac{5}{6}+\frac{12}{3}\\=\frac{9}{8}+\frac{5}{6}+\frac{4}{1}\\=\frac{27}{24}+\frac{20}{24}+\frac{96}{24}\\=\frac{27+20+96}{24}\\=\frac{143}{24}\)
6. \(-\left(\frac{-10}{-3}\right) +\left(\frac{8}{5}\right) +\left(\frac{11}{3}\right)\\= \frac{-10}{3}+ \frac{8}{5}+\frac{11}{3}\\=\frac{-50}{15}+\frac{24}{15}+\frac{55}{15}\\=\frac{-50+24+55}{15}\\=\frac{29}{15}\)
7. \(-\left(\frac{-10}{-7}\right) -\left(\frac{6}{-3}\right) +\left(\frac{8}{8}\right)\\= \frac{-10}{7}+ \frac{6}{3}+\frac{8}{8}\\=\frac{-10}{7}+\frac{2}{1}+\frac{1}{1}\\=\frac{-10+2+1}{7}\\=\frac{-7}{7}\\=\frac{-1}{1}\)
8. \(+\left(\frac{-10}{-3}\right) -\left(\frac{10}{7}\right) +\left(\frac{7}{-10}\right)\\= \frac{10}{3}- \frac{10}{7}-\frac{7}{10}\\=\frac{700}{210}-\frac{300}{210}-\frac{147}{210}\\=\frac{700-300-147}{210}\\=\frac{253}{210}\)
9. \(-\left(\frac{9}{-8}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{9}{2}\right)\\= \frac{9}{8}- \frac{2}{10}+\frac{9}{2}\\=\frac{9}{8}-\frac{1}{5}+\frac{9}{2}\\=\frac{45}{40}-\frac{8}{40}+\frac{180}{40}\\=\frac{45-8+180}{40}\\=\frac{217}{40}\)
10. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-8}{8}\right) -\left(\frac{12}{12}\right)\\= \frac{6}{5}+ \frac{8}{8}-\frac{12}{12}\\=\frac{6}{5}+\frac{1}{1}-\frac{1}{1}\\=\frac{6+1-1}{5}\\=\frac{6}{5}\)
11. \(+\left(\frac{3}{-5}\right) +\left(\frac{-6}{2}\right) +\left(\frac{-8}{-7}\right)\\= \frac{-3}{5}- \frac{6}{2}+\frac{8}{7}\\=\frac{-3}{5}-\frac{3}{1}+\frac{8}{7}\\=\frac{-21}{35}-\frac{105}{35}+\frac{40}{35}\\=\frac{-21-105+40}{35}\\=\frac{-86}{35}\)
12. \(+\left(\frac{-2}{9}\right) +\left(\frac{5}{5}\right) -\left(\frac{-5}{-6}\right)\\= \frac{-2}{9}+ \frac{5}{5}-\frac{5}{6}\\=\frac{-2}{9}+\frac{1}{1}-\frac{5}{6}\\=\frac{-4}{18}+\frac{18}{18}-\frac{15}{18}\\=\frac{-4+18-15}{18}\\=\frac{-1}{18}\)