Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{7}\right) +\left(\frac{3}{2}\right) -\left(\frac{-7}{3}\right)\\= \frac{6}{7}+ \frac{3}{2}+\frac{7}{3}\\=\frac{36}{42}+\frac{63}{42}+\frac{98}{42}\\=\frac{36+63+98}{42}\\=\frac{197}{42}\)
2. \(+\left(\frac{4}{-7}\right) +\left(\frac{8}{-9}\right) +\left(\frac{10}{-8}\right)\\= \frac{-4}{7}- \frac{8}{9}-\frac{10}{8}\\=\frac{-4}{7}-\frac{8}{9}-\frac{5}{4}\\=\frac{-144}{252}-\frac{224}{252}-\frac{315}{252}\\=\frac{-144-224-315}{252}\\=\frac{-683}{252}\)
3. \(-\left(\frac{4}{5}\right) +\left(\frac{3}{9}\right) +\left(\frac{-4}{-8}\right)\\= \frac{-4}{5}+ \frac{3}{9}+\frac{4}{8}\\=\frac{-4}{5}+\frac{1}{3}+\frac{1}{2}\\=\frac{-24}{30}+\frac{10}{30}+\frac{15}{30}\\=\frac{-24+10+15}{30}\\=\frac{1}{30}\)
4. \(-\left(\frac{7}{-2}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{11}{-9}\right)\\= \frac{7}{2}- \frac{3}{7}+\frac{11}{9}\\=\frac{441}{126}-\frac{54}{126}+\frac{154}{126}\\=\frac{441-54+154}{126}\\=\frac{541}{126}\)
5. \(-\left(\frac{9}{4}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{5}{5}\right)\\= \frac{-9}{4}+ \frac{6}{5}+\frac{5}{5}\\=\frac{-9}{4}+\frac{6}{5}+\frac{1}{1}\\=\frac{-45}{20}+\frac{24}{20}+\frac{20}{20}\\=\frac{-45+24+20}{20}\\=\frac{-1}{20}\)
6. \(-\left(\frac{-2}{-3}\right) -\left(\frac{2}{-10}\right) -\left(\frac{-3}{-9}\right)\\= \frac{-2}{3}+ \frac{2}{10}-\frac{3}{9}\\=\frac{-2}{3}+\frac{1}{5}-\frac{1}{3}\\=\frac{-10}{15}+\frac{3}{15}-\frac{5}{15}\\=\frac{-10+3-5}{15}\\=\frac{-12}{15}\\=\frac{-4}{5}\)
7. \(-\left(\frac{9}{4}\right) -\left(\frac{7}{-4}\right) -\left(\frac{-3}{5}\right)\\= \frac{-9}{4}+ \frac{7}{4}+\frac{3}{5}\\=\frac{-45}{20}+\frac{35}{20}+\frac{12}{20}\\=\frac{-45+35+12}{20}\\=\frac{2}{20}\\=\frac{1}{10}\)
8. \(+\left(\frac{2}{9}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{-12}{8}\right)\\= \frac{2}{9}- \frac{8}{6}-\frac{12}{8}\\=\frac{2}{9}-\frac{4}{3}-\frac{3}{2}\\=\frac{4}{18}-\frac{24}{18}-\frac{27}{18}\\=\frac{4-24-27}{18}\\=\frac{-47}{18}\)
9. \(+\left(\frac{-10}{3}\right) -\left(\frac{3}{3}\right) +\left(\frac{3}{-10}\right)\\= \frac{-10}{3}- \frac{3}{3}-\frac{3}{10}\\=\frac{-10}{3}-\frac{1}{1}-\frac{3}{10}\\=\frac{-100}{30}-\frac{30}{30}-\frac{9}{30}\\=\frac{-100-30-9}{30}\\=\frac{-139}{30}\)
10. \(+\left(\frac{10}{3}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-6}{5}\right)\\= \frac{10}{3}- \frac{5}{8}+\frac{6}{5}\\=\frac{400}{120}-\frac{75}{120}+\frac{144}{120}\\=\frac{400-75+144}{120}\\=\frac{469}{120}\)
11. \(+\left(\frac{-2}{3}\right) -\left(\frac{2}{4}\right) +\left(\frac{-10}{-5}\right)\\= \frac{-2}{3}- \frac{2}{4}+\frac{10}{5}\\=\frac{-2}{3}-\frac{1}{2}+\frac{2}{1}\\=\frac{-4}{6}-\frac{3}{6}+\frac{12}{6}\\=\frac{-4-3+12}{6}\\=\frac{5}{6}\)
12. \(+\left(\frac{3}{7}\right) +\left(\frac{-10}{3}\right) -\left(\frac{-5}{-12}\right)\\= \frac{3}{7}- \frac{10}{3}-\frac{5}{12}\\=\frac{36}{84}-\frac{280}{84}-\frac{35}{84}\\=\frac{36-280-35}{84}\\=\frac{-279}{84}\\=\frac{-93}{28}\)