Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{2}\right) -\left(\frac{2}{5}\right) -\left(\frac{10}{8}\right)\\= \frac{-3}{2}- \frac{2}{5}-\frac{10}{8}\\=\frac{-3}{2}-\frac{2}{5}-\frac{5}{4}\\=\frac{-30}{20}-\frac{8}{20}-\frac{25}{20}\\=\frac{-30-8-25}{20}\\=\frac{-63}{20}\)
2. \(+\left(\frac{-7}{-2}\right) +\left(\frac{2}{-6}\right) -\left(\frac{2}{10}\right)\\= \frac{7}{2}- \frac{2}{6}-\frac{2}{10}\\=\frac{7}{2}-\frac{1}{3}-\frac{1}{5}\\=\frac{105}{30}-\frac{10}{30}-\frac{6}{30}\\=\frac{105-10-6}{30}\\=\frac{89}{30}\)
3. \(+\left(\frac{4}{5}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{3}{9}\right)\\= \frac{4}{5}+ \frac{6}{3}-\frac{3}{9}\\=\frac{4}{5}+\frac{2}{1}-\frac{1}{3}\\=\frac{12}{15}+\frac{30}{15}-\frac{5}{15}\\=\frac{12+30-5}{15}\\=\frac{37}{15}\)
4. \(-\left(\frac{-8}{-3}\right) -\left(\frac{-5}{5}\right) -\left(\frac{-5}{-7}\right)\\= \frac{-8}{3}+ \frac{5}{5}-\frac{5}{7}\\=\frac{-8}{3}+\frac{1}{1}-\frac{5}{7}\\=\frac{-56}{21}+\frac{21}{21}-\frac{15}{21}\\=\frac{-56+21-15}{21}\\=\frac{-50}{21}\)
5. \(+\left(\frac{4}{-3}\right) -\left(\frac{-4}{2}\right) -\left(\frac{5}{7}\right)\\= \frac{-4}{3}+ \frac{4}{2}-\frac{5}{7}\\=\frac{-4}{3}+\frac{2}{1}-\frac{5}{7}\\=\frac{-28}{21}+\frac{42}{21}-\frac{15}{21}\\=\frac{-28+42-15}{21}\\=\frac{-1}{21}\)
6. \(-\left(\frac{7}{6}\right) +\left(\frac{4}{5}\right) -\left(\frac{-12}{10}\right)\\= \frac{-7}{6}+ \frac{4}{5}+\frac{12}{10}\\=\frac{-7}{6}+\frac{4}{5}+\frac{6}{5}\\=\frac{-35}{30}+\frac{24}{30}+\frac{36}{30}\\=\frac{-35+24+36}{30}\\=\frac{25}{30}\\=\frac{5}{6}\)
7. \(-\left(\frac{5}{8}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-6}{12}\right)\\= \frac{-5}{8}- \frac{10}{5}+\frac{6}{12}\\=\frac{-5}{8}-\frac{2}{1}+\frac{1}{2}\\=\frac{-5-2+1}{8}\\=\frac{-6}{8}\\=\frac{-3}{4}\)
8. \(-\left(\frac{6}{-5}\right) +\left(\frac{-3}{3}\right) +\left(\frac{12}{10}\right)\\= \frac{6}{5}- \frac{3}{3}+\frac{12}{10}\\=\frac{6}{5}-\frac{1}{1}+\frac{6}{5}\\=\frac{6-1+6}{5}\\=\frac{11}{5}\)
9. \(-\left(\frac{-2}{7}\right) -\left(\frac{6}{9}\right) -\left(\frac{-7}{-10}\right)\\= \frac{2}{7}- \frac{6}{9}-\frac{7}{10}\\=\frac{2}{7}-\frac{2}{3}-\frac{7}{10}\\=\frac{60}{210}-\frac{140}{210}-\frac{147}{210}\\=\frac{60-140-147}{210}\\=\frac{-227}{210}\)
10. \(-\left(\frac{2}{7}\right) +\left(\frac{9}{-7}\right) +\left(\frac{6}{-12}\right)\\= \frac{-2}{7}- \frac{9}{7}-\frac{6}{12}\\=\frac{-2}{7}-\frac{9}{7}-\frac{1}{2}\\=\frac{-4}{14}-\frac{18}{14}-\frac{7}{14}\\=\frac{-4-18-7}{14}\\=\frac{-29}{14}\)
11. \(-\left(\frac{-7}{4}\right) +\left(\frac{-9}{5}\right) -\left(\frac{-5}{3}\right)\\= \frac{7}{4}- \frac{9}{5}+\frac{5}{3}\\=\frac{105}{60}-\frac{108}{60}+\frac{100}{60}\\=\frac{105-108+100}{60}\\=\frac{97}{60}\)
12. \(+\left(\frac{-10}{-3}\right) +\left(\frac{6}{7}\right) +\left(\frac{10}{11}\right)\\= \frac{10}{3}+ \frac{6}{7}+\frac{10}{11}\\=\frac{770}{231}+\frac{198}{231}+\frac{210}{231}\\=\frac{770+198+210}{231}\\=\frac{1178}{231}\)