Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-9}\right) +\left(\frac{7}{-9}\right) -\left(\frac{-12}{2}\right)\\= \frac{2}{9}- \frac{7}{9}+\frac{12}{2}\\=\frac{2}{9}-\frac{7}{9}+\frac{6}{1}\\=\frac{2-7+6}{9}\\=\frac{1}{9}\)
2. \(+\left(\frac{-3}{8}\right) +\left(\frac{9}{4}\right) -\left(\frac{-12}{-12}\right)\\= \frac{-3}{8}+ \frac{9}{4}-\frac{12}{12}\\=\frac{-3}{8}+\frac{9}{4}-\frac{1}{1}\\=\frac{-3+9-1}{8}\\=\frac{5}{8}\)
3. \(-\left(\frac{-5}{3}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{10}{3}\right)\\= \frac{5}{3}+ \frac{9}{9}+\frac{10}{3}\\=\frac{5}{3}+\frac{1}{1}+\frac{10}{3}\\=\frac{5+1+10}{3}\\=\frac{16}{3}\)
4. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-9}{6}\right) +\left(\frac{12}{4}\right)\\= \frac{-3}{2}- \frac{9}{6}+\frac{12}{4}\\=\frac{-3}{2}-\frac{3}{2}+\frac{3}{1}\\=\frac{-3-3+3}{2}\\=\frac{-3}{2}\)
5. \(-\left(\frac{-7}{9}\right) -\left(\frac{7}{-4}\right) +\left(\frac{-10}{-11}\right)\\= \frac{7}{9}+ \frac{7}{4}+\frac{10}{11}\\=\frac{308}{396}+\frac{693}{396}+\frac{360}{396}\\=\frac{308+693+360}{396}\\=\frac{1361}{396}\)
6. \(+\left(\frac{4}{-9}\right) +\left(\frac{6}{-5}\right) -\left(\frac{-7}{-8}\right)\\= \frac{-4}{9}- \frac{6}{5}-\frac{7}{8}\\=\frac{-160}{360}-\frac{432}{360}-\frac{315}{360}\\=\frac{-160-432-315}{360}\\=\frac{-907}{360}\)
7. \(+\left(\frac{4}{3}\right) -\left(\frac{-3}{6}\right) -\left(\frac{-2}{5}\right)\\= \frac{4}{3}+ \frac{3}{6}+\frac{2}{5}\\=\frac{4}{3}+\frac{1}{2}+\frac{2}{5}\\=\frac{40}{30}+\frac{15}{30}+\frac{12}{30}\\=\frac{40+15+12}{30}\\=\frac{67}{30}\)
8. \(-\left(\frac{2}{-9}\right) +\left(\frac{3}{7}\right) +\left(\frac{7}{-11}\right)\\= \frac{2}{9}+ \frac{3}{7}-\frac{7}{11}\\=\frac{154}{693}+\frac{297}{693}-\frac{441}{693}\\=\frac{154+297-441}{693}\\=\frac{10}{693}\)
9. \(-\left(\frac{10}{9}\right) +\left(\frac{2}{-8}\right) +\left(\frac{4}{10}\right)\\= \frac{-10}{9}- \frac{2}{8}+\frac{4}{10}\\=\frac{-10}{9}-\frac{1}{4}+\frac{2}{5}\\=\frac{-200}{180}-\frac{45}{180}+\frac{72}{180}\\=\frac{-200-45+72}{180}\\=\frac{-173}{180}\)
10. \(-\left(\frac{-5}{3}\right) +\left(\frac{-6}{-6}\right) +\left(\frac{-6}{5}\right)\\= \frac{5}{3}+ \frac{6}{6}-\frac{6}{5}\\=\frac{5}{3}+\frac{1}{1}-\frac{6}{5}\\=\frac{25}{15}+\frac{15}{15}-\frac{18}{15}\\=\frac{25+15-18}{15}\\=\frac{22}{15}\)
11. \(+\left(\frac{5}{-9}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{2}{11}\right)\\= \frac{-5}{9}- \frac{6}{2}+\frac{2}{11}\\=\frac{-5}{9}-\frac{3}{1}+\frac{2}{11}\\=\frac{-55}{99}-\frac{297}{99}+\frac{18}{99}\\=\frac{-55-297+18}{99}\\=\frac{-334}{99}\)
12. \(+\left(\frac{5}{-8}\right) +\left(\frac{7}{8}\right) -\left(\frac{-4}{2}\right)\\= \frac{-5}{8}+ \frac{7}{8}+\frac{4}{2}\\=\frac{-5}{8}+\frac{7}{8}+\frac{2}{1}\\=\frac{-5+7+2}{8}\\=\frac{4}{8}\\=\frac{1}{2}\)