Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-2}\right) +\left(\frac{3}{3}\right) +\left(\frac{9}{-12}\right)\\= \frac{-3}{2}+ \frac{3}{3}-\frac{9}{12}\\=\frac{-3}{2}+\frac{1}{1}-\frac{3}{4}\\=\frac{-6}{4}+\frac{4}{4}-\frac{3}{4}\\=\frac{-6+4-3}{4}\\=\frac{-5}{4}\)
2. \(-\left(\frac{5}{7}\right) +\left(\frac{-2}{2}\right) -\left(\frac{-2}{-7}\right)\\= \frac{-5}{7}- \frac{2}{2}-\frac{2}{7}\\=\frac{-5}{7}-\frac{1}{1}-\frac{2}{7}\\=\frac{-5-1-2}{7}\\=\frac{-8}{7}\)
3. \(-\left(\frac{-7}{8}\right) +\left(\frac{-5}{2}\right) -\left(\frac{-9}{8}\right)\\= \frac{7}{8}- \frac{5}{2}+\frac{9}{8}\\=\frac{7-5+9}{8}\\=\frac{11}{8}\)
4. \(+\left(\frac{10}{7}\right) -\left(\frac{-4}{7}\right) +\left(\frac{-10}{-3}\right)\\= \frac{10}{7}+ \frac{4}{7}+\frac{10}{3}\\=\frac{30}{21}+\frac{12}{21}+\frac{70}{21}\\=\frac{30+12+70}{21}\\=\frac{112}{21}\\=\frac{16}{3}\)
5. \(+\left(\frac{7}{2}\right) -\left(\frac{2}{6}\right) -\left(\frac{6}{-6}\right)\\= \frac{7}{2}- \frac{2}{6}+\frac{6}{6}\\=\frac{7}{2}-\frac{1}{3}+\frac{1}{1}\\=\frac{21}{6}-\frac{2}{6}+\frac{6}{6}\\=\frac{21-2+6}{6}\\=\frac{25}{6}\)
6. \(+\left(\frac{4}{3}\right) -\left(\frac{-8}{-2}\right) -\left(\frac{-6}{-4}\right)\\= \frac{4}{3}- \frac{8}{2}-\frac{6}{4}\\=\frac{4}{3}-\frac{4}{1}-\frac{3}{2}\\=\frac{8}{6}-\frac{24}{6}-\frac{9}{6}\\=\frac{8-24-9}{6}\\=\frac{-25}{6}\)
7. \(+\left(\frac{6}{5}\right) -\left(\frac{10}{-8}\right) -\left(\frac{12}{-3}\right)\\= \frac{6}{5}+ \frac{10}{8}+\frac{12}{3}\\=\frac{6}{5}+\frac{5}{4}+\frac{4}{1}\\=\frac{24}{20}+\frac{25}{20}+\frac{80}{20}\\=\frac{24+25+80}{20}\\=\frac{129}{20}\)
8. \(+\left(\frac{-3}{8}\right) +\left(\frac{8}{9}\right) +\left(\frac{8}{-3}\right)\\= \frac{-3}{8}+ \frac{8}{9}-\frac{8}{3}\\=\frac{-27}{72}+\frac{64}{72}-\frac{192}{72}\\=\frac{-27+64-192}{72}\\=\frac{-155}{72}\)
9. \(-\left(\frac{10}{-9}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{3}{-12}\right)\\= \frac{10}{9}- \frac{6}{3}-\frac{3}{12}\\=\frac{10}{9}-\frac{2}{1}-\frac{1}{4}\\=\frac{40}{36}-\frac{72}{36}-\frac{9}{36}\\=\frac{40-72-9}{36}\\=\frac{-41}{36}\)
10. \(+\left(\frac{4}{-7}\right) +\left(\frac{5}{-7}\right) +\left(\frac{10}{-7}\right)\\= \frac{-4}{7}- \frac{5}{7}-\frac{10}{7}\\=\frac{-4-5-10}{7}\\=\frac{-19}{7}\)
11. \(-\left(\frac{3}{-4}\right) -\left(\frac{-9}{5}\right) -\left(\frac{3}{-8}\right)\\= \frac{3}{4}+ \frac{9}{5}+\frac{3}{8}\\=\frac{30}{40}+\frac{72}{40}+\frac{15}{40}\\=\frac{30+72+15}{40}\\=\frac{117}{40}\)
12. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-9}{8}\right) +\left(\frac{8}{3}\right)\\= \frac{-2}{5}+ \frac{9}{8}+\frac{8}{3}\\=\frac{-48}{120}+\frac{135}{120}+\frac{320}{120}\\=\frac{-48+135+320}{120}\\=\frac{407}{120}\)