Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{2}\right) +\left(\frac{9}{-2}\right) -\left(\frac{-9}{10}\right)\\= \frac{-3}{2}- \frac{9}{2}+\frac{9}{10}\\=\frac{-15}{10}-\frac{45}{10}+\frac{9}{10}\\=\frac{-15-45+9}{10}\\=\frac{-51}{10}\)
2. \(-\left(\frac{-6}{5}\right) +\left(\frac{-8}{6}\right) +\left(\frac{2}{-3}\right)\\= \frac{6}{5}- \frac{8}{6}-\frac{2}{3}\\=\frac{6}{5}-\frac{4}{3}-\frac{2}{3}\\=\frac{18}{15}-\frac{20}{15}-\frac{10}{15}\\=\frac{18-20-10}{15}\\=\frac{-12}{15}\\=\frac{-4}{5}\)
3. \(+\left(\frac{3}{2}\right) -\left(\frac{10}{-5}\right) -\left(\frac{-6}{-2}\right)\\= \frac{3}{2}+ \frac{10}{5}-\frac{6}{2}\\=\frac{3}{2}+\frac{2}{1}-\frac{3}{1}\\=\frac{3+2-3}{2}\\=\frac{2}{2}\\=\frac{1}{1}\)
4. \(+\left(\frac{4}{-3}\right) +\left(\frac{-6}{3}\right) -\left(\frac{11}{8}\right)\\= \frac{-4}{3}- \frac{6}{3}-\frac{11}{8}\\=\frac{-4}{3}-\frac{2}{1}-\frac{11}{8}\\=\frac{-32}{24}-\frac{48}{24}-\frac{33}{24}\\=\frac{-32-48-33}{24}\\=\frac{-113}{24}\)
5. \(-\left(\frac{9}{2}\right) +\left(\frac{5}{3}\right) -\left(\frac{-7}{5}\right)\\= \frac{-9}{2}+ \frac{5}{3}+\frac{7}{5}\\=\frac{-135}{30}+\frac{50}{30}+\frac{42}{30}\\=\frac{-135+50+42}{30}\\=\frac{-43}{30}\)
6. \(+\left(\frac{-7}{-6}\right) +\left(\frac{8}{7}\right) -\left(\frac{10}{-7}\right)\\= \frac{7}{6}+ \frac{8}{7}+\frac{10}{7}\\=\frac{49}{42}+\frac{48}{42}+\frac{60}{42}\\=\frac{49+48+60}{42}\\=\frac{157}{42}\)
7. \(-\left(\frac{9}{-7}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-12}{11}\right)\\= \frac{9}{7}+ \frac{8}{8}-\frac{12}{11}\\=\frac{9}{7}+\frac{1}{1}-\frac{12}{11}\\=\frac{99}{77}+\frac{77}{77}-\frac{84}{77}\\=\frac{99+77-84}{77}\\=\frac{92}{77}\)
8. \(-\left(\frac{3}{-5}\right) -\left(\frac{7}{-8}\right) -\left(\frac{7}{6}\right)\\= \frac{3}{5}+ \frac{7}{8}-\frac{7}{6}\\=\frac{72}{120}+\frac{105}{120}-\frac{140}{120}\\=\frac{72+105-140}{120}\\=\frac{37}{120}\)
9. \(-\left(\frac{4}{-7}\right) -\left(\frac{6}{-3}\right) +\left(\frac{-11}{-7}\right)\\= \frac{4}{7}+ \frac{6}{3}+\frac{11}{7}\\=\frac{4}{7}+\frac{2}{1}+\frac{11}{7}\\=\frac{4+2+11}{7}\\=\frac{17}{7}\)
10. \(-\left(\frac{2}{3}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{-9}{8}\right)\\= \frac{-2}{3}+ \frac{5}{10}-\frac{9}{8}\\=\frac{-2}{3}+\frac{1}{2}-\frac{9}{8}\\=\frac{-16}{24}+\frac{12}{24}-\frac{27}{24}\\=\frac{-16+12-27}{24}\\=\frac{-31}{24}\)
11. \(-\left(\frac{-2}{-9}\right) +\left(\frac{3}{10}\right) -\left(\frac{-8}{5}\right)\\= \frac{-2}{9}+ \frac{3}{10}+\frac{8}{5}\\=\frac{-20}{90}+\frac{27}{90}+\frac{144}{90}\\=\frac{-20+27+144}{90}\\=\frac{151}{90}\)
12. \(+\left(\frac{2}{-9}\right) +\left(\frac{10}{3}\right) -\left(\frac{5}{12}\right)\\= \frac{-2}{9}+ \frac{10}{3}-\frac{5}{12}\\=\frac{-8}{36}+\frac{120}{36}-\frac{15}{36}\\=\frac{-8+120-15}{36}\\=\frac{97}{36}\)