Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{9}\right) -\left(\frac{-2}{5}\right) +\left(\frac{12}{6}\right)\\= \frac{-2}{9}+ \frac{2}{5}+\frac{12}{6}\\=\frac{-2}{9}+\frac{2}{5}+\frac{2}{1}\\=\frac{-10}{45}+\frac{18}{45}+\frac{90}{45}\\=\frac{-10+18+90}{45}\\=\frac{98}{45}\)
2. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-10}{7}\right) -\left(\frac{-3}{-8}\right)\\= \frac{9}{2}+ \frac{10}{7}-\frac{3}{8}\\=\frac{252}{56}+\frac{80}{56}-\frac{21}{56}\\=\frac{252+80-21}{56}\\=\frac{311}{56}\)
3. \(+\left(\frac{-3}{8}\right) +\left(\frac{2}{8}\right) +\left(\frac{-3}{-11}\right)\\= \frac{-3}{8}+ \frac{2}{8}+\frac{3}{11}\\=\frac{-3}{8}+\frac{1}{4}+\frac{3}{11}\\=\frac{-33}{88}+\frac{22}{88}+\frac{24}{88}\\=\frac{-33+22+24}{88}\\=\frac{13}{88}\)
4. \(-\left(\frac{9}{-2}\right) +\left(\frac{-10}{5}\right) +\left(\frac{-2}{7}\right)\\= \frac{9}{2}- \frac{10}{5}-\frac{2}{7}\\=\frac{9}{2}-\frac{2}{1}-\frac{2}{7}\\=\frac{63}{14}-\frac{28}{14}-\frac{4}{14}\\=\frac{63-28-4}{14}\\=\frac{31}{14}\)
5. \(+\left(\frac{2}{9}\right) +\left(\frac{5}{6}\right) +\left(\frac{-8}{-4}\right)\\= \frac{2}{9}+ \frac{5}{6}+\frac{8}{4}\\=\frac{2}{9}+\frac{5}{6}+\frac{2}{1}\\=\frac{4}{18}+\frac{15}{18}+\frac{36}{18}\\=\frac{4+15+36}{18}\\=\frac{55}{18}\)
6. \(+\left(\frac{9}{2}\right) -\left(\frac{3}{8}\right) +\left(\frac{-7}{8}\right)\\= \frac{9}{2}- \frac{3}{8}-\frac{7}{8}\\=\frac{36}{8}-\frac{3}{8}-\frac{7}{8}\\=\frac{36-3-7}{8}\\=\frac{26}{8}\\=\frac{13}{4}\)
7. \(-\left(\frac{8}{3}\right) -\left(\frac{8}{-6}\right) +\left(\frac{9}{3}\right)\\= \frac{-8}{3}+ \frac{8}{6}+\frac{9}{3}\\=\frac{-8}{3}+\frac{4}{3}+\frac{3}{1}\\=\frac{-8+4+3}{3}\\=\frac{-1}{3}\)
8. \(+\left(\frac{-9}{-2}\right) +\left(\frac{4}{-5}\right) +\left(\frac{-8}{6}\right)\\= \frac{9}{2}- \frac{4}{5}-\frac{8}{6}\\=\frac{9}{2}-\frac{4}{5}-\frac{4}{3}\\=\frac{135}{30}-\frac{24}{30}-\frac{40}{30}\\=\frac{135-24-40}{30}\\=\frac{71}{30}\)
9. \(-\left(\frac{9}{-4}\right) -\left(\frac{-10}{2}\right) -\left(\frac{3}{-12}\right)\\= \frac{9}{4}+ \frac{10}{2}+\frac{3}{12}\\=\frac{9}{4}+\frac{5}{1}+\frac{1}{4}\\=\frac{9+5+1}{4}\\=\frac{15}{4}\)
10. \(-\left(\frac{-9}{-4}\right) +\left(\frac{6}{-5}\right) -\left(\frac{10}{5}\right)\\= \frac{-9}{4}- \frac{6}{5}-\frac{10}{5}\\=\frac{-9}{4}-\frac{6}{5}-\frac{2}{1}\\=\frac{-45}{20}-\frac{24}{20}-\frac{40}{20}\\=\frac{-45-24-40}{20}\\=\frac{-109}{20}\)
11. \(-\left(\frac{3}{2}\right) -\left(\frac{4}{-3}\right) -\left(\frac{-9}{-9}\right)\\= \frac{-3}{2}+ \frac{4}{3}-\frac{9}{9}\\=\frac{-3}{2}+\frac{4}{3}-\frac{1}{1}\\=\frac{-9}{6}+\frac{8}{6}-\frac{6}{6}\\=\frac{-9+8-6}{6}\\=\frac{-7}{6}\)
12. \(+\left(\frac{-9}{2}\right) +\left(\frac{8}{10}\right) +\left(\frac{-12}{-7}\right)\\= \frac{-9}{2}+ \frac{8}{10}+\frac{12}{7}\\=\frac{-9}{2}+\frac{4}{5}+\frac{12}{7}\\=\frac{-315}{70}+\frac{56}{70}+\frac{120}{70}\\=\frac{-315+56+120}{70}\\=\frac{-139}{70}\)