Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{9}\right) +\left(\frac{7}{2}\right) +\left(\frac{8}{-3}\right)\\= \frac{-2}{9}+ \frac{7}{2}-\frac{8}{3}\\=\frac{-4}{18}+\frac{63}{18}-\frac{48}{18}\\=\frac{-4+63-48}{18}\\=\frac{11}{18}\)
2. \(+\left(\frac{10}{-9}\right) +\left(\frac{-5}{9}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-10}{9}- \frac{5}{9}-\frac{5}{3}\\=\frac{-10-5-5}{9}\\=\frac{-20}{9}\)
3. \(-\left(\frac{-9}{-2}\right) +\left(\frac{6}{-7}\right) +\left(\frac{2}{5}\right)\\= \frac{-9}{2}- \frac{6}{7}+\frac{2}{5}\\=\frac{-315}{70}-\frac{60}{70}+\frac{28}{70}\\=\frac{-315-60+28}{70}\\=\frac{-347}{70}\)
4. \(-\left(\frac{-7}{-8}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-7}{-5}\right)\\= \frac{-7}{8}+ \frac{4}{8}+\frac{7}{5}\\=\frac{-7}{8}+\frac{1}{2}+\frac{7}{5}\\=\frac{-35}{40}+\frac{20}{40}+\frac{56}{40}\\=\frac{-35+20+56}{40}\\=\frac{41}{40}\)
5. \(-\left(\frac{-8}{-5}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{-11}{-7}\right)\\= \frac{-8}{5}- \frac{10}{10}-\frac{11}{7}\\=\frac{-8}{5}-\frac{1}{1}-\frac{11}{7}\\=\frac{-56}{35}-\frac{35}{35}-\frac{55}{35}\\=\frac{-56-35-55}{35}\\=\frac{-146}{35}\)
6. \(-\left(\frac{-8}{-7}\right) +\left(\frac{2}{7}\right) +\left(\frac{-2}{4}\right)\\= \frac{-8}{7}+ \frac{2}{7}-\frac{2}{4}\\=\frac{-8}{7}+\frac{2}{7}-\frac{1}{2}\\=\frac{-16}{14}+\frac{4}{14}-\frac{7}{14}\\=\frac{-16+4-7}{14}\\=\frac{-19}{14}\)
7. \(-\left(\frac{7}{-2}\right) -\left(\frac{10}{-3}\right) -\left(\frac{12}{11}\right)\\= \frac{7}{2}+ \frac{10}{3}-\frac{12}{11}\\=\frac{231}{66}+\frac{220}{66}-\frac{72}{66}\\=\frac{231+220-72}{66}\\=\frac{379}{66}\)
8. \(+\left(\frac{-6}{-5}\right) +\left(\frac{5}{-3}\right) +\left(\frac{-11}{-5}\right)\\= \frac{6}{5}- \frac{5}{3}+\frac{11}{5}\\=\frac{18}{15}-\frac{25}{15}+\frac{33}{15}\\=\frac{18-25+33}{15}\\=\frac{26}{15}\)
9. \(-\left(\frac{8}{-7}\right) -\left(\frac{-7}{2}\right) +\left(\frac{-7}{10}\right)\\= \frac{8}{7}+ \frac{7}{2}-\frac{7}{10}\\=\frac{80}{70}+\frac{245}{70}-\frac{49}{70}\\=\frac{80+245-49}{70}\\=\frac{276}{70}\\=\frac{138}{35}\)
10. \(-\left(\frac{-4}{5}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{7}{-3}\right)\\= \frac{4}{5}+ \frac{5}{9}+\frac{7}{3}\\=\frac{36}{45}+\frac{25}{45}+\frac{105}{45}\\=\frac{36+25+105}{45}\\=\frac{166}{45}\)
11. \(+\left(\frac{-5}{-2}\right) +\left(\frac{2}{4}\right) +\left(\frac{6}{8}\right)\\= \frac{5}{2}+ \frac{2}{4}+\frac{6}{8}\\=\frac{5}{2}+\frac{1}{2}+\frac{3}{4}\\=\frac{10}{4}+\frac{2}{4}+\frac{3}{4}\\=\frac{10+2+3}{4}\\=\frac{15}{4}\)
12. \(-\left(\frac{-4}{9}\right) -\left(\frac{7}{-4}\right) +\left(\frac{2}{-8}\right)\\= \frac{4}{9}+ \frac{7}{4}-\frac{2}{8}\\=\frac{4}{9}+\frac{7}{4}-\frac{1}{4}\\=\frac{16}{36}+\frac{63}{36}-\frac{9}{36}\\=\frac{16+63-9}{36}\\=\frac{70}{36}\\=\frac{35}{18}\)