Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{7}\right) -\left(\frac{-2}{7}\right) +\left(\frac{5}{2}\right)\\= \frac{-2}{7}+ \frac{2}{7}+\frac{5}{2}\\=\frac{-4}{14}+\frac{4}{14}+\frac{35}{14}\\=\frac{-4+4+35}{14}\\=\frac{35}{14}\\=\frac{5}{2}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{9}{-4}\right) -\left(\frac{6}{10}\right)\\= \frac{6}{5}- \frac{9}{4}-\frac{6}{10}\\=\frac{6}{5}-\frac{9}{4}-\frac{3}{5}\\=\frac{24}{20}-\frac{45}{20}-\frac{12}{20}\\=\frac{24-45-12}{20}\\=\frac{-33}{20}\)
3. \(+\left(\frac{4}{7}\right) +\left(\frac{2}{-3}\right) -\left(\frac{7}{-12}\right)\\= \frac{4}{7}- \frac{2}{3}+\frac{7}{12}\\=\frac{48}{84}-\frac{56}{84}+\frac{49}{84}\\=\frac{48-56+49}{84}\\=\frac{41}{84}\)
4. \(-\left(\frac{4}{-3}\right) +\left(\frac{10}{3}\right) -\left(\frac{11}{-9}\right)\\= \frac{4}{3}+ \frac{10}{3}+\frac{11}{9}\\=\frac{12}{9}+\frac{30}{9}+\frac{11}{9}\\=\frac{12+30+11}{9}\\=\frac{53}{9}\)
5. \(+\left(\frac{6}{-5}\right) +\left(\frac{9}{-9}\right) +\left(\frac{-10}{7}\right)\\= \frac{-6}{5}- \frac{9}{9}-\frac{10}{7}\\=\frac{-6}{5}-\frac{1}{1}-\frac{10}{7}\\=\frac{-42}{35}-\frac{35}{35}-\frac{50}{35}\\=\frac{-42-35-50}{35}\\=\frac{-127}{35}\)
6. \(+\left(\frac{-4}{9}\right) +\left(\frac{8}{2}\right) +\left(\frac{12}{5}\right)\\= \frac{-4}{9}+ \frac{8}{2}+\frac{12}{5}\\=\frac{-4}{9}+\frac{4}{1}+\frac{12}{5}\\=\frac{-20}{45}+\frac{180}{45}+\frac{108}{45}\\=\frac{-20+180+108}{45}\\=\frac{268}{45}\)
7. \(+\left(\frac{8}{-3}\right) +\left(\frac{-10}{10}\right) -\left(\frac{8}{2}\right)\\= \frac{-8}{3}- \frac{10}{10}-\frac{8}{2}\\=\frac{-8}{3}-\frac{1}{1}-\frac{4}{1}\\=\frac{-8-1-4}{3}\\=\frac{-13}{3}\)
8. \(+\left(\frac{2}{3}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-8}{-5}\right)\\= \frac{2}{3}+ \frac{8}{10}-\frac{8}{5}\\=\frac{2}{3}+\frac{4}{5}-\frac{8}{5}\\=\frac{10}{15}+\frac{12}{15}-\frac{24}{15}\\=\frac{10+12-24}{15}\\=\frac{-2}{15}\)
9. \(+\left(\frac{-8}{3}\right) +\left(\frac{2}{-7}\right) +\left(\frac{-3}{-6}\right)\\= \frac{-8}{3}- \frac{2}{7}+\frac{3}{6}\\=\frac{-8}{3}-\frac{2}{7}+\frac{1}{2}\\=\frac{-112}{42}-\frac{12}{42}+\frac{21}{42}\\=\frac{-112-12+21}{42}\\=\frac{-103}{42}\)
10. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{12}{-2}\right)\\= \frac{-6}{5}+ \frac{9}{9}-\frac{12}{2}\\=\frac{-6}{5}+\frac{1}{1}-\frac{6}{1}\\=\frac{-6+1-6}{5}\\=\frac{-11}{5}\)
11. \(+\left(\frac{2}{3}\right) +\left(\frac{5}{-5}\right) +\left(\frac{-11}{-6}\right)\\= \frac{2}{3}- \frac{5}{5}+\frac{11}{6}\\=\frac{2}{3}-\frac{1}{1}+\frac{11}{6}\\=\frac{4}{6}-\frac{6}{6}+\frac{11}{6}\\=\frac{4-6+11}{6}\\=\frac{9}{6}\\=\frac{3}{2}\)
12. \(+\left(\frac{-9}{2}\right) +\left(\frac{-10}{10}\right) +\left(\frac{-2}{-3}\right)\\= \frac{-9}{2}- \frac{10}{10}+\frac{2}{3}\\=\frac{-9}{2}-\frac{1}{1}+\frac{2}{3}\\=\frac{-27}{6}-\frac{6}{6}+\frac{4}{6}\\=\frac{-27-6+4}{6}\\=\frac{-29}{6}\)