Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{3}\right) -\left(\frac{-5}{3}\right) +\left(\frac{5}{-12}\right)\\= \frac{-8}{3}+ \frac{5}{3}-\frac{5}{12}\\=\frac{-32}{12}+\frac{20}{12}-\frac{5}{12}\\=\frac{-32+20-5}{12}\\=\frac{-17}{12}\)
2. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{5}{10}\right)\\= \frac{4}{7}- \frac{4}{2}+\frac{5}{10}\\=\frac{4}{7}-\frac{2}{1}+\frac{1}{2}\\=\frac{8}{14}-\frac{28}{14}+\frac{7}{14}\\=\frac{8-28+7}{14}\\=\frac{-13}{14}\)
3. \(+\left(\frac{-10}{7}\right) -\left(\frac{3}{10}\right) +\left(\frac{-3}{8}\right)\\= \frac{-10}{7}- \frac{3}{10}-\frac{3}{8}\\=\frac{-400}{280}-\frac{84}{280}-\frac{105}{280}\\=\frac{-400-84-105}{280}\\=\frac{-589}{280}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{-8}{-9}\right) +\left(\frac{9}{-11}\right)\\= \frac{-6}{5}+ \frac{8}{9}-\frac{9}{11}\\=\frac{-594}{495}+\frac{440}{495}-\frac{405}{495}\\=\frac{-594+440-405}{495}\\=\frac{-559}{495}\)
5. \(+\left(\frac{10}{3}\right) -\left(\frac{-6}{6}\right) +\left(\frac{-11}{8}\right)\\= \frac{10}{3}+ \frac{6}{6}-\frac{11}{8}\\=\frac{10}{3}+\frac{1}{1}-\frac{11}{8}\\=\frac{80}{24}+\frac{24}{24}-\frac{33}{24}\\=\frac{80+24-33}{24}\\=\frac{71}{24}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-6}{8}\right) +\left(\frac{12}{-3}\right)\\= \frac{3}{2}- \frac{6}{8}-\frac{12}{3}\\=\frac{3}{2}-\frac{3}{4}-\frac{4}{1}\\=\frac{6}{4}-\frac{3}{4}-\frac{16}{4}\\=\frac{6-3-16}{4}\\=\frac{-13}{4}\)
7. \(-\left(\frac{6}{-7}\right) -\left(\frac{8}{7}\right) -\left(\frac{6}{6}\right)\\= \frac{6}{7}- \frac{8}{7}-\frac{6}{6}\\=\frac{6}{7}-\frac{8}{7}-\frac{1}{1}\\=\frac{6-8-1}{7}\\=\frac{-3}{7}\)
8. \(+\left(\frac{-4}{-5}\right) -\left(\frac{5}{-8}\right) +\left(\frac{5}{4}\right)\\= \frac{4}{5}+ \frac{5}{8}+\frac{5}{4}\\=\frac{32}{40}+\frac{25}{40}+\frac{50}{40}\\=\frac{32+25+50}{40}\\=\frac{107}{40}\)
9. \(+\left(\frac{-7}{2}\right) -\left(\frac{5}{9}\right) -\left(\frac{4}{7}\right)\\= \frac{-7}{2}- \frac{5}{9}-\frac{4}{7}\\=\frac{-441}{126}-\frac{70}{126}-\frac{72}{126}\\=\frac{-441-70-72}{126}\\=\frac{-583}{126}\)
10. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-3}{5}\right) -\left(\frac{5}{-3}\right)\\= \frac{10}{3}- \frac{3}{5}+\frac{5}{3}\\=\frac{50}{15}-\frac{9}{15}+\frac{25}{15}\\=\frac{50-9+25}{15}\\=\frac{66}{15}\\=\frac{22}{5}\)
11. \(+\left(\frac{-4}{-3}\right) -\left(\frac{6}{10}\right) +\left(\frac{-5}{9}\right)\\= \frac{4}{3}- \frac{6}{10}-\frac{5}{9}\\=\frac{4}{3}-\frac{3}{5}-\frac{5}{9}\\=\frac{60}{45}-\frac{27}{45}-\frac{25}{45}\\=\frac{60-27-25}{45}\\=\frac{8}{45}\)
12. \(+\left(\frac{-3}{2}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{11}{-9}\right)\\= \frac{-3}{2}- \frac{10}{5}+\frac{11}{9}\\=\frac{-3}{2}-\frac{2}{1}+\frac{11}{9}\\=\frac{-27}{18}-\frac{36}{18}+\frac{22}{18}\\=\frac{-27-36+22}{18}\\=\frac{-41}{18}\)