Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-5}\right) +\left(\frac{3}{3}\right) -\left(\frac{6}{8}\right)\\= \frac{-2}{5}+ \frac{3}{3}-\frac{6}{8}\\=\frac{-2}{5}+\frac{1}{1}-\frac{3}{4}\\=\frac{-8}{20}+\frac{20}{20}-\frac{15}{20}\\=\frac{-8+20-15}{20}\\=\frac{-3}{20}\)
2. \(+\left(\frac{5}{-3}\right) +\left(\frac{8}{10}\right) +\left(\frac{10}{10}\right)\\= \frac{-5}{3}+ \frac{8}{10}+\frac{10}{10}\\=\frac{-5}{3}+\frac{4}{5}+\frac{1}{1}\\=\frac{-25}{15}+\frac{12}{15}+\frac{15}{15}\\=\frac{-25+12+15}{15}\\=\frac{2}{15}\)
3. \(-\left(\frac{-7}{-2}\right) -\left(\frac{4}{10}\right) +\left(\frac{-2}{7}\right)\\= \frac{-7}{2}- \frac{4}{10}-\frac{2}{7}\\=\frac{-7}{2}-\frac{2}{5}-\frac{2}{7}\\=\frac{-245}{70}-\frac{28}{70}-\frac{20}{70}\\=\frac{-245-28-20}{70}\\=\frac{-293}{70}\)
4. \(-\left(\frac{2}{3}\right) +\left(\frac{-5}{-7}\right) +\left(\frac{-12}{7}\right)\\= \frac{-2}{3}+ \frac{5}{7}-\frac{12}{7}\\=\frac{-14}{21}+\frac{15}{21}-\frac{36}{21}\\=\frac{-14+15-36}{21}\\=\frac{-35}{21}\\=\frac{-5}{3}\)
5. \(-\left(\frac{-10}{9}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-8}{7}\right)\\= \frac{10}{9}- \frac{8}{9}-\frac{8}{7}\\=\frac{70}{63}-\frac{56}{63}-\frac{72}{63}\\=\frac{70-56-72}{63}\\=\frac{-58}{63}\)
6. \(+\left(\frac{-6}{7}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{-4}{-2}\right)\\= \frac{-6}{7}- \frac{2}{8}-\frac{4}{2}\\=\frac{-6}{7}-\frac{1}{4}-\frac{2}{1}\\=\frac{-24}{28}-\frac{7}{28}-\frac{56}{28}\\=\frac{-24-7-56}{28}\\=\frac{-87}{28}\)
7. \(-\left(\frac{5}{2}\right) +\left(\frac{5}{-10}\right) -\left(\frac{3}{12}\right)\\= \frac{-5}{2}- \frac{5}{10}-\frac{3}{12}\\=\frac{-5}{2}-\frac{1}{2}-\frac{1}{4}\\=\frac{-10}{4}-\frac{2}{4}-\frac{1}{4}\\=\frac{-10-2-1}{4}\\=\frac{-13}{4}\)
8. \(-\left(\frac{4}{3}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-12}{-2}\right)\\= \frac{-4}{3}- \frac{10}{5}-\frac{12}{2}\\=\frac{-4}{3}-\frac{2}{1}-\frac{6}{1}\\=\frac{-4-2-6}{3}\\=\frac{-12}{3}\\=\frac{-4}{1}\)
9. \(+\left(\frac{4}{5}\right) -\left(\frac{9}{4}\right) +\left(\frac{2}{-11}\right)\\= \frac{4}{5}- \frac{9}{4}-\frac{2}{11}\\=\frac{176}{220}-\frac{495}{220}-\frac{40}{220}\\=\frac{176-495-40}{220}\\=\frac{-359}{220}\)
10. \(-\left(\frac{-5}{-8}\right) +\left(\frac{4}{-4}\right) +\left(\frac{3}{-12}\right)\\= \frac{-5}{8}- \frac{4}{4}-\frac{3}{12}\\=\frac{-5}{8}-\frac{1}{1}-\frac{1}{4}\\=\frac{-5-1-1}{8}\\=\frac{-7}{8}\)
11. \(+\left(\frac{-4}{3}\right) +\left(\frac{-7}{2}\right) -\left(\frac{11}{-5}\right)\\= \frac{-4}{3}- \frac{7}{2}+\frac{11}{5}\\=\frac{-40}{30}-\frac{105}{30}+\frac{66}{30}\\=\frac{-40-105+66}{30}\\=\frac{-79}{30}\)
12. \(+\left(\frac{2}{3}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{-3}{-11}\right)\\= \frac{2}{3}+ \frac{8}{6}+\frac{3}{11}\\=\frac{2}{3}+\frac{4}{3}+\frac{3}{11}\\=\frac{22}{33}+\frac{44}{33}+\frac{9}{33}\\=\frac{22+44+9}{33}\\=\frac{75}{33}\\=\frac{25}{11}\)