Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{6}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{10}{11}\right)\\= \frac{5}{6}+ \frac{9}{2}-\frac{10}{11}\\=\frac{55}{66}+\frac{297}{66}-\frac{60}{66}\\=\frac{55+297-60}{66}\\=\frac{292}{66}\\=\frac{146}{33}\)
2. \(-\left(\frac{5}{4}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{3}{11}\right)\\= \frac{-5}{4}+ \frac{6}{5}+\frac{3}{11}\\=\frac{-275}{220}+\frac{264}{220}+\frac{60}{220}\\=\frac{-275+264+60}{220}\\=\frac{49}{220}\)
3. \(+\left(\frac{-7}{2}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{-5}{8}\right)\\= \frac{-7}{2}+ \frac{2}{8}-\frac{5}{8}\\=\frac{-7}{2}+\frac{1}{4}-\frac{5}{8}\\=\frac{-28}{8}+\frac{2}{8}-\frac{5}{8}\\=\frac{-28+2-5}{8}\\=\frac{-31}{8}\)
4. \(-\left(\frac{-10}{9}\right) +\left(\frac{9}{-9}\right) +\left(\frac{-12}{12}\right)\\= \frac{10}{9}- \frac{9}{9}-\frac{12}{12}\\=\frac{10}{9}-\frac{1}{1}-\frac{1}{1}\\=\frac{10-1-1}{9}\\=\frac{8}{9}\)
5. \(+\left(\frac{2}{3}\right) +\left(\frac{-10}{-2}\right) -\left(\frac{-3}{8}\right)\\= \frac{2}{3}+ \frac{10}{2}+\frac{3}{8}\\=\frac{2}{3}+\frac{5}{1}+\frac{3}{8}\\=\frac{16}{24}+\frac{120}{24}+\frac{9}{24}\\=\frac{16+120+9}{24}\\=\frac{145}{24}\)
6. \(+\left(\frac{4}{-3}\right) +\left(\frac{10}{2}\right) +\left(\frac{11}{-2}\right)\\= \frac{-4}{3}+ \frac{10}{2}-\frac{11}{2}\\=\frac{-4}{3}+\frac{5}{1}-\frac{11}{2}\\=\frac{-8}{6}+\frac{30}{6}-\frac{33}{6}\\=\frac{-8+30-33}{6}\\=\frac{-11}{6}\)
7. \(+\left(\frac{-8}{3}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{8}{-7}\right)\\= \frac{-8}{3}+ \frac{10}{6}-\frac{8}{7}\\=\frac{-8}{3}+\frac{5}{3}-\frac{8}{7}\\=\frac{-56}{21}+\frac{35}{21}-\frac{24}{21}\\=\frac{-56+35-24}{21}\\=\frac{-45}{21}\\=\frac{-15}{7}\)
8. \(-\left(\frac{3}{7}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-2}{-8}\right)\\= \frac{-3}{7}- \frac{10}{5}-\frac{2}{8}\\=\frac{-3}{7}-\frac{2}{1}-\frac{1}{4}\\=\frac{-12}{28}-\frac{56}{28}-\frac{7}{28}\\=\frac{-12-56-7}{28}\\=\frac{-75}{28}\)
9. \(+\left(\frac{-9}{-7}\right) -\left(\frac{-5}{5}\right) -\left(\frac{-3}{12}\right)\\= \frac{9}{7}+ \frac{5}{5}+\frac{3}{12}\\=\frac{9}{7}+\frac{1}{1}+\frac{1}{4}\\=\frac{36}{28}+\frac{28}{28}+\frac{7}{28}\\=\frac{36+28+7}{28}\\=\frac{71}{28}\)
10. \(+\left(\frac{7}{3}\right) +\left(\frac{6}{-8}\right) -\left(\frac{9}{2}\right)\\= \frac{7}{3}- \frac{6}{8}-\frac{9}{2}\\=\frac{7}{3}-\frac{3}{4}-\frac{9}{2}\\=\frac{28}{12}-\frac{9}{12}-\frac{54}{12}\\=\frac{28-9-54}{12}\\=\frac{-35}{12}\)
11. \(-\left(\frac{8}{-7}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{10}{11}\right)\\= \frac{8}{7}- \frac{10}{8}+\frac{10}{11}\\=\frac{8}{7}-\frac{5}{4}+\frac{10}{11}\\=\frac{352}{308}-\frac{385}{308}+\frac{280}{308}\\=\frac{352-385+280}{308}\\=\frac{247}{308}\)
12. \(-\left(\frac{9}{2}\right) +\left(\frac{-8}{2}\right) -\left(\frac{12}{-12}\right)\\= \frac{-9}{2}- \frac{8}{2}+\frac{12}{12}\\=\frac{-9}{2}-\frac{4}{1}+\frac{1}{1}\\=\frac{-9-4+1}{2}\\=\frac{-12}{2}\\=\frac{-6}{1}\)