Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{3}\right) -\left(\frac{10}{-8}\right) -\left(\frac{-6}{2}\right)\\= \frac{-2}{3}+ \frac{10}{8}+\frac{6}{2}\\=\frac{-2}{3}+\frac{5}{4}+\frac{3}{1}\\=\frac{-8}{12}+\frac{15}{12}+\frac{36}{12}\\=\frac{-8+15+36}{12}\\=\frac{43}{12}\)
2. \(+\left(\frac{2}{-5}\right) +\left(\frac{3}{-9}\right) -\left(\frac{7}{-11}\right)\\= \frac{-2}{5}- \frac{3}{9}+\frac{7}{11}\\=\frac{-2}{5}-\frac{1}{3}+\frac{7}{11}\\=\frac{-66}{165}-\frac{55}{165}+\frac{105}{165}\\=\frac{-66-55+105}{165}\\=\frac{-16}{165}\)
3. \(+\left(\frac{-10}{-3}\right) +\left(\frac{8}{9}\right) +\left(\frac{-8}{-8}\right)\\= \frac{10}{3}+ \frac{8}{9}+\frac{8}{8}\\=\frac{10}{3}+\frac{8}{9}+\frac{1}{1}\\=\frac{30}{9}+\frac{8}{9}+\frac{9}{9}\\=\frac{30+8+9}{9}\\=\frac{47}{9}\)
4. \(+\left(\frac{-6}{5}\right) +\left(\frac{-4}{-2}\right) +\left(\frac{-10}{-11}\right)\\= \frac{-6}{5}+ \frac{4}{2}+\frac{10}{11}\\=\frac{-6}{5}+\frac{2}{1}+\frac{10}{11}\\=\frac{-66}{55}+\frac{110}{55}+\frac{50}{55}\\=\frac{-66+110+50}{55}\\=\frac{94}{55}\)
5. \(+\left(\frac{-4}{7}\right) -\left(\frac{-5}{-7}\right) +\left(\frac{9}{9}\right)\\= \frac{-4}{7}- \frac{5}{7}+\frac{9}{9}\\=\frac{-4}{7}-\frac{5}{7}+\frac{1}{1}\\=\frac{-4-5+1}{7}\\=\frac{-8}{7}\)
6. \(-\left(\frac{-7}{-9}\right) -\left(\frac{-8}{-4}\right) -\left(\frac{-12}{-2}\right)\\= \frac{-7}{9}- \frac{8}{4}-\frac{12}{2}\\=\frac{-7}{9}-\frac{2}{1}-\frac{6}{1}\\=\frac{-7-2-6}{9}\\=\frac{-15}{9}\\=\frac{-5}{3}\)
7. \(+\left(\frac{7}{8}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-7}{11}\right)\\= \frac{7}{8}- \frac{7}{8}-\frac{7}{11}\\=\frac{77}{88}-\frac{77}{88}-\frac{56}{88}\\=\frac{77-77-56}{88}\\=\frac{-56}{88}\\=\frac{-7}{11}\)
8. \(-\left(\frac{-4}{-9}\right) -\left(\frac{7}{3}\right) -\left(\frac{-4}{8}\right)\\= \frac{-4}{9}- \frac{7}{3}+\frac{4}{8}\\=\frac{-4}{9}-\frac{7}{3}+\frac{1}{2}\\=\frac{-8}{18}-\frac{42}{18}+\frac{9}{18}\\=\frac{-8-42+9}{18}\\=\frac{-41}{18}\)
9. \(-\left(\frac{8}{5}\right) -\left(\frac{-8}{6}\right) +\left(\frac{-6}{3}\right)\\= \frac{-8}{5}+ \frac{8}{6}-\frac{6}{3}\\=\frac{-8}{5}+\frac{4}{3}-\frac{2}{1}\\=\frac{-24}{15}+\frac{20}{15}-\frac{30}{15}\\=\frac{-24+20-30}{15}\\=\frac{-34}{15}\)
10. \(-\left(\frac{-3}{7}\right) -\left(\frac{-7}{3}\right) +\left(\frac{5}{-11}\right)\\= \frac{3}{7}+ \frac{7}{3}-\frac{5}{11}\\=\frac{99}{231}+\frac{539}{231}-\frac{105}{231}\\=\frac{99+539-105}{231}\\=\frac{533}{231}\)
11. \(-\left(\frac{-6}{5}\right) -\left(\frac{7}{-5}\right) -\left(\frac{12}{-5}\right)\\= \frac{6}{5}+ \frac{7}{5}+\frac{12}{5}\\=\frac{6+7+12}{5}\\=\frac{25}{5}\\=\frac{5}{1}\)
12. \(-\left(\frac{8}{9}\right) -\left(\frac{-2}{2}\right) +\left(\frac{3}{4}\right)\\= \frac{-8}{9}+ \frac{2}{2}+\frac{3}{4}\\=\frac{-8}{9}+\frac{1}{1}+\frac{3}{4}\\=\frac{-32}{36}+\frac{36}{36}+\frac{27}{36}\\=\frac{-32+36+27}{36}\\=\frac{31}{36}\)