Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{7}\right) -\left(\frac{2}{-7}\right) -\left(\frac{7}{7}\right)\\= \frac{-5}{7}+ \frac{2}{7}-\frac{7}{7}\\=\frac{-5}{7}+\frac{2}{7}-\frac{1}{1}\\=\frac{-5+2-1}{7}\\=\frac{-4}{7}\)
2. \(-\left(\frac{-10}{-7}\right) -\left(\frac{8}{-9}\right) -\left(\frac{-3}{-3}\right)\\= \frac{-10}{7}+ \frac{8}{9}-\frac{3}{3}\\=\frac{-10}{7}+\frac{8}{9}-\frac{1}{1}\\=\frac{-90}{63}+\frac{56}{63}-\frac{63}{63}\\=\frac{-90+56-63}{63}\\=\frac{-97}{63}\)
3. \(-\left(\frac{3}{8}\right) -\left(\frac{4}{-6}\right) -\left(\frac{-2}{9}\right)\\= \frac{-3}{8}+ \frac{4}{6}+\frac{2}{9}\\=\frac{-3}{8}+\frac{2}{3}+\frac{2}{9}\\=\frac{-27}{72}+\frac{48}{72}+\frac{16}{72}\\=\frac{-27+48+16}{72}\\=\frac{37}{72}\)
4. \(+\left(\frac{3}{8}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{7}{6}\right)\\= \frac{3}{8}- \frac{7}{9}-\frac{7}{6}\\=\frac{27}{72}-\frac{56}{72}-\frac{84}{72}\\=\frac{27-56-84}{72}\\=\frac{-113}{72}\)
5. \(+\left(\frac{8}{-9}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{7}{-6}\right)\\= \frac{-8}{9}+ \frac{9}{4}+\frac{7}{6}\\=\frac{-32}{36}+\frac{81}{36}+\frac{42}{36}\\=\frac{-32+81+42}{36}\\=\frac{91}{36}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{-5}{4}\right)\\= \frac{3}{2}+ \frac{10}{9}+\frac{5}{4}\\=\frac{54}{36}+\frac{40}{36}+\frac{45}{36}\\=\frac{54+40+45}{36}\\=\frac{139}{36}\)
7. \(-\left(\frac{-8}{-9}\right) -\left(\frac{9}{-4}\right) +\left(\frac{10}{11}\right)\\= \frac{-8}{9}+ \frac{9}{4}+\frac{10}{11}\\=\frac{-352}{396}+\frac{891}{396}+\frac{360}{396}\\=\frac{-352+891+360}{396}\\=\frac{899}{396}\)
8. \(-\left(\frac{9}{-4}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{-5}{-3}\right)\\= \frac{9}{4}- \frac{2}{8}-\frac{5}{3}\\=\frac{9}{4}-\frac{1}{4}-\frac{5}{3}\\=\frac{27}{12}-\frac{3}{12}-\frac{20}{12}\\=\frac{27-3-20}{12}\\=\frac{4}{12}\\=\frac{1}{3}\)
9. \(+\left(\frac{-10}{3}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{-4}{-9}\right)\\= \frac{-10}{3}- \frac{3}{6}-\frac{4}{9}\\=\frac{-10}{3}-\frac{1}{2}-\frac{4}{9}\\=\frac{-60}{18}-\frac{9}{18}-\frac{8}{18}\\=\frac{-60-9-8}{18}\\=\frac{-77}{18}\)
10. \(-\left(\frac{9}{5}\right) +\left(\frac{8}{-3}\right) -\left(\frac{11}{-5}\right)\\= \frac{-9}{5}- \frac{8}{3}+\frac{11}{5}\\=\frac{-27}{15}-\frac{40}{15}+\frac{33}{15}\\=\frac{-27-40+33}{15}\\=\frac{-34}{15}\)
11. \(-\left(\frac{-5}{7}\right) -\left(\frac{5}{-5}\right) -\left(\frac{-3}{3}\right)\\= \frac{5}{7}+ \frac{5}{5}+\frac{3}{3}\\=\frac{5}{7}+\frac{1}{1}+\frac{1}{1}\\=\frac{5+1+1}{7}\\=\frac{7}{7}\\=\frac{1}{1}\)
12. \(+\left(\frac{-2}{-7}\right) +\left(\frac{6}{9}\right) -\left(\frac{4}{-8}\right)\\= \frac{2}{7}+ \frac{6}{9}+\frac{4}{8}\\=\frac{2}{7}+\frac{2}{3}+\frac{1}{2}\\=\frac{12}{42}+\frac{28}{42}+\frac{21}{42}\\=\frac{12+28+21}{42}\\=\frac{61}{42}\)