Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{4}\right) +\left(\frac{-5}{-4}\right) -\left(\frac{-8}{8}\right)\\= \frac{-3}{4}+ \frac{5}{4}+\frac{8}{8}\\=\frac{-3}{4}+\frac{5}{4}+\frac{1}{1}\\=\frac{-3+5+1}{4}\\=\frac{3}{4}\)
2. \(+\left(\frac{5}{-7}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{10}{8}\right)\\= \frac{-5}{7}+ \frac{6}{3}-\frac{10}{8}\\=\frac{-5}{7}+\frac{2}{1}-\frac{5}{4}\\=\frac{-20}{28}+\frac{56}{28}-\frac{35}{28}\\=\frac{-20+56-35}{28}\\=\frac{1}{28}\)
3. \(+\left(\frac{9}{8}\right) +\left(\frac{7}{2}\right) +\left(\frac{-7}{9}\right)\\= \frac{9}{8}+ \frac{7}{2}-\frac{7}{9}\\=\frac{81}{72}+\frac{252}{72}-\frac{56}{72}\\=\frac{81+252-56}{72}\\=\frac{277}{72}\)
4. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-8}{8}\right) -\left(\frac{12}{-8}\right)\\= \frac{8}{5}+ \frac{8}{8}+\frac{12}{8}\\=\frac{8}{5}+\frac{1}{1}+\frac{3}{2}\\=\frac{16}{10}+\frac{10}{10}+\frac{15}{10}\\=\frac{16+10+15}{10}\\=\frac{41}{10}\)
5. \(-\left(\frac{-5}{2}\right) +\left(\frac{-2}{9}\right) +\left(\frac{5}{-12}\right)\\= \frac{5}{2}- \frac{2}{9}-\frac{5}{12}\\=\frac{90}{36}-\frac{8}{36}-\frac{15}{36}\\=\frac{90-8-15}{36}\\=\frac{67}{36}\)
6. \(+\left(\frac{9}{2}\right) -\left(\frac{-10}{-9}\right) -\left(\frac{-4}{-10}\right)\\= \frac{9}{2}- \frac{10}{9}-\frac{4}{10}\\=\frac{9}{2}-\frac{10}{9}-\frac{2}{5}\\=\frac{405}{90}-\frac{100}{90}-\frac{36}{90}\\=\frac{405-100-36}{90}\\=\frac{269}{90}\)
7. \(-\left(\frac{-6}{7}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{8}{-2}\right)\\= \frac{6}{7}+ \frac{6}{10}-\frac{8}{2}\\=\frac{6}{7}+\frac{3}{5}-\frac{4}{1}\\=\frac{30}{35}+\frac{21}{35}-\frac{140}{35}\\=\frac{30+21-140}{35}\\=\frac{-89}{35}\)
8. \(-\left(\frac{-4}{3}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{6}{3}\right)\\= \frac{4}{3}+ \frac{5}{3}-\frac{6}{3}\\=\frac{4}{3}+\frac{5}{3}-\frac{2}{1}\\=\frac{4+5-2}{3}\\=\frac{7}{3}\)
9. \(-\left(\frac{-3}{-4}\right) -\left(\frac{-3}{-2}\right) -\left(\frac{2}{-7}\right)\\= \frac{-3}{4}- \frac{3}{2}+\frac{2}{7}\\=\frac{-21}{28}-\frac{42}{28}+\frac{8}{28}\\=\frac{-21-42+8}{28}\\=\frac{-55}{28}\)
10. \(-\left(\frac{-10}{-7}\right) +\left(\frac{2}{3}\right) -\left(\frac{2}{12}\right)\\= \frac{-10}{7}+ \frac{2}{3}-\frac{2}{12}\\=\frac{-10}{7}+\frac{2}{3}-\frac{1}{6}\\=\frac{-60}{42}+\frac{28}{42}-\frac{7}{42}\\=\frac{-60+28-7}{42}\\=\frac{-39}{42}\\=\frac{-13}{14}\)
11. \(-\left(\frac{-9}{4}\right) +\left(\frac{-8}{6}\right) -\left(\frac{-8}{11}\right)\\= \frac{9}{4}- \frac{8}{6}+\frac{8}{11}\\=\frac{9}{4}-\frac{4}{3}+\frac{8}{11}\\=\frac{297}{132}-\frac{176}{132}+\frac{96}{132}\\=\frac{297-176+96}{132}\\=\frac{217}{132}\)
12. \(+\left(\frac{-3}{2}\right) +\left(\frac{4}{-10}\right) -\left(\frac{-8}{10}\right)\\= \frac{-3}{2}- \frac{4}{10}+\frac{8}{10}\\=\frac{-3}{2}-\frac{2}{5}+\frac{4}{5}\\=\frac{-15}{10}-\frac{4}{10}+\frac{8}{10}\\=\frac{-15-4+8}{10}\\=\frac{-11}{10}\)