Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{9}\right) +\left(\frac{7}{7}\right) -\left(\frac{3}{10}\right)\\= \frac{-4}{9}+ \frac{7}{7}-\frac{3}{10}\\=\frac{-4}{9}+\frac{1}{1}-\frac{3}{10}\\=\frac{-40}{90}+\frac{90}{90}-\frac{27}{90}\\=\frac{-40+90-27}{90}\\=\frac{23}{90}\)
2. \(+\left(\frac{8}{-5}\right) -\left(\frac{4}{-7}\right) +\left(\frac{8}{-6}\right)\\= \frac{-8}{5}+ \frac{4}{7}-\frac{8}{6}\\=\frac{-8}{5}+\frac{4}{7}-\frac{4}{3}\\=\frac{-168}{105}+\frac{60}{105}-\frac{140}{105}\\=\frac{-168+60-140}{105}\\=\frac{-248}{105}\)
3. \(+\left(\frac{8}{-9}\right) +\left(\frac{-5}{2}\right) -\left(\frac{-11}{5}\right)\\= \frac{-8}{9}- \frac{5}{2}+\frac{11}{5}\\=\frac{-80}{90}-\frac{225}{90}+\frac{198}{90}\\=\frac{-80-225+198}{90}\\=\frac{-107}{90}\)
4. \(+\left(\frac{-9}{2}\right) +\left(\frac{5}{-3}\right) +\left(\frac{7}{5}\right)\\= \frac{-9}{2}- \frac{5}{3}+\frac{7}{5}\\=\frac{-135}{30}-\frac{50}{30}+\frac{42}{30}\\=\frac{-135-50+42}{30}\\=\frac{-143}{30}\)
5. \(+\left(\frac{4}{5}\right) -\left(\frac{2}{8}\right) -\left(\frac{5}{2}\right)\\= \frac{4}{5}- \frac{2}{8}-\frac{5}{2}\\=\frac{4}{5}-\frac{1}{4}-\frac{5}{2}\\=\frac{16}{20}-\frac{5}{20}-\frac{50}{20}\\=\frac{16-5-50}{20}\\=\frac{-39}{20}\)
6. \(-\left(\frac{-6}{-5}\right) -\left(\frac{8}{-7}\right) +\left(\frac{6}{6}\right)\\= \frac{-6}{5}+ \frac{8}{7}+\frac{6}{6}\\=\frac{-6}{5}+\frac{8}{7}+\frac{1}{1}\\=\frac{-42}{35}+\frac{40}{35}+\frac{35}{35}\\=\frac{-42+40+35}{35}\\=\frac{33}{35}\)
7. \(-\left(\frac{-4}{9}\right) +\left(\frac{-4}{9}\right) -\left(\frac{-3}{-2}\right)\\= \frac{4}{9}- \frac{4}{9}-\frac{3}{2}\\=\frac{8}{18}-\frac{8}{18}-\frac{27}{18}\\=\frac{8-8-27}{18}\\=\frac{-27}{18}\\=\frac{-3}{2}\)
8. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-6}{4}\right) +\left(\frac{3}{5}\right)\\= \frac{2}{3}- \frac{6}{4}+\frac{3}{5}\\=\frac{2}{3}-\frac{3}{2}+\frac{3}{5}\\=\frac{20}{30}-\frac{45}{30}+\frac{18}{30}\\=\frac{20-45+18}{30}\\=\frac{-7}{30}\)
9. \(-\left(\frac{10}{-3}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{-9}{10}\right)\\= \frac{10}{3}+ \frac{6}{3}+\frac{9}{10}\\=\frac{10}{3}+\frac{2}{1}+\frac{9}{10}\\=\frac{100}{30}+\frac{60}{30}+\frac{27}{30}\\=\frac{100+60+27}{30}\\=\frac{187}{30}\)
10. \(+\left(\frac{-4}{9}\right) +\left(\frac{-4}{-7}\right) +\left(\frac{-3}{-2}\right)\\= \frac{-4}{9}+ \frac{4}{7}+\frac{3}{2}\\=\frac{-56}{126}+\frac{72}{126}+\frac{189}{126}\\=\frac{-56+72+189}{126}\\=\frac{205}{126}\)
11. \(+\left(\frac{-5}{7}\right) +\left(\frac{-7}{-9}\right) -\left(\frac{-11}{5}\right)\\= \frac{-5}{7}+ \frac{7}{9}+\frac{11}{5}\\=\frac{-225}{315}+\frac{245}{315}+\frac{693}{315}\\=\frac{-225+245+693}{315}\\=\frac{713}{315}\)
12. \(+\left(\frac{2}{9}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{4}{-9}\right)\\= \frac{2}{9}- \frac{3}{10}-\frac{4}{9}\\=\frac{20}{90}-\frac{27}{90}-\frac{40}{90}\\=\frac{20-27-40}{90}\\=\frac{-47}{90}\)