Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-2}\right) -\left(\frac{4}{-6}\right) +\left(\frac{5}{-4}\right)\\= \frac{7}{2}+ \frac{4}{6}-\frac{5}{4}\\=\frac{7}{2}+\frac{2}{3}-\frac{5}{4}\\=\frac{42}{12}+\frac{8}{12}-\frac{15}{12}\\=\frac{42+8-15}{12}\\=\frac{35}{12}\)
2. \(+\left(\frac{-4}{-5}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{-10}{-9}\right)\\= \frac{4}{5}+ \frac{3}{2}-\frac{10}{9}\\=\frac{72}{90}+\frac{135}{90}-\frac{100}{90}\\=\frac{72+135-100}{90}\\=\frac{107}{90}\)
3. \(-\left(\frac{2}{-9}\right) -\left(\frac{-10}{9}\right) -\left(\frac{2}{9}\right)\\= \frac{2}{9}+ \frac{10}{9}-\frac{2}{9}\\=\frac{2+10-2}{9}\\=\frac{10}{9}\)
4. \(-\left(\frac{-6}{7}\right) -\left(\frac{9}{-3}\right) +\left(\frac{11}{2}\right)\\= \frac{6}{7}+ \frac{9}{3}+\frac{11}{2}\\=\frac{6}{7}+\frac{3}{1}+\frac{11}{2}\\=\frac{12}{14}+\frac{42}{14}+\frac{77}{14}\\=\frac{12+42+77}{14}\\=\frac{131}{14}\)
5. \(-\left(\frac{4}{3}\right) +\left(\frac{2}{4}\right) +\left(\frac{2}{5}\right)\\= \frac{-4}{3}+ \frac{2}{4}+\frac{2}{5}\\=\frac{-4}{3}+\frac{1}{2}+\frac{2}{5}\\=\frac{-40}{30}+\frac{15}{30}+\frac{12}{30}\\=\frac{-40+15+12}{30}\\=\frac{-13}{30}\)
6. \(-\left(\frac{-10}{9}\right) -\left(\frac{-8}{3}\right) +\left(\frac{-11}{6}\right)\\= \frac{10}{9}+ \frac{8}{3}-\frac{11}{6}\\=\frac{20}{18}+\frac{48}{18}-\frac{33}{18}\\=\frac{20+48-33}{18}\\=\frac{35}{18}\)
7. \(-\left(\frac{3}{2}\right) -\left(\frac{7}{8}\right) +\left(\frac{12}{-4}\right)\\= \frac{-3}{2}- \frac{7}{8}-\frac{12}{4}\\=\frac{-3}{2}-\frac{7}{8}-\frac{3}{1}\\=\frac{-12}{8}-\frac{7}{8}-\frac{24}{8}\\=\frac{-12-7-24}{8}\\=\frac{-43}{8}\)
8. \(-\left(\frac{10}{7}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-10}{7}+ \frac{10}{9}-\frac{7}{11}\\=\frac{-990}{693}+\frac{770}{693}-\frac{441}{693}\\=\frac{-990+770-441}{693}\\=\frac{-661}{693}\)
9. \(-\left(\frac{-4}{-5}\right) -\left(\frac{5}{-7}\right) -\left(\frac{12}{-4}\right)\\= \frac{-4}{5}+ \frac{5}{7}+\frac{12}{4}\\=\frac{-4}{5}+\frac{5}{7}+\frac{3}{1}\\=\frac{-28}{35}+\frac{25}{35}+\frac{105}{35}\\=\frac{-28+25+105}{35}\\=\frac{102}{35}\)
10. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-6}{2}\right) -\left(\frac{9}{3}\right)\\= \frac{-10}{7}+ \frac{6}{2}-\frac{9}{3}\\=\frac{-10}{7}+\frac{3}{1}-\frac{3}{1}\\=\frac{-10+3-3}{7}\\=\frac{-10}{7}\)
11. \(+\left(\frac{-6}{7}\right) -\left(\frac{3}{-4}\right) +\left(\frac{-9}{4}\right)\\= \frac{-6}{7}+ \frac{3}{4}-\frac{9}{4}\\=\frac{-24}{28}+\frac{21}{28}-\frac{63}{28}\\=\frac{-24+21-63}{28}\\=\frac{-66}{28}\\=\frac{-33}{14}\)
12. \(+\left(\frac{6}{5}\right) -\left(\frac{10}{10}\right) +\left(\frac{9}{4}\right)\\= \frac{6}{5}- \frac{10}{10}+\frac{9}{4}\\=\frac{6}{5}-\frac{1}{1}+\frac{9}{4}\\=\frac{24}{20}-\frac{20}{20}+\frac{45}{20}\\=\frac{24-20+45}{20}\\=\frac{49}{20}\)