Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-2}\right) +\left(\frac{-5}{7}\right) -\left(\frac{-2}{-12}\right)\\= \frac{-3}{2}- \frac{5}{7}-\frac{2}{12}\\=\frac{-3}{2}-\frac{5}{7}-\frac{1}{6}\\=\frac{-63}{42}-\frac{30}{42}-\frac{7}{42}\\=\frac{-63-30-7}{42}\\=\frac{-100}{42}\\=\frac{-50}{21}\)
2. \(+\left(\frac{-4}{-9}\right) +\left(\frac{7}{-7}\right) -\left(\frac{-5}{4}\right)\\= \frac{4}{9}- \frac{7}{7}+\frac{5}{4}\\=\frac{4}{9}-\frac{1}{1}+\frac{5}{4}\\=\frac{16}{36}-\frac{36}{36}+\frac{45}{36}\\=\frac{16-36+45}{36}\\=\frac{25}{36}\)
3. \(+\left(\frac{-3}{4}\right) +\left(\frac{10}{-2}\right) -\left(\frac{-4}{5}\right)\\= \frac{-3}{4}- \frac{10}{2}+\frac{4}{5}\\=\frac{-3}{4}-\frac{5}{1}+\frac{4}{5}\\=\frac{-15}{20}-\frac{100}{20}+\frac{16}{20}\\=\frac{-15-100+16}{20}\\=\frac{-99}{20}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-4}\right) -\left(\frac{-3}{-10}\right)\\= \frac{6}{5}- \frac{3}{4}-\frac{3}{10}\\=\frac{24}{20}-\frac{15}{20}-\frac{6}{20}\\=\frac{24-15-6}{20}\\=\frac{3}{20}\)
5. \(-\left(\frac{2}{-9}\right) +\left(\frac{4}{7}\right) -\left(\frac{6}{8}\right)\\= \frac{2}{9}+ \frac{4}{7}-\frac{6}{8}\\=\frac{2}{9}+\frac{4}{7}-\frac{3}{4}\\=\frac{56}{252}+\frac{144}{252}-\frac{189}{252}\\=\frac{56+144-189}{252}\\=\frac{11}{252}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{-8}{10}\right) -\left(\frac{12}{10}\right)\\= \frac{6}{5}+ \frac{8}{10}-\frac{12}{10}\\=\frac{6}{5}+\frac{4}{5}-\frac{6}{5}\\=\frac{6+4-6}{5}\\=\frac{4}{5}\)
7. \(-\left(\frac{-7}{3}\right) +\left(\frac{10}{-5}\right) +\left(\frac{5}{-7}\right)\\= \frac{7}{3}- \frac{10}{5}-\frac{5}{7}\\=\frac{7}{3}-\frac{2}{1}-\frac{5}{7}\\=\frac{49}{21}-\frac{42}{21}-\frac{15}{21}\\=\frac{49-42-15}{21}\\=\frac{-8}{21}\)
8. \(+\left(\frac{5}{6}\right) -\left(\frac{-8}{-3}\right) -\left(\frac{2}{-2}\right)\\= \frac{5}{6}- \frac{8}{3}+\frac{2}{2}\\=\frac{5}{6}-\frac{8}{3}+\frac{1}{1}\\=\frac{5-8+1}{6}\\=\frac{-2}{6}\\=\frac{-1}{3}\)
9. \(-\left(\frac{-6}{5}\right) +\left(\frac{10}{-6}\right) +\left(\frac{3}{11}\right)\\= \frac{6}{5}- \frac{10}{6}+\frac{3}{11}\\=\frac{6}{5}-\frac{5}{3}+\frac{3}{11}\\=\frac{198}{165}-\frac{275}{165}+\frac{45}{165}\\=\frac{198-275+45}{165}\\=\frac{-32}{165}\)
10. \(-\left(\frac{-5}{8}\right) +\left(\frac{8}{4}\right) +\left(\frac{-5}{8}\right)\\= \frac{5}{8}+ \frac{8}{4}-\frac{5}{8}\\=\frac{5}{8}+\frac{2}{1}-\frac{5}{8}\\=\frac{5+2-5}{8}\\=\frac{2}{8}\\=\frac{1}{4}\)
11. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{-11}{6}\right)\\= \frac{3}{7}+ \frac{6}{8}-\frac{11}{6}\\=\frac{3}{7}+\frac{3}{4}-\frac{11}{6}\\=\frac{36}{84}+\frac{63}{84}-\frac{154}{84}\\=\frac{36+63-154}{84}\\=\frac{-55}{84}\)
12. \(-\left(\frac{-5}{-2}\right) +\left(\frac{2}{3}\right) +\left(\frac{-12}{-12}\right)\\= \frac{-5}{2}+ \frac{2}{3}+\frac{12}{12}\\=\frac{-5}{2}+\frac{2}{3}+\frac{1}{1}\\=\frac{-15}{6}+\frac{4}{6}+\frac{6}{6}\\=\frac{-15+4+6}{6}\\=\frac{-5}{6}\)