Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-7}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{-3}{9}\right)\\= \frac{9}{7}- \frac{4}{2}-\frac{3}{9}\\=\frac{9}{7}-\frac{2}{1}-\frac{1}{3}\\=\frac{27}{21}-\frac{42}{21}-\frac{7}{21}\\=\frac{27-42-7}{21}\\=\frac{-22}{21}\)
2. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{-4}{-8}\right)\\= \frac{3}{2}+ \frac{6}{9}+\frac{4}{8}\\=\frac{3}{2}+\frac{2}{3}+\frac{1}{2}\\=\frac{9}{6}+\frac{4}{6}+\frac{3}{6}\\=\frac{9+4+3}{6}\\=\frac{16}{6}\\=\frac{8}{3}\)
3. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-8}{6}\right) -\left(\frac{-6}{8}\right)\\= \frac{-9}{2}- \frac{8}{6}+\frac{6}{8}\\=\frac{-9}{2}-\frac{4}{3}+\frac{3}{4}\\=\frac{-54}{12}-\frac{16}{12}+\frac{9}{12}\\=\frac{-54-16+9}{12}\\=\frac{-61}{12}\)
4. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{12}{-3}\right)\\= \frac{-6}{5}- \frac{4}{10}+\frac{12}{3}\\=\frac{-6}{5}-\frac{2}{5}+\frac{4}{1}\\=\frac{-6-2+4}{5}\\=\frac{-4}{5}\)
5. \(+\left(\frac{3}{-2}\right) +\left(\frac{5}{-4}\right) +\left(\frac{12}{-7}\right)\\= \frac{-3}{2}- \frac{5}{4}-\frac{12}{7}\\=\frac{-42}{28}-\frac{35}{28}-\frac{48}{28}\\=\frac{-42-35-48}{28}\\=\frac{-125}{28}\)
6. \(-\left(\frac{-6}{-7}\right) -\left(\frac{8}{-10}\right) -\left(\frac{-5}{-8}\right)\\= \frac{-6}{7}+ \frac{8}{10}-\frac{5}{8}\\=\frac{-6}{7}+\frac{4}{5}-\frac{5}{8}\\=\frac{-240}{280}+\frac{224}{280}-\frac{175}{280}\\=\frac{-240+224-175}{280}\\=\frac{-191}{280}\)
7. \(+\left(\frac{7}{3}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{-10}{7}\right)\\= \frac{7}{3}- \frac{3}{8}+\frac{10}{7}\\=\frac{392}{168}-\frac{63}{168}+\frac{240}{168}\\=\frac{392-63+240}{168}\\=\frac{569}{168}\)
8. \(+\left(\frac{-5}{8}\right) +\left(\frac{-3}{9}\right) -\left(\frac{-12}{-7}\right)\\= \frac{-5}{8}- \frac{3}{9}-\frac{12}{7}\\=\frac{-5}{8}-\frac{1}{3}-\frac{12}{7}\\=\frac{-105}{168}-\frac{56}{168}-\frac{288}{168}\\=\frac{-105-56-288}{168}\\=\frac{-449}{168}\)
9. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-7}{8}\right) +\left(\frac{9}{7}\right)\\= \frac{5}{2}+ \frac{7}{8}+\frac{9}{7}\\=\frac{140}{56}+\frac{49}{56}+\frac{72}{56}\\=\frac{140+49+72}{56}\\=\frac{261}{56}\)
10. \(-\left(\frac{4}{-5}\right) +\left(\frac{-2}{3}\right) -\left(\frac{-10}{11}\right)\\= \frac{4}{5}- \frac{2}{3}+\frac{10}{11}\\=\frac{132}{165}-\frac{110}{165}+\frac{150}{165}\\=\frac{132-110+150}{165}\\=\frac{172}{165}\)
11. \(-\left(\frac{9}{-5}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{-7}{-11}\right)\\= \frac{9}{5}+ \frac{9}{2}-\frac{7}{11}\\=\frac{198}{110}+\frac{495}{110}-\frac{70}{110}\\=\frac{198+495-70}{110}\\=\frac{623}{110}\)
12. \(+\left(\frac{3}{-4}\right) -\left(\frac{-9}{7}\right) +\left(\frac{-12}{10}\right)\\= \frac{-3}{4}+ \frac{9}{7}-\frac{12}{10}\\=\frac{-3}{4}+\frac{9}{7}-\frac{6}{5}\\=\frac{-105}{140}+\frac{180}{140}-\frac{168}{140}\\=\frac{-105+180-168}{140}\\=\frac{-93}{140}\)