Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-7}\right) -\left(\frac{6}{-10}\right) -\left(\frac{-6}{6}\right)\\= \frac{5}{7}+ \frac{6}{10}+\frac{6}{6}\\=\frac{5}{7}+\frac{3}{5}+\frac{1}{1}\\=\frac{25}{35}+\frac{21}{35}+\frac{35}{35}\\=\frac{25+21+35}{35}\\=\frac{81}{35}\)
2. \(-\left(\frac{-9}{7}\right) -\left(\frac{2}{-5}\right) +\left(\frac{5}{2}\right)\\= \frac{9}{7}+ \frac{2}{5}+\frac{5}{2}\\=\frac{90}{70}+\frac{28}{70}+\frac{175}{70}\\=\frac{90+28+175}{70}\\=\frac{293}{70}\)
3. \(+\left(\frac{-5}{7}\right) -\left(\frac{-8}{2}\right) -\left(\frac{12}{7}\right)\\= \frac{-5}{7}+ \frac{8}{2}-\frac{12}{7}\\=\frac{-5}{7}+\frac{4}{1}-\frac{12}{7}\\=\frac{-5+4-12}{7}\\=\frac{-13}{7}\)
4. \(+\left(\frac{-5}{8}\right) +\left(\frac{6}{3}\right) +\left(\frac{-2}{-7}\right)\\= \frac{-5}{8}+ \frac{6}{3}+\frac{2}{7}\\=\frac{-5}{8}+\frac{2}{1}+\frac{2}{7}\\=\frac{-35}{56}+\frac{112}{56}+\frac{16}{56}\\=\frac{-35+112+16}{56}\\=\frac{93}{56}\)
5. \(+\left(\frac{-5}{-4}\right) -\left(\frac{9}{10}\right) -\left(\frac{8}{11}\right)\\= \frac{5}{4}- \frac{9}{10}-\frac{8}{11}\\=\frac{275}{220}-\frac{198}{220}-\frac{160}{220}\\=\frac{275-198-160}{220}\\=\frac{-83}{220}\)
6. \(+\left(\frac{8}{-9}\right) -\left(\frac{5}{-7}\right) +\left(\frac{-4}{-6}\right)\\= \frac{-8}{9}+ \frac{5}{7}+\frac{4}{6}\\=\frac{-8}{9}+\frac{5}{7}+\frac{2}{3}\\=\frac{-56}{63}+\frac{45}{63}+\frac{42}{63}\\=\frac{-56+45+42}{63}\\=\frac{31}{63}\)
7. \(+\left(\frac{3}{4}\right) +\left(\frac{7}{9}\right) -\left(\frac{-8}{-5}\right)\\= \frac{3}{4}+ \frac{7}{9}-\frac{8}{5}\\=\frac{135}{180}+\frac{140}{180}-\frac{288}{180}\\=\frac{135+140-288}{180}\\=\frac{-13}{180}\)
8. \(+\left(\frac{-6}{7}\right) -\left(\frac{2}{2}\right) +\left(\frac{-5}{10}\right)\\= \frac{-6}{7}- \frac{2}{2}-\frac{5}{10}\\=\frac{-6}{7}-\frac{1}{1}-\frac{1}{2}\\=\frac{-12}{14}-\frac{14}{14}-\frac{7}{14}\\=\frac{-12-14-7}{14}\\=\frac{-33}{14}\)
9. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{11}{-3}\right)\\= \frac{-8}{3}+ \frac{4}{7}+\frac{11}{3}\\=\frac{-56}{21}+\frac{12}{21}+\frac{77}{21}\\=\frac{-56+12+77}{21}\\=\frac{33}{21}\\=\frac{11}{7}\)
10. \(-\left(\frac{7}{-2}\right) +\left(\frac{7}{-9}\right) -\left(\frac{11}{-5}\right)\\= \frac{7}{2}- \frac{7}{9}+\frac{11}{5}\\=\frac{315}{90}-\frac{70}{90}+\frac{198}{90}\\=\frac{315-70+198}{90}\\=\frac{443}{90}\)
11. \(-\left(\frac{-5}{9}\right) +\left(\frac{-6}{2}\right) +\left(\frac{-8}{7}\right)\\= \frac{5}{9}- \frac{6}{2}-\frac{8}{7}\\=\frac{5}{9}-\frac{3}{1}-\frac{8}{7}\\=\frac{35}{63}-\frac{189}{63}-\frac{72}{63}\\=\frac{35-189-72}{63}\\=\frac{-226}{63}\)
12. \(-\left(\frac{7}{8}\right) +\left(\frac{-5}{-2}\right) +\left(\frac{8}{-2}\right)\\= \frac{-7}{8}+ \frac{5}{2}-\frac{8}{2}\\=\frac{-7}{8}+\frac{5}{2}-\frac{4}{1}\\=\frac{-7+5-4}{8}\\=\frac{-6}{8}\\=\frac{-3}{4}\)