Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-7}\right) -\left(\frac{7}{7}\right) -\left(\frac{12}{-6}\right)\\= \frac{3}{7}- \frac{7}{7}+\frac{12}{6}\\=\frac{3}{7}-\frac{1}{1}+\frac{2}{1}\\=\frac{3-1+2}{7}\\=\frac{4}{7}\)
2. \(-\left(\frac{-8}{3}\right) +\left(\frac{-4}{-7}\right) +\left(\frac{-11}{3}\right)\\= \frac{8}{3}+ \frac{4}{7}-\frac{11}{3}\\=\frac{56}{21}+\frac{12}{21}-\frac{77}{21}\\=\frac{56+12-77}{21}\\=\frac{-9}{21}\\=\frac{-3}{7}\)
3. \(-\left(\frac{3}{-2}\right) +\left(\frac{5}{-3}\right) -\left(\frac{-5}{-10}\right)\\= \frac{3}{2}- \frac{5}{3}-\frac{5}{10}\\=\frac{3}{2}-\frac{5}{3}-\frac{1}{2}\\=\frac{9}{6}-\frac{10}{6}-\frac{3}{6}\\=\frac{9-10-3}{6}\\=\frac{-4}{6}\\=\frac{-2}{3}\)
4. \(-\left(\frac{-5}{6}\right) +\left(\frac{9}{5}\right) -\left(\frac{-8}{4}\right)\\= \frac{5}{6}+ \frac{9}{5}+\frac{8}{4}\\=\frac{5}{6}+\frac{9}{5}+\frac{2}{1}\\=\frac{25}{30}+\frac{54}{30}+\frac{60}{30}\\=\frac{25+54+60}{30}\\=\frac{139}{30}\)
5. \(-\left(\frac{-8}{-7}\right) +\left(\frac{4}{-3}\right) +\left(\frac{-6}{8}\right)\\= \frac{-8}{7}- \frac{4}{3}-\frac{6}{8}\\=\frac{-8}{7}-\frac{4}{3}-\frac{3}{4}\\=\frac{-96}{84}-\frac{112}{84}-\frac{63}{84}\\=\frac{-96-112-63}{84}\\=\frac{-271}{84}\)
6. \(-\left(\frac{-9}{2}\right) -\left(\frac{9}{-5}\right) -\left(\frac{8}{10}\right)\\= \frac{9}{2}+ \frac{9}{5}-\frac{8}{10}\\=\frac{9}{2}+\frac{9}{5}-\frac{4}{5}\\=\frac{45}{10}+\frac{18}{10}-\frac{8}{10}\\=\frac{45+18-8}{10}\\=\frac{55}{10}\\=\frac{11}{2}\)
7. \(+\left(\frac{2}{-7}\right) -\left(\frac{8}{7}\right) -\left(\frac{-3}{-8}\right)\\= \frac{-2}{7}- \frac{8}{7}-\frac{3}{8}\\=\frac{-16}{56}-\frac{64}{56}-\frac{21}{56}\\=\frac{-16-64-21}{56}\\=\frac{-101}{56}\)
8. \(+\left(\frac{-3}{2}\right) -\left(\frac{6}{7}\right) +\left(\frac{-4}{5}\right)\\= \frac{-3}{2}- \frac{6}{7}-\frac{4}{5}\\=\frac{-105}{70}-\frac{60}{70}-\frac{56}{70}\\=\frac{-105-60-56}{70}\\=\frac{-221}{70}\)
9. \(+\left(\frac{-2}{5}\right) +\left(\frac{-4}{9}\right) +\left(\frac{12}{7}\right)\\= \frac{-2}{5}- \frac{4}{9}+\frac{12}{7}\\=\frac{-126}{315}-\frac{140}{315}+\frac{540}{315}\\=\frac{-126-140+540}{315}\\=\frac{274}{315}\)
10. \(+\left(\frac{-3}{-7}\right) +\left(\frac{4}{-4}\right) +\left(\frac{-5}{6}\right)\\= \frac{3}{7}- \frac{4}{4}-\frac{5}{6}\\=\frac{3}{7}-\frac{1}{1}-\frac{5}{6}\\=\frac{18}{42}-\frac{42}{42}-\frac{35}{42}\\=\frac{18-42-35}{42}\\=\frac{-59}{42}\)
11. \(+\left(\frac{-4}{3}\right) -\left(\frac{4}{2}\right) +\left(\frac{3}{-10}\right)\\= \frac{-4}{3}- \frac{4}{2}-\frac{3}{10}\\=\frac{-4}{3}-\frac{2}{1}-\frac{3}{10}\\=\frac{-40}{30}-\frac{60}{30}-\frac{9}{30}\\=\frac{-40-60-9}{30}\\=\frac{-109}{30}\)
12. \(+\left(\frac{-9}{2}\right) +\left(\frac{4}{10}\right) -\left(\frac{6}{-2}\right)\\= \frac{-9}{2}+ \frac{4}{10}+\frac{6}{2}\\=\frac{-9}{2}+\frac{2}{5}+\frac{3}{1}\\=\frac{-45}{10}+\frac{4}{10}+\frac{30}{10}\\=\frac{-45+4+30}{10}\\=\frac{-11}{10}\)