Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{-2}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-9}{3}\right)\\= \frac{-9}{2}- \frac{10}{5}+\frac{9}{3}\\=\frac{-9}{2}-\frac{2}{1}+\frac{3}{1}\\=\frac{-9-2+3}{2}\\=\frac{-8}{2}\\=\frac{-4}{1}\)
2. \(+\left(\frac{5}{-3}\right) -\left(\frac{-6}{6}\right) -\left(\frac{12}{-9}\right)\\= \frac{-5}{3}+ \frac{6}{6}+\frac{12}{9}\\=\frac{-5}{3}+\frac{1}{1}+\frac{4}{3}\\=\frac{-5+1+4}{3}\\=\frac{0}{3}\\=\frac{0}{1}\)
3. \(+\left(\frac{9}{-7}\right) -\left(\frac{2}{6}\right) -\left(\frac{-9}{-9}\right)\\= \frac{-9}{7}- \frac{2}{6}-\frac{9}{9}\\=\frac{-9}{7}-\frac{1}{3}-\frac{1}{1}\\=\frac{-27}{21}-\frac{7}{21}-\frac{21}{21}\\=\frac{-27-7-21}{21}\\=\frac{-55}{21}\)
4. \(-\left(\frac{3}{-4}\right) -\left(\frac{2}{-5}\right) +\left(\frac{10}{6}\right)\\= \frac{3}{4}+ \frac{2}{5}+\frac{10}{6}\\=\frac{3}{4}+\frac{2}{5}+\frac{5}{3}\\=\frac{45}{60}+\frac{24}{60}+\frac{100}{60}\\=\frac{45+24+100}{60}\\=\frac{169}{60}\)
5. \(+\left(\frac{-3}{-7}\right) -\left(\frac{7}{-4}\right) -\left(\frac{12}{-10}\right)\\= \frac{3}{7}+ \frac{7}{4}+\frac{12}{10}\\=\frac{3}{7}+\frac{7}{4}+\frac{6}{5}\\=\frac{60}{140}+\frac{245}{140}+\frac{168}{140}\\=\frac{60+245+168}{140}\\=\frac{473}{140}\)
6. \(+\left(\frac{-5}{-9}\right) +\left(\frac{4}{-7}\right) +\left(\frac{-11}{-6}\right)\\= \frac{5}{9}- \frac{4}{7}+\frac{11}{6}\\=\frac{70}{126}-\frac{72}{126}+\frac{231}{126}\\=\frac{70-72+231}{126}\\=\frac{229}{126}\)
7. \(-\left(\frac{-9}{-7}\right) -\left(\frac{8}{-5}\right) +\left(\frac{6}{-4}\right)\\= \frac{-9}{7}+ \frac{8}{5}-\frac{6}{4}\\=\frac{-9}{7}+\frac{8}{5}-\frac{3}{2}\\=\frac{-90}{70}+\frac{112}{70}-\frac{105}{70}\\=\frac{-90+112-105}{70}\\=\frac{-83}{70}\)
8. \(-\left(\frac{-5}{-3}\right) +\left(\frac{-7}{-7}\right) -\left(\frac{11}{-9}\right)\\= \frac{-5}{3}+ \frac{7}{7}+\frac{11}{9}\\=\frac{-5}{3}+\frac{1}{1}+\frac{11}{9}\\=\frac{-15}{9}+\frac{9}{9}+\frac{11}{9}\\=\frac{-15+9+11}{9}\\=\frac{5}{9}\)
9. \(+\left(\frac{-6}{5}\right) -\left(\frac{-5}{8}\right) -\left(\frac{2}{-5}\right)\\= \frac{-6}{5}+ \frac{5}{8}+\frac{2}{5}\\=\frac{-48}{40}+\frac{25}{40}+\frac{16}{40}\\=\frac{-48+25+16}{40}\\=\frac{-7}{40}\)
10. \(+\left(\frac{3}{5}\right) +\left(\frac{9}{-8}\right) +\left(\frac{-10}{9}\right)\\= \frac{3}{5}- \frac{9}{8}-\frac{10}{9}\\=\frac{216}{360}-\frac{405}{360}-\frac{400}{360}\\=\frac{216-405-400}{360}\\=\frac{-589}{360}\)
11. \(+\left(\frac{3}{7}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{-11}{-11}\right)\\= \frac{3}{7}+ \frac{5}{9}-\frac{11}{11}\\=\frac{3}{7}+\frac{5}{9}-\frac{1}{1}\\=\frac{27}{63}+\frac{35}{63}-\frac{63}{63}\\=\frac{27+35-63}{63}\\=\frac{-1}{63}\)
12. \(-\left(\frac{4}{-5}\right) +\left(\frac{-7}{3}\right) +\left(\frac{5}{-6}\right)\\= \frac{4}{5}- \frac{7}{3}-\frac{5}{6}\\=\frac{24}{30}-\frac{70}{30}-\frac{25}{30}\\=\frac{24-70-25}{30}\\=\frac{-71}{30}\)