Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-10}{-3}\right) +\left(\frac{-3}{-10}\right)\\= \frac{3}{2}+ \frac{10}{3}+\frac{3}{10}\\=\frac{45}{30}+\frac{100}{30}+\frac{9}{30}\\=\frac{45+100+9}{30}\\=\frac{154}{30}\\=\frac{77}{15}\)
2. \(-\left(\frac{4}{-9}\right) +\left(\frac{4}{9}\right) -\left(\frac{5}{-3}\right)\\= \frac{4}{9}+ \frac{4}{9}+\frac{5}{3}\\=\frac{4+4+5}{9}\\=\frac{13}{9}\)
3. \(-\left(\frac{5}{2}\right) +\left(\frac{4}{5}\right) +\left(\frac{-7}{10}\right)\\= \frac{-5}{2}+ \frac{4}{5}-\frac{7}{10}\\=\frac{-25}{10}+\frac{8}{10}-\frac{7}{10}\\=\frac{-25+8-7}{10}\\=\frac{-24}{10}\\=\frac{-12}{5}\)
4. \(+\left(\frac{8}{-7}\right) +\left(\frac{9}{10}\right) +\left(\frac{6}{7}\right)\\= \frac{-8}{7}+ \frac{9}{10}+\frac{6}{7}\\=\frac{-80}{70}+\frac{63}{70}+\frac{60}{70}\\=\frac{-80+63+60}{70}\\=\frac{43}{70}\)
5. \(+\left(\frac{-6}{7}\right) -\left(\frac{2}{5}\right) +\left(\frac{4}{4}\right)\\= \frac{-6}{7}- \frac{2}{5}+\frac{4}{4}\\=\frac{-6}{7}-\frac{2}{5}+\frac{1}{1}\\=\frac{-30}{35}-\frac{14}{35}+\frac{35}{35}\\=\frac{-30-14+35}{35}\\=\frac{-9}{35}\)
6. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-7}{7}\right) +\left(\frac{2}{11}\right)\\= \frac{10}{7}+ \frac{7}{7}+\frac{2}{11}\\=\frac{10}{7}+\frac{1}{1}+\frac{2}{11}\\=\frac{110}{77}+\frac{77}{77}+\frac{14}{77}\\=\frac{110+77+14}{77}\\=\frac{201}{77}\)
7. \(-\left(\frac{5}{4}\right) -\left(\frac{-2}{8}\right) -\left(\frac{3}{-5}\right)\\= \frac{-5}{4}+ \frac{2}{8}+\frac{3}{5}\\=\frac{-5}{4}+\frac{1}{4}+\frac{3}{5}\\=\frac{-25}{20}+\frac{5}{20}+\frac{12}{20}\\=\frac{-25+5+12}{20}\\=\frac{-8}{20}\\=\frac{-2}{5}\)
8. \(-\left(\frac{5}{-8}\right) -\left(\frac{-4}{8}\right) -\left(\frac{8}{3}\right)\\= \frac{5}{8}+ \frac{4}{8}-\frac{8}{3}\\=\frac{5}{8}+\frac{1}{2}-\frac{8}{3}\\=\frac{15}{24}+\frac{12}{24}-\frac{64}{24}\\=\frac{15+12-64}{24}\\=\frac{-37}{24}\)
9. \(+\left(\frac{3}{-8}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{-2}{-4}\right)\\= \frac{-3}{8}- \frac{7}{4}-\frac{2}{4}\\=\frac{-3}{8}-\frac{7}{4}-\frac{1}{2}\\=\frac{-3-7-1}{8}\\=\frac{-11}{8}\)
10. \(-\left(\frac{9}{4}\right) +\left(\frac{-4}{9}\right) -\left(\frac{11}{11}\right)\\= \frac{-9}{4}- \frac{4}{9}-\frac{11}{11}\\=\frac{-9}{4}-\frac{4}{9}-\frac{1}{1}\\=\frac{-81}{36}-\frac{16}{36}-\frac{36}{36}\\=\frac{-81-16-36}{36}\\=\frac{-133}{36}\)
11. \(+\left(\frac{10}{7}\right) -\left(\frac{-5}{-3}\right) +\left(\frac{-6}{3}\right)\\= \frac{10}{7}- \frac{5}{3}-\frac{6}{3}\\=\frac{10}{7}-\frac{5}{3}-\frac{2}{1}\\=\frac{30}{21}-\frac{35}{21}-\frac{42}{21}\\=\frac{30-35-42}{21}\\=\frac{-47}{21}\)
12. \(-\left(\frac{-5}{-9}\right) -\left(\frac{7}{4}\right) -\left(\frac{10}{-8}\right)\\= \frac{-5}{9}- \frac{7}{4}+\frac{10}{8}\\=\frac{-5}{9}-\frac{7}{4}+\frac{5}{4}\\=\frac{-20}{36}-\frac{63}{36}+\frac{45}{36}\\=\frac{-20-63+45}{36}\\=\frac{-38}{36}\\=\frac{-19}{18}\)