Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-4}\right) -\left(\frac{-10}{-4}\right) +\left(\frac{6}{-7}\right)\\= \frac{7}{4}- \frac{10}{4}-\frac{6}{7}\\=\frac{7}{4}-\frac{5}{2}-\frac{6}{7}\\=\frac{49}{28}-\frac{70}{28}-\frac{24}{28}\\=\frac{49-70-24}{28}\\=\frac{-45}{28}\)
2. \(+\left(\frac{-9}{5}\right) -\left(\frac{-7}{2}\right) -\left(\frac{-3}{-9}\right)\\= \frac{-9}{5}+ \frac{7}{2}-\frac{3}{9}\\=\frac{-9}{5}+\frac{7}{2}-\frac{1}{3}\\=\frac{-54}{30}+\frac{105}{30}-\frac{10}{30}\\=\frac{-54+105-10}{30}\\=\frac{41}{30}\)
3. \(-\left(\frac{4}{7}\right) -\left(\frac{6}{9}\right) +\left(\frac{12}{4}\right)\\= \frac{-4}{7}- \frac{6}{9}+\frac{12}{4}\\=\frac{-4}{7}-\frac{2}{3}+\frac{3}{1}\\=\frac{-12}{21}-\frac{14}{21}+\frac{63}{21}\\=\frac{-12-14+63}{21}\\=\frac{37}{21}\)
4. \(-\left(\frac{8}{-9}\right) -\left(\frac{5}{10}\right) +\left(\frac{6}{-6}\right)\\= \frac{8}{9}- \frac{5}{10}-\frac{6}{6}\\=\frac{8}{9}-\frac{1}{2}-\frac{1}{1}\\=\frac{16}{18}-\frac{9}{18}-\frac{18}{18}\\=\frac{16-9-18}{18}\\=\frac{-11}{18}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{2}{7}\right) -\left(\frac{5}{5}\right)\\= \frac{-6}{5}+ \frac{2}{7}-\frac{5}{5}\\=\frac{-6}{5}+\frac{2}{7}-\frac{1}{1}\\=\frac{-42}{35}+\frac{10}{35}-\frac{35}{35}\\=\frac{-42+10-35}{35}\\=\frac{-67}{35}\)
6. \(-\left(\frac{4}{-3}\right) -\left(\frac{8}{-4}\right) -\left(\frac{5}{-4}\right)\\= \frac{4}{3}+ \frac{8}{4}+\frac{5}{4}\\=\frac{4}{3}+\frac{2}{1}+\frac{5}{4}\\=\frac{16}{12}+\frac{24}{12}+\frac{15}{12}\\=\frac{16+24+15}{12}\\=\frac{55}{12}\)
7. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-5}{9}\right) -\left(\frac{-3}{11}\right)\\= \frac{10}{9}+ \frac{5}{9}+\frac{3}{11}\\=\frac{110}{99}+\frac{55}{99}+\frac{27}{99}\\=\frac{110+55+27}{99}\\=\frac{192}{99}\\=\frac{64}{33}\)
8. \(+\left(\frac{-7}{2}\right) +\left(\frac{-7}{5}\right) +\left(\frac{-3}{4}\right)\\= \frac{-7}{2}- \frac{7}{5}-\frac{3}{4}\\=\frac{-70}{20}-\frac{28}{20}-\frac{15}{20}\\=\frac{-70-28-15}{20}\\=\frac{-113}{20}\)
9. \(+\left(\frac{10}{9}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-2}{10}\right)\\= \frac{10}{9}+ \frac{4}{7}+\frac{2}{10}\\=\frac{10}{9}+\frac{4}{7}+\frac{1}{5}\\=\frac{350}{315}+\frac{180}{315}+\frac{63}{315}\\=\frac{350+180+63}{315}\\=\frac{593}{315}\)
10. \(+\left(\frac{-7}{-9}\right) -\left(\frac{10}{-10}\right) -\left(\frac{-10}{-11}\right)\\= \frac{7}{9}+ \frac{10}{10}-\frac{10}{11}\\=\frac{7}{9}+\frac{1}{1}-\frac{10}{11}\\=\frac{77}{99}+\frac{99}{99}-\frac{90}{99}\\=\frac{77+99-90}{99}\\=\frac{86}{99}\)
11. \(+\left(\frac{8}{-3}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{12}{-9}\right)\\= \frac{-8}{3}- \frac{4}{3}+\frac{12}{9}\\=\frac{-8}{3}-\frac{4}{3}+\frac{4}{3}\\=\frac{-8-4+4}{3}\\=\frac{-8}{3}\)
12. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-6}{6}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-10}{7}+ \frac{6}{6}-\frac{2}{11}\\=\frac{-10}{7}+\frac{1}{1}-\frac{2}{11}\\=\frac{-110}{77}+\frac{77}{77}-\frac{14}{77}\\=\frac{-110+77-14}{77}\\=\frac{-47}{77}\)