Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-12}{-7}\right)\\= \frac{10}{3}+ \frac{8}{4}-\frac{12}{7}\\=\frac{10}{3}+\frac{2}{1}-\frac{12}{7}\\=\frac{70}{21}+\frac{42}{21}-\frac{36}{21}\\=\frac{70+42-36}{21}\\=\frac{76}{21}\)
2. \(+\left(\frac{-3}{-7}\right) -\left(\frac{3}{7}\right) -\left(\frac{9}{12}\right)\\= \frac{3}{7}- \frac{3}{7}-\frac{9}{12}\\=\frac{3}{7}-\frac{3}{7}-\frac{3}{4}\\=\frac{12}{28}-\frac{12}{28}-\frac{21}{28}\\=\frac{12-12-21}{28}\\=\frac{-21}{28}\\=\frac{-3}{4}\)
3. \(-\left(\frac{-9}{2}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{6}{-5}\right)\\= \frac{9}{2}+ \frac{8}{4}+\frac{6}{5}\\=\frac{9}{2}+\frac{2}{1}+\frac{6}{5}\\=\frac{45}{10}+\frac{20}{10}+\frac{12}{10}\\=\frac{45+20+12}{10}\\=\frac{77}{10}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{8}{-3}\right) +\left(\frac{-11}{-2}\right)\\= \frac{6}{5}+ \frac{8}{3}+\frac{11}{2}\\=\frac{36}{30}+\frac{80}{30}+\frac{165}{30}\\=\frac{36+80+165}{30}\\=\frac{281}{30}\)
5. \(+\left(\frac{-4}{-7}\right) -\left(\frac{9}{6}\right) +\left(\frac{7}{-10}\right)\\= \frac{4}{7}- \frac{9}{6}-\frac{7}{10}\\=\frac{4}{7}-\frac{3}{2}-\frac{7}{10}\\=\frac{40}{70}-\frac{105}{70}-\frac{49}{70}\\=\frac{40-105-49}{70}\\=\frac{-114}{70}\\=\frac{-57}{35}\)
6. \(-\left(\frac{-4}{-3}\right) -\left(\frac{9}{9}\right) -\left(\frac{5}{11}\right)\\= \frac{-4}{3}- \frac{9}{9}-\frac{5}{11}\\=\frac{-4}{3}-\frac{1}{1}-\frac{5}{11}\\=\frac{-44}{33}-\frac{33}{33}-\frac{15}{33}\\=\frac{-44-33-15}{33}\\=\frac{-92}{33}\)
7. \(-\left(\frac{-10}{-3}\right) -\left(\frac{2}{-6}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-10}{3}+ \frac{2}{6}-\frac{6}{3}\\=\frac{-10}{3}+\frac{1}{3}-\frac{2}{1}\\=\frac{-10+1-2}{3}\\=\frac{-11}{3}\)
8. \(-\left(\frac{5}{4}\right) -\left(\frac{3}{-7}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-5}{4}+ \frac{3}{7}+\frac{5}{12}\\=\frac{-105}{84}+\frac{36}{84}+\frac{35}{84}\\=\frac{-105+36+35}{84}\\=\frac{-34}{84}\\=\frac{-17}{42}\)
9. \(+\left(\frac{10}{-3}\right) -\left(\frac{7}{-4}\right) +\left(\frac{12}{4}\right)\\= \frac{-10}{3}+ \frac{7}{4}+\frac{12}{4}\\=\frac{-10}{3}+\frac{7}{4}+\frac{3}{1}\\=\frac{-40}{12}+\frac{21}{12}+\frac{36}{12}\\=\frac{-40+21+36}{12}\\=\frac{17}{12}\)
10. \(+\left(\frac{6}{-7}\right) +\left(\frac{4}{-9}\right) -\left(\frac{-5}{9}\right)\\= \frac{-6}{7}- \frac{4}{9}+\frac{5}{9}\\=\frac{-54}{63}-\frac{28}{63}+\frac{35}{63}\\=\frac{-54-28+35}{63}\\=\frac{-47}{63}\)
11. \(-\left(\frac{2}{3}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{-11}{10}\right)\\= \frac{-2}{3}+ \frac{4}{10}-\frac{11}{10}\\=\frac{-2}{3}+\frac{2}{5}-\frac{11}{10}\\=\frac{-20}{30}+\frac{12}{30}-\frac{33}{30}\\=\frac{-20+12-33}{30}\\=\frac{-41}{30}\)
12. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-8}{3}\right) +\left(\frac{-11}{9}\right)\\= \frac{-10}{7}- \frac{8}{3}-\frac{11}{9}\\=\frac{-90}{63}-\frac{168}{63}-\frac{77}{63}\\=\frac{-90-168-77}{63}\\=\frac{-335}{63}\)