Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{3}\right) +\left(\frac{-7}{2}\right) -\left(\frac{-8}{10}\right)\\= \frac{-10}{3}- \frac{7}{2}+\frac{8}{10}\\=\frac{-10}{3}-\frac{7}{2}+\frac{4}{5}\\=\frac{-100}{30}-\frac{105}{30}+\frac{24}{30}\\=\frac{-100-105+24}{30}\\=\frac{-181}{30}\)
2. \(-\left(\frac{-4}{7}\right) +\left(\frac{6}{-4}\right) +\left(\frac{6}{-2}\right)\\= \frac{4}{7}- \frac{6}{4}-\frac{6}{2}\\=\frac{4}{7}-\frac{3}{2}-\frac{3}{1}\\=\frac{8}{14}-\frac{21}{14}-\frac{42}{14}\\=\frac{8-21-42}{14}\\=\frac{-55}{14}\)
3. \(-\left(\frac{7}{4}\right) +\left(\frac{-9}{2}\right) +\left(\frac{-5}{-5}\right)\\= \frac{-7}{4}- \frac{9}{2}+\frac{5}{5}\\=\frac{-7}{4}-\frac{9}{2}+\frac{1}{1}\\=\frac{-7-9+1}{4}\\=\frac{-15}{4}\)
4. \(+\left(\frac{6}{5}\right) -\left(\frac{-3}{7}\right) +\left(\frac{10}{3}\right)\\= \frac{6}{5}+ \frac{3}{7}+\frac{10}{3}\\=\frac{126}{105}+\frac{45}{105}+\frac{350}{105}\\=\frac{126+45+350}{105}\\=\frac{521}{105}\)
5. \(-\left(\frac{3}{4}\right) +\left(\frac{-6}{9}\right) +\left(\frac{-10}{-9}\right)\\= \frac{-3}{4}- \frac{6}{9}+\frac{10}{9}\\=\frac{-3}{4}-\frac{2}{3}+\frac{10}{9}\\=\frac{-27}{36}-\frac{24}{36}+\frac{40}{36}\\=\frac{-27-24+40}{36}\\=\frac{-11}{36}\)
6. \(-\left(\frac{6}{5}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{7}{-4}\right)\\= \frac{-6}{5}+ \frac{10}{8}-\frac{7}{4}\\=\frac{-6}{5}+\frac{5}{4}-\frac{7}{4}\\=\frac{-24}{20}+\frac{25}{20}-\frac{35}{20}\\=\frac{-24+25-35}{20}\\=\frac{-34}{20}\\=\frac{-17}{10}\)
7. \(-\left(\frac{-3}{7}\right) +\left(\frac{4}{2}\right) -\left(\frac{9}{5}\right)\\= \frac{3}{7}+ \frac{4}{2}-\frac{9}{5}\\=\frac{3}{7}+\frac{2}{1}-\frac{9}{5}\\=\frac{15}{35}+\frac{70}{35}-\frac{63}{35}\\=\frac{15+70-63}{35}\\=\frac{22}{35}\)
8. \(+\left(\frac{-5}{3}\right) +\left(\frac{9}{9}\right) +\left(\frac{-2}{-2}\right)\\= \frac{-5}{3}+ \frac{9}{9}+\frac{2}{2}\\=\frac{-5}{3}+\frac{1}{1}+\frac{1}{1}\\=\frac{-5+1+1}{3}\\=\frac{-3}{3}\\=\frac{-1}{1}\)
9. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-6}{8}\right) -\left(\frac{-3}{12}\right)\\= \frac{8}{3}+ \frac{6}{8}+\frac{3}{12}\\=\frac{8}{3}+\frac{3}{4}+\frac{1}{4}\\=\frac{32}{12}+\frac{9}{12}+\frac{3}{12}\\=\frac{32+9+3}{12}\\=\frac{44}{12}\\=\frac{11}{3}\)
10. \(-\left(\frac{5}{-6}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{12}{3}\right)\\= \frac{5}{6}+ \frac{8}{5}-\frac{12}{3}\\=\frac{5}{6}+\frac{8}{5}-\frac{4}{1}\\=\frac{25}{30}+\frac{48}{30}-\frac{120}{30}\\=\frac{25+48-120}{30}\\=\frac{-47}{30}\)
11. \(+\left(\frac{-8}{9}\right) -\left(\frac{6}{-7}\right) -\left(\frac{4}{4}\right)\\= \frac{-8}{9}+ \frac{6}{7}-\frac{4}{4}\\=\frac{-8}{9}+\frac{6}{7}-\frac{1}{1}\\=\frac{-56}{63}+\frac{54}{63}-\frac{63}{63}\\=\frac{-56+54-63}{63}\\=\frac{-65}{63}\)
12. \(-\left(\frac{9}{5}\right) -\left(\frac{-8}{-7}\right) -\left(\frac{8}{-5}\right)\\= \frac{-9}{5}- \frac{8}{7}+\frac{8}{5}\\=\frac{-63}{35}-\frac{40}{35}+\frac{56}{35}\\=\frac{-63-40+56}{35}\\=\frac{-47}{35}\)