Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{8}\right) -\left(\frac{7}{-5}\right) +\left(\frac{5}{8}\right)\\= \frac{9}{8}+ \frac{7}{5}+\frac{5}{8}\\=\frac{45}{40}+\frac{56}{40}+\frac{25}{40}\\=\frac{45+56+25}{40}\\=\frac{126}{40}\\=\frac{63}{20}\)
2. \(+\left(\frac{-7}{3}\right) +\left(\frac{6}{4}\right) +\left(\frac{6}{3}\right)\\= \frac{-7}{3}+ \frac{6}{4}+\frac{6}{3}\\=\frac{-7}{3}+\frac{3}{2}+\frac{2}{1}\\=\frac{-14}{6}+\frac{9}{6}+\frac{12}{6}\\=\frac{-14+9+12}{6}\\=\frac{7}{6}\)
3. \(-\left(\frac{3}{-7}\right) +\left(\frac{-6}{9}\right) +\left(\frac{-2}{3}\right)\\= \frac{3}{7}- \frac{6}{9}-\frac{2}{3}\\=\frac{3}{7}-\frac{2}{3}-\frac{2}{3}\\=\frac{9}{21}-\frac{14}{21}-\frac{14}{21}\\=\frac{9-14-14}{21}\\=\frac{-19}{21}\)
4. \(+\left(\frac{-3}{8}\right) +\left(\frac{-3}{4}\right) +\left(\frac{-12}{-12}\right)\\= \frac{-3}{8}- \frac{3}{4}+\frac{12}{12}\\=\frac{-3}{8}-\frac{3}{4}+\frac{1}{1}\\=\frac{-3-3+1}{8}\\=\frac{-5}{8}\)
5. \(-\left(\frac{-5}{7}\right) +\left(\frac{6}{9}\right) +\left(\frac{5}{-12}\right)\\= \frac{5}{7}+ \frac{6}{9}-\frac{5}{12}\\=\frac{5}{7}+\frac{2}{3}-\frac{5}{12}\\=\frac{60}{84}+\frac{56}{84}-\frac{35}{84}\\=\frac{60+56-35}{84}\\=\frac{81}{84}\\=\frac{27}{28}\)
6. \(-\left(\frac{-10}{9}\right) -\left(\frac{-6}{8}\right) -\left(\frac{-5}{-5}\right)\\= \frac{10}{9}+ \frac{6}{8}-\frac{5}{5}\\=\frac{10}{9}+\frac{3}{4}-\frac{1}{1}\\=\frac{40}{36}+\frac{27}{36}-\frac{36}{36}\\=\frac{40+27-36}{36}\\=\frac{31}{36}\)
7. \(+\left(\frac{10}{-9}\right) -\left(\frac{-5}{5}\right) +\left(\frac{7}{11}\right)\\= \frac{-10}{9}+ \frac{5}{5}+\frac{7}{11}\\=\frac{-10}{9}+\frac{1}{1}+\frac{7}{11}\\=\frac{-110}{99}+\frac{99}{99}+\frac{63}{99}\\=\frac{-110+99+63}{99}\\=\frac{52}{99}\)
8. \(+\left(\frac{10}{-3}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-10}{3}+ \frac{8}{5}-\frac{10}{10}\\=\frac{-10}{3}+\frac{8}{5}-\frac{1}{1}\\=\frac{-50}{15}+\frac{24}{15}-\frac{15}{15}\\=\frac{-50+24-15}{15}\\=\frac{-41}{15}\)
9. \(+\left(\frac{-8}{9}\right) -\left(\frac{10}{4}\right) -\left(\frac{6}{-2}\right)\\= \frac{-8}{9}- \frac{10}{4}+\frac{6}{2}\\=\frac{-8}{9}-\frac{5}{2}+\frac{3}{1}\\=\frac{-16}{18}-\frac{45}{18}+\frac{54}{18}\\=\frac{-16-45+54}{18}\\=\frac{-7}{18}\)
10. \(+\left(\frac{-2}{5}\right) +\left(\frac{-9}{5}\right) -\left(\frac{-2}{-6}\right)\\= \frac{-2}{5}- \frac{9}{5}-\frac{2}{6}\\=\frac{-2}{5}-\frac{9}{5}-\frac{1}{3}\\=\frac{-6}{15}-\frac{27}{15}-\frac{5}{15}\\=\frac{-6-27-5}{15}\\=\frac{-38}{15}\)
11. \(-\left(\frac{-3}{-10}\right) +\left(\frac{-9}{9}\right) -\left(\frac{9}{2}\right)\\= \frac{-3}{10}- \frac{9}{9}-\frac{9}{2}\\=\frac{-3}{10}-\frac{1}{1}-\frac{9}{2}\\=\frac{-3-1-9}{10}\\=\frac{-13}{10}\)
12. \(+\left(\frac{4}{3}\right) -\left(\frac{-4}{-5}\right) -\left(\frac{9}{7}\right)\\= \frac{4}{3}- \frac{4}{5}-\frac{9}{7}\\=\frac{140}{105}-\frac{84}{105}-\frac{135}{105}\\=\frac{140-84-135}{105}\\=\frac{-79}{105}\)