Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-7}\right) +\left(\frac{5}{4}\right) -\left(\frac{-3}{-7}\right)\\= \frac{8}{7}+ \frac{5}{4}-\frac{3}{7}\\=\frac{32}{28}+\frac{35}{28}-\frac{12}{28}\\=\frac{32+35-12}{28}\\=\frac{55}{28}\)
2. \(+\left(\frac{2}{9}\right) +\left(\frac{-2}{9}\right) +\left(\frac{-3}{10}\right)\\= \frac{2}{9}- \frac{2}{9}-\frac{3}{10}\\=\frac{20}{90}-\frac{20}{90}-\frac{27}{90}\\=\frac{20-20-27}{90}\\=\frac{-27}{90}\\=\frac{-3}{10}\)
3. \(+\left(\frac{-10}{7}\right) -\left(\frac{-4}{5}\right) +\left(\frac{9}{-3}\right)\\= \frac{-10}{7}+ \frac{4}{5}-\frac{9}{3}\\=\frac{-10}{7}+\frac{4}{5}-\frac{3}{1}\\=\frac{-50}{35}+\frac{28}{35}-\frac{105}{35}\\=\frac{-50+28-105}{35}\\=\frac{-127}{35}\)
4. \(-\left(\frac{2}{5}\right) +\left(\frac{-2}{4}\right) +\left(\frac{-7}{11}\right)\\= \frac{-2}{5}- \frac{2}{4}-\frac{7}{11}\\=\frac{-2}{5}-\frac{1}{2}-\frac{7}{11}\\=\frac{-44}{110}-\frac{55}{110}-\frac{70}{110}\\=\frac{-44-55-70}{110}\\=\frac{-169}{110}\)
5. \(+\left(\frac{4}{7}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{-4}{9}\right)\\= \frac{4}{7}- \frac{7}{4}+\frac{4}{9}\\=\frac{144}{252}-\frac{441}{252}+\frac{112}{252}\\=\frac{144-441+112}{252}\\=\frac{-185}{252}\)
6. \(-\left(\frac{5}{7}\right) +\left(\frac{-10}{3}\right) -\left(\frac{12}{-9}\right)\\= \frac{-5}{7}- \frac{10}{3}+\frac{12}{9}\\=\frac{-5}{7}-\frac{10}{3}+\frac{4}{3}\\=\frac{-15}{21}-\frac{70}{21}+\frac{28}{21}\\=\frac{-15-70+28}{21}\\=\frac{-57}{21}\\=\frac{-19}{7}\)
7. \(-\left(\frac{-2}{9}\right) -\left(\frac{-4}{-7}\right) +\left(\frac{-9}{12}\right)\\= \frac{2}{9}- \frac{4}{7}-\frac{9}{12}\\=\frac{2}{9}-\frac{4}{7}-\frac{3}{4}\\=\frac{56}{252}-\frac{144}{252}-\frac{189}{252}\\=\frac{56-144-189}{252}\\=\frac{-277}{252}\)
8. \(+\left(\frac{4}{3}\right) -\left(\frac{-3}{-6}\right) +\left(\frac{4}{8}\right)\\= \frac{4}{3}- \frac{3}{6}+\frac{4}{8}\\=\frac{4}{3}-\frac{1}{2}+\frac{1}{2}\\=\frac{8}{6}-\frac{3}{6}+\frac{3}{6}\\=\frac{8-3+3}{6}\\=\frac{8}{6}\\=\frac{4}{3}\)
9. \(+\left(\frac{3}{-7}\right) -\left(\frac{2}{7}\right) -\left(\frac{9}{7}\right)\\= \frac{-3}{7}- \frac{2}{7}-\frac{9}{7}\\=\frac{-3-2-9}{7}\\=\frac{-14}{7}\\=\frac{-2}{1}\)
10. \(-\left(\frac{-2}{-7}\right) -\left(\frac{8}{6}\right) -\left(\frac{10}{5}\right)\\= \frac{-2}{7}- \frac{8}{6}-\frac{10}{5}\\=\frac{-2}{7}-\frac{4}{3}-\frac{2}{1}\\=\frac{-6}{21}-\frac{28}{21}-\frac{42}{21}\\=\frac{-6-28-42}{21}\\=\frac{-76}{21}\)
11. \(+\left(\frac{-8}{5}\right) -\left(\frac{8}{-3}\right) -\left(\frac{-12}{12}\right)\\= \frac{-8}{5}+ \frac{8}{3}+\frac{12}{12}\\=\frac{-8}{5}+\frac{8}{3}+\frac{1}{1}\\=\frac{-24}{15}+\frac{40}{15}+\frac{15}{15}\\=\frac{-24+40+15}{15}\\=\frac{31}{15}\)
12. \(+\left(\frac{10}{-7}\right) +\left(\frac{-5}{7}\right) -\left(\frac{5}{-7}\right)\\= \frac{-10}{7}- \frac{5}{7}+\frac{5}{7}\\=\frac{-10-5+5}{7}\\=\frac{-10}{7}\)