Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{3}\right) +\left(\frac{3}{4}\right) -\left(\frac{-9}{-11}\right)\\= \frac{4}{3}+ \frac{3}{4}-\frac{9}{11}\\=\frac{176}{132}+\frac{99}{132}-\frac{108}{132}\\=\frac{176+99-108}{132}\\=\frac{167}{132}\)
2. \(+\left(\frac{10}{7}\right) +\left(\frac{9}{4}\right) -\left(\frac{4}{-6}\right)\\= \frac{10}{7}+ \frac{9}{4}+\frac{4}{6}\\=\frac{10}{7}+\frac{9}{4}+\frac{2}{3}\\=\frac{120}{84}+\frac{189}{84}+\frac{56}{84}\\=\frac{120+189+56}{84}\\=\frac{365}{84}\)
3. \(-\left(\frac{5}{6}\right) +\left(\frac{7}{5}\right) +\left(\frac{9}{8}\right)\\= \frac{-5}{6}+ \frac{7}{5}+\frac{9}{8}\\=\frac{-100}{120}+\frac{168}{120}+\frac{135}{120}\\=\frac{-100+168+135}{120}\\=\frac{203}{120}\)
4. \(-\left(\frac{5}{8}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{-3}{2}\right)\\= \frac{-5}{8}- \frac{2}{2}-\frac{3}{2}\\=\frac{-5}{8}-\frac{1}{1}-\frac{3}{2}\\=\frac{-5-1-3}{8}\\=\frac{-9}{8}\)
5. \(-\left(\frac{10}{9}\right) -\left(\frac{-5}{5}\right) -\left(\frac{3}{-12}\right)\\= \frac{-10}{9}+ \frac{5}{5}+\frac{3}{12}\\=\frac{-10}{9}+\frac{1}{1}+\frac{1}{4}\\=\frac{-40}{36}+\frac{36}{36}+\frac{9}{36}\\=\frac{-40+36+9}{36}\\=\frac{5}{36}\)
6. \(+\left(\frac{3}{4}\right) -\left(\frac{3}{7}\right) +\left(\frac{-8}{-5}\right)\\= \frac{3}{4}- \frac{3}{7}+\frac{8}{5}\\=\frac{105}{140}-\frac{60}{140}+\frac{224}{140}\\=\frac{105-60+224}{140}\\=\frac{269}{140}\)
7. \(-\left(\frac{-7}{-4}\right) +\left(\frac{10}{-8}\right) +\left(\frac{-6}{5}\right)\\= \frac{-7}{4}- \frac{10}{8}-\frac{6}{5}\\=\frac{-7}{4}-\frac{5}{4}-\frac{6}{5}\\=\frac{-35}{20}-\frac{25}{20}-\frac{24}{20}\\=\frac{-35-25-24}{20}\\=\frac{-84}{20}\\=\frac{-21}{5}\)
8. \(+\left(\frac{2}{-3}\right) +\left(\frac{4}{9}\right) -\left(\frac{6}{9}\right)\\= \frac{-2}{3}+ \frac{4}{9}-\frac{6}{9}\\=\frac{-2}{3}+\frac{4}{9}-\frac{2}{3}\\=\frac{-6}{9}+\frac{4}{9}-\frac{6}{9}\\=\frac{-6+4-6}{9}\\=\frac{-8}{9}\)
9. \(-\left(\frac{-4}{-9}\right) +\left(\frac{4}{7}\right) +\left(\frac{6}{5}\right)\\= \frac{-4}{9}+ \frac{4}{7}+\frac{6}{5}\\=\frac{-140}{315}+\frac{180}{315}+\frac{378}{315}\\=\frac{-140+180+378}{315}\\=\frac{418}{315}\)
10. \(-\left(\frac{6}{-5}\right) -\left(\frac{-2}{4}\right) +\left(\frac{-3}{10}\right)\\= \frac{6}{5}+ \frac{2}{4}-\frac{3}{10}\\=\frac{6}{5}+\frac{1}{2}-\frac{3}{10}\\=\frac{12}{10}+\frac{5}{10}-\frac{3}{10}\\=\frac{12+5-3}{10}\\=\frac{14}{10}\\=\frac{7}{5}\)
11. \(+\left(\frac{3}{4}\right) -\left(\frac{-5}{2}\right) -\left(\frac{-2}{-12}\right)\\= \frac{3}{4}+ \frac{5}{2}-\frac{2}{12}\\=\frac{3}{4}+\frac{5}{2}-\frac{1}{6}\\=\frac{9}{12}+\frac{30}{12}-\frac{2}{12}\\=\frac{9+30-2}{12}\\=\frac{37}{12}\)
12. \(-\left(\frac{3}{7}\right) -\left(\frac{7}{2}\right) +\left(\frac{2}{-5}\right)\\= \frac{-3}{7}- \frac{7}{2}-\frac{2}{5}\\=\frac{-30}{70}-\frac{245}{70}-\frac{28}{70}\\=\frac{-30-245-28}{70}\\=\frac{-303}{70}\)