Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{6}\right) +\left(\frac{-2}{-6}\right) +\left(\frac{-6}{8}\right)\\= \frac{-7}{6}+ \frac{2}{6}-\frac{6}{8}\\=\frac{-7}{6}+\frac{1}{3}-\frac{3}{4}\\=\frac{-14}{12}+\frac{4}{12}-\frac{9}{12}\\=\frac{-14+4-9}{12}\\=\frac{-19}{12}\)
2. \(-\left(\frac{7}{4}\right) +\left(\frac{8}{-4}\right) -\left(\frac{-6}{12}\right)\\= \frac{-7}{4}- \frac{8}{4}+\frac{6}{12}\\=\frac{-7}{4}-\frac{2}{1}+\frac{1}{2}\\=\frac{-7-2+1}{4}\\=\frac{-8}{4}\\=\frac{-2}{1}\)
3. \(+\left(\frac{-2}{-3}\right) +\left(\frac{10}{4}\right) -\left(\frac{-9}{5}\right)\\= \frac{2}{3}+ \frac{10}{4}+\frac{9}{5}\\=\frac{2}{3}+\frac{5}{2}+\frac{9}{5}\\=\frac{20}{30}+\frac{75}{30}+\frac{54}{30}\\=\frac{20+75+54}{30}\\=\frac{149}{30}\)
4. \(-\left(\frac{2}{5}\right) -\left(\frac{-10}{2}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-2}{5}+ \frac{10}{2}+\frac{5}{4}\\=\frac{-2}{5}+\frac{5}{1}+\frac{5}{4}\\=\frac{-8}{20}+\frac{100}{20}+\frac{25}{20}\\=\frac{-8+100+25}{20}\\=\frac{117}{20}\)
5. \(+\left(\frac{-2}{5}\right) -\left(\frac{6}{-7}\right) +\left(\frac{3}{-2}\right)\\= \frac{-2}{5}+ \frac{6}{7}-\frac{3}{2}\\=\frac{-28}{70}+\frac{60}{70}-\frac{105}{70}\\=\frac{-28+60-105}{70}\\=\frac{-73}{70}\)
6. \(-\left(\frac{9}{4}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{12}{5}\right)\\= \frac{-9}{4}- \frac{7}{9}+\frac{12}{5}\\=\frac{-405}{180}-\frac{140}{180}+\frac{432}{180}\\=\frac{-405-140+432}{180}\\=\frac{-113}{180}\)
7. \(+\left(\frac{8}{7}\right) -\left(\frac{9}{-8}\right) -\left(\frac{3}{3}\right)\\= \frac{8}{7}+ \frac{9}{8}-\frac{3}{3}\\=\frac{8}{7}+\frac{9}{8}-\frac{1}{1}\\=\frac{64}{56}+\frac{63}{56}-\frac{56}{56}\\=\frac{64+63-56}{56}\\=\frac{71}{56}\)
8. \(+\left(\frac{4}{-7}\right) +\left(\frac{7}{-8}\right) +\left(\frac{8}{10}\right)\\= \frac{-4}{7}- \frac{7}{8}+\frac{8}{10}\\=\frac{-4}{7}-\frac{7}{8}+\frac{4}{5}\\=\frac{-160}{280}-\frac{245}{280}+\frac{224}{280}\\=\frac{-160-245+224}{280}\\=\frac{-181}{280}\)
9. \(-\left(\frac{-6}{5}\right) +\left(\frac{-8}{3}\right) -\left(\frac{2}{7}\right)\\= \frac{6}{5}- \frac{8}{3}-\frac{2}{7}\\=\frac{126}{105}-\frac{280}{105}-\frac{30}{105}\\=\frac{126-280-30}{105}\\=\frac{-184}{105}\)
10. \(+\left(\frac{9}{4}\right) -\left(\frac{-8}{-4}\right) -\left(\frac{10}{8}\right)\\= \frac{9}{4}- \frac{8}{4}-\frac{10}{8}\\=\frac{9}{4}-\frac{2}{1}-\frac{5}{4}\\=\frac{9-2-5}{4}\\=\frac{2}{4}\\=\frac{1}{2}\)
11. \(-\left(\frac{7}{2}\right) +\left(\frac{-9}{3}\right) +\left(\frac{4}{9}\right)\\= \frac{-7}{2}- \frac{9}{3}+\frac{4}{9}\\=\frac{-7}{2}-\frac{3}{1}+\frac{4}{9}\\=\frac{-63}{18}-\frac{54}{18}+\frac{8}{18}\\=\frac{-63-54+8}{18}\\=\frac{-109}{18}\)
12. \(+\left(\frac{-5}{4}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-5}{4}+ \frac{5}{8}-\frac{7}{11}\\=\frac{-110}{88}+\frac{55}{88}-\frac{56}{88}\\=\frac{-110+55-56}{88}\\=\frac{-111}{88}\)