Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{8}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{3}{9}\right)\\= \frac{9}{8}+ \frac{7}{8}+\frac{3}{9}\\=\frac{9}{8}+\frac{7}{8}+\frac{1}{3}\\=\frac{27}{24}+\frac{21}{24}+\frac{8}{24}\\=\frac{27+21+8}{24}\\=\frac{56}{24}\\=\frac{7}{3}\)
2. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{-10}{-11}\right)\\= \frac{-5}{6}+ \frac{4}{2}-\frac{10}{11}\\=\frac{-5}{6}+\frac{2}{1}-\frac{10}{11}\\=\frac{-55}{66}+\frac{132}{66}-\frac{60}{66}\\=\frac{-55+132-60}{66}\\=\frac{17}{66}\)
3. \(+\left(\frac{-10}{3}\right) -\left(\frac{10}{-3}\right) -\left(\frac{4}{-11}\right)\\= \frac{-10}{3}+ \frac{10}{3}+\frac{4}{11}\\=\frac{-110}{33}+\frac{110}{33}+\frac{12}{33}\\=\frac{-110+110+12}{33}\\=\frac{12}{33}\\=\frac{4}{11}\)
4. \(-\left(\frac{4}{-3}\right) -\left(\frac{-3}{-2}\right) +\left(\frac{6}{-3}\right)\\= \frac{4}{3}- \frac{3}{2}-\frac{6}{3}\\=\frac{4}{3}-\frac{3}{2}-\frac{2}{1}\\=\frac{8}{6}-\frac{9}{6}-\frac{12}{6}\\=\frac{8-9-12}{6}\\=\frac{-13}{6}\)
5. \(+\left(\frac{3}{2}\right) +\left(\frac{-8}{-7}\right) -\left(\frac{-6}{-10}\right)\\= \frac{3}{2}+ \frac{8}{7}-\frac{6}{10}\\=\frac{3}{2}+\frac{8}{7}-\frac{3}{5}\\=\frac{105}{70}+\frac{80}{70}-\frac{42}{70}\\=\frac{105+80-42}{70}\\=\frac{143}{70}\)
6. \(+\left(\frac{-8}{-5}\right) -\left(\frac{10}{-6}\right) -\left(\frac{6}{7}\right)\\= \frac{8}{5}+ \frac{10}{6}-\frac{6}{7}\\=\frac{8}{5}+\frac{5}{3}-\frac{6}{7}\\=\frac{168}{105}+\frac{175}{105}-\frac{90}{105}\\=\frac{168+175-90}{105}\\=\frac{253}{105}\)
7. \(+\left(\frac{-7}{-3}\right) -\left(\frac{9}{-9}\right) +\left(\frac{-2}{12}\right)\\= \frac{7}{3}+ \frac{9}{9}-\frac{2}{12}\\=\frac{7}{3}+\frac{1}{1}-\frac{1}{6}\\=\frac{14}{6}+\frac{6}{6}-\frac{1}{6}\\=\frac{14+6-1}{6}\\=\frac{19}{6}\)
8. \(-\left(\frac{6}{-5}\right) +\left(\frac{9}{7}\right) -\left(\frac{-8}{-11}\right)\\= \frac{6}{5}+ \frac{9}{7}-\frac{8}{11}\\=\frac{462}{385}+\frac{495}{385}-\frac{280}{385}\\=\frac{462+495-280}{385}\\=\frac{677}{385}\)
9. \(-\left(\frac{6}{5}\right) +\left(\frac{9}{8}\right) +\left(\frac{-6}{10}\right)\\= \frac{-6}{5}+ \frac{9}{8}-\frac{6}{10}\\=\frac{-6}{5}+\frac{9}{8}-\frac{3}{5}\\=\frac{-48}{40}+\frac{45}{40}-\frac{24}{40}\\=\frac{-48+45-24}{40}\\=\frac{-27}{40}\)
10. \(+\left(\frac{5}{6}\right) +\left(\frac{-2}{10}\right) -\left(\frac{-8}{9}\right)\\= \frac{5}{6}- \frac{2}{10}+\frac{8}{9}\\=\frac{5}{6}-\frac{1}{5}+\frac{8}{9}\\=\frac{75}{90}-\frac{18}{90}+\frac{80}{90}\\=\frac{75-18+80}{90}\\=\frac{137}{90}\)
11. \(+\left(\frac{5}{-6}\right) +\left(\frac{-9}{8}\right) -\left(\frac{4}{-12}\right)\\= \frac{-5}{6}- \frac{9}{8}+\frac{4}{12}\\=\frac{-5}{6}-\frac{9}{8}+\frac{1}{3}\\=\frac{-20}{24}-\frac{27}{24}+\frac{8}{24}\\=\frac{-20-27+8}{24}\\=\frac{-39}{24}\\=\frac{-13}{8}\)
12. \(+\left(\frac{-4}{-7}\right) -\left(\frac{10}{9}\right) +\left(\frac{5}{12}\right)\\= \frac{4}{7}- \frac{10}{9}+\frac{5}{12}\\=\frac{144}{252}-\frac{280}{252}+\frac{105}{252}\\=\frac{144-280+105}{252}\\=\frac{-31}{252}\)