Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{9}\right) -\left(\frac{8}{-7}\right) -\left(\frac{10}{-12}\right)\\= \frac{7}{9}+ \frac{8}{7}+\frac{10}{12}\\=\frac{7}{9}+\frac{8}{7}+\frac{5}{6}\\=\frac{98}{126}+\frac{144}{126}+\frac{105}{126}\\=\frac{98+144+105}{126}\\=\frac{347}{126}\)
2. \(-\left(\frac{7}{4}\right) -\left(\frac{-5}{8}\right) -\left(\frac{-2}{5}\right)\\= \frac{-7}{4}+ \frac{5}{8}+\frac{2}{5}\\=\frac{-70}{40}+\frac{25}{40}+\frac{16}{40}\\=\frac{-70+25+16}{40}\\=\frac{-29}{40}\)
3. \(+\left(\frac{3}{2}\right) +\left(\frac{5}{9}\right) -\left(\frac{-3}{2}\right)\\= \frac{3}{2}+ \frac{5}{9}+\frac{3}{2}\\=\frac{27}{18}+\frac{10}{18}+\frac{27}{18}\\=\frac{27+10+27}{18}\\=\frac{64}{18}\\=\frac{32}{9}\)
4. \(+\left(\frac{5}{-8}\right) +\left(\frac{-10}{7}\right) -\left(\frac{-10}{-5}\right)\\= \frac{-5}{8}- \frac{10}{7}-\frac{10}{5}\\=\frac{-5}{8}-\frac{10}{7}-\frac{2}{1}\\=\frac{-35}{56}-\frac{80}{56}-\frac{112}{56}\\=\frac{-35-80-112}{56}\\=\frac{-227}{56}\)
5. \(-\left(\frac{-7}{-2}\right) +\left(\frac{4}{6}\right) -\left(\frac{8}{-8}\right)\\= \frac{-7}{2}+ \frac{4}{6}+\frac{8}{8}\\=\frac{-7}{2}+\frac{2}{3}+\frac{1}{1}\\=\frac{-21}{6}+\frac{4}{6}+\frac{6}{6}\\=\frac{-21+4+6}{6}\\=\frac{-11}{6}\)
6. \(-\left(\frac{3}{-7}\right) +\left(\frac{4}{5}\right) -\left(\frac{-11}{6}\right)\\= \frac{3}{7}+ \frac{4}{5}+\frac{11}{6}\\=\frac{90}{210}+\frac{168}{210}+\frac{385}{210}\\=\frac{90+168+385}{210}\\=\frac{643}{210}\)
7. \(+\left(\frac{-6}{7}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{12}{10}\right)\\= \frac{-6}{7}+ \frac{7}{5}+\frac{12}{10}\\=\frac{-6}{7}+\frac{7}{5}+\frac{6}{5}\\=\frac{-30}{35}+\frac{49}{35}+\frac{42}{35}\\=\frac{-30+49+42}{35}\\=\frac{61}{35}\)
8. \(+\left(\frac{3}{7}\right) +\left(\frac{3}{9}\right) -\left(\frac{-3}{9}\right)\\= \frac{3}{7}+ \frac{3}{9}+\frac{3}{9}\\=\frac{3}{7}+\frac{1}{3}+\frac{1}{3}\\=\frac{9}{21}+\frac{7}{21}+\frac{7}{21}\\=\frac{9+7+7}{21}\\=\frac{23}{21}\)
9. \(+\left(\frac{-10}{-9}\right) -\left(\frac{10}{6}\right) +\left(\frac{-3}{3}\right)\\= \frac{10}{9}- \frac{10}{6}-\frac{3}{3}\\=\frac{10}{9}-\frac{5}{3}-\frac{1}{1}\\=\frac{10-5-1}{9}\\=\frac{4}{9}\)
10. \(-\left(\frac{10}{9}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{-8}{9}\right)\\= \frac{-10}{9}+ \frac{6}{8}+\frac{8}{9}\\=\frac{-10}{9}+\frac{3}{4}+\frac{8}{9}\\=\frac{-40}{36}+\frac{27}{36}+\frac{32}{36}\\=\frac{-40+27+32}{36}\\=\frac{19}{36}\)
11. \(-\left(\frac{-5}{9}\right) +\left(\frac{9}{-4}\right) +\left(\frac{-12}{10}\right)\\= \frac{5}{9}- \frac{9}{4}-\frac{12}{10}\\=\frac{5}{9}-\frac{9}{4}-\frac{6}{5}\\=\frac{100}{180}-\frac{405}{180}-\frac{216}{180}\\=\frac{100-405-216}{180}\\=\frac{-521}{180}\)
12. \(-\left(\frac{-6}{5}\right) -\left(\frac{-10}{-8}\right) -\left(\frac{-2}{4}\right)\\= \frac{6}{5}- \frac{10}{8}+\frac{2}{4}\\=\frac{6}{5}-\frac{5}{4}+\frac{1}{2}\\=\frac{24}{20}-\frac{25}{20}+\frac{10}{20}\\=\frac{24-25+10}{20}\\=\frac{9}{20}\)