Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-8}{-5}\right) +\left(\frac{5}{-8}\right)\\= \frac{-6}{7}- \frac{8}{5}-\frac{5}{8}\\=\frac{-240}{280}-\frac{448}{280}-\frac{175}{280}\\=\frac{-240-448-175}{280}\\=\frac{-863}{280}\)
2. \(+\left(\frac{-9}{-8}\right) -\left(\frac{10}{5}\right) +\left(\frac{3}{4}\right)\\= \frac{9}{8}- \frac{10}{5}+\frac{3}{4}\\=\frac{9}{8}-\frac{2}{1}+\frac{3}{4}\\=\frac{9-2+3}{8}\\=\frac{10}{8}\\=\frac{5}{4}\)
3. \(-\left(\frac{4}{9}\right) -\left(\frac{3}{3}\right) -\left(\frac{10}{11}\right)\\= \frac{-4}{9}- \frac{3}{3}-\frac{10}{11}\\=\frac{-4}{9}-\frac{1}{1}-\frac{10}{11}\\=\frac{-44}{99}-\frac{99}{99}-\frac{90}{99}\\=\frac{-44-99-90}{99}\\=\frac{-233}{99}\)
4. \(-\left(\frac{-8}{5}\right) -\left(\frac{2}{5}\right) -\left(\frac{-12}{-3}\right)\\= \frac{8}{5}- \frac{2}{5}-\frac{12}{3}\\=\frac{8}{5}-\frac{2}{5}-\frac{4}{1}\\=\frac{8-2-4}{5}\\=\frac{2}{5}\)
5. \(-\left(\frac{2}{-7}\right) -\left(\frac{9}{9}\right) -\left(\frac{3}{-11}\right)\\= \frac{2}{7}- \frac{9}{9}+\frac{3}{11}\\=\frac{2}{7}-\frac{1}{1}+\frac{3}{11}\\=\frac{22}{77}-\frac{77}{77}+\frac{21}{77}\\=\frac{22-77+21}{77}\\=\frac{-34}{77}\)
6. \(+\left(\frac{-9}{8}\right) -\left(\frac{-3}{9}\right) +\left(\frac{-11}{6}\right)\\= \frac{-9}{8}+ \frac{3}{9}-\frac{11}{6}\\=\frac{-9}{8}+\frac{1}{3}-\frac{11}{6}\\=\frac{-27}{24}+\frac{8}{24}-\frac{44}{24}\\=\frac{-27+8-44}{24}\\=\frac{-63}{24}\\=\frac{-21}{8}\)
7. \(+\left(\frac{4}{5}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{12}{-6}\right)\\= \frac{4}{5}+ \frac{5}{5}+\frac{12}{6}\\=\frac{4}{5}+\frac{1}{1}+\frac{2}{1}\\=\frac{4+1+2}{5}\\=\frac{7}{5}\)
8. \(-\left(\frac{10}{-7}\right) -\left(\frac{-7}{9}\right) -\left(\frac{8}{9}\right)\\= \frac{10}{7}+ \frac{7}{9}-\frac{8}{9}\\=\frac{90}{63}+\frac{49}{63}-\frac{56}{63}\\=\frac{90+49-56}{63}\\=\frac{83}{63}\)
9. \(-\left(\frac{-8}{9}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{3}{-9}\right)\\= \frac{8}{9}+ \frac{3}{6}+\frac{3}{9}\\=\frac{8}{9}+\frac{1}{2}+\frac{1}{3}\\=\frac{16}{18}+\frac{9}{18}+\frac{6}{18}\\=\frac{16+9+6}{18}\\=\frac{31}{18}\)
10. \(-\left(\frac{-3}{-5}\right) +\left(\frac{8}{-2}\right) +\left(\frac{6}{9}\right)\\= \frac{-3}{5}- \frac{8}{2}+\frac{6}{9}\\=\frac{-3}{5}-\frac{4}{1}+\frac{2}{3}\\=\frac{-9}{15}-\frac{60}{15}+\frac{10}{15}\\=\frac{-9-60+10}{15}\\=\frac{-59}{15}\)
11. \(-\left(\frac{7}{-9}\right) -\left(\frac{7}{-6}\right) +\left(\frac{-5}{7}\right)\\= \frac{7}{9}+ \frac{7}{6}-\frac{5}{7}\\=\frac{98}{126}+\frac{147}{126}-\frac{90}{126}\\=\frac{98+147-90}{126}\\=\frac{155}{126}\)
12. \(-\left(\frac{-6}{5}\right) -\left(\frac{-6}{4}\right) +\left(\frac{-4}{3}\right)\\= \frac{6}{5}+ \frac{6}{4}-\frac{4}{3}\\=\frac{6}{5}+\frac{3}{2}-\frac{4}{3}\\=\frac{36}{30}+\frac{45}{30}-\frac{40}{30}\\=\frac{36+45-40}{30}\\=\frac{41}{30}\)