Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{-2}\right) -\left(\frac{6}{-7}\right) +\left(\frac{4}{3}\right)\\= \frac{-9}{2}+ \frac{6}{7}+\frac{4}{3}\\=\frac{-189}{42}+\frac{36}{42}+\frac{56}{42}\\=\frac{-189+36+56}{42}\\=\frac{-97}{42}\)
2. \(-\left(\frac{9}{-7}\right) -\left(\frac{-7}{4}\right) +\left(\frac{3}{-12}\right)\\= \frac{9}{7}+ \frac{7}{4}-\frac{3}{12}\\=\frac{9}{7}+\frac{7}{4}-\frac{1}{4}\\=\frac{36}{28}+\frac{49}{28}-\frac{7}{28}\\=\frac{36+49-7}{28}\\=\frac{78}{28}\\=\frac{39}{14}\)
3. \(+\left(\frac{-10}{-7}\right) +\left(\frac{9}{-5}\right) -\left(\frac{-11}{-3}\right)\\= \frac{10}{7}- \frac{9}{5}-\frac{11}{3}\\=\frac{150}{105}-\frac{189}{105}-\frac{385}{105}\\=\frac{150-189-385}{105}\\=\frac{-424}{105}\)
4. \(-\left(\frac{4}{-3}\right) +\left(\frac{4}{8}\right) +\left(\frac{-7}{-8}\right)\\= \frac{4}{3}+ \frac{4}{8}+\frac{7}{8}\\=\frac{4}{3}+\frac{1}{2}+\frac{7}{8}\\=\frac{32}{24}+\frac{12}{24}+\frac{21}{24}\\=\frac{32+12+21}{24}\\=\frac{65}{24}\)
5. \(-\left(\frac{2}{-5}\right) +\left(\frac{9}{4}\right) +\left(\frac{-7}{11}\right)\\= \frac{2}{5}+ \frac{9}{4}-\frac{7}{11}\\=\frac{88}{220}+\frac{495}{220}-\frac{140}{220}\\=\frac{88+495-140}{220}\\=\frac{443}{220}\)
6. \(+\left(\frac{-4}{3}\right) +\left(\frac{10}{-3}\right) +\left(\frac{5}{3}\right)\\= \frac{-4}{3}- \frac{10}{3}+\frac{5}{3}\\=\frac{-4-10+5}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
7. \(+\left(\frac{4}{-5}\right) +\left(\frac{-6}{-2}\right) +\left(\frac{-2}{-12}\right)\\= \frac{-4}{5}+ \frac{6}{2}+\frac{2}{12}\\=\frac{-4}{5}+\frac{3}{1}+\frac{1}{6}\\=\frac{-24}{30}+\frac{90}{30}+\frac{5}{30}\\=\frac{-24+90+5}{30}\\=\frac{71}{30}\)
8. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-10}{8}\right) -\left(\frac{-5}{-3}\right)\\= \frac{8}{9}+ \frac{10}{8}-\frac{5}{3}\\=\frac{8}{9}+\frac{5}{4}-\frac{5}{3}\\=\frac{32}{36}+\frac{45}{36}-\frac{60}{36}\\=\frac{32+45-60}{36}\\=\frac{17}{36}\)
9. \(-\left(\frac{6}{-5}\right) +\left(\frac{-8}{7}\right) -\left(\frac{11}{-10}\right)\\= \frac{6}{5}- \frac{8}{7}+\frac{11}{10}\\=\frac{84}{70}-\frac{80}{70}+\frac{77}{70}\\=\frac{84-80+77}{70}\\=\frac{81}{70}\)
10. \(-\left(\frac{3}{7}\right) -\left(\frac{-6}{-8}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-3}{7}- \frac{6}{8}-\frac{11}{10}\\=\frac{-3}{7}-\frac{3}{4}-\frac{11}{10}\\=\frac{-60}{140}-\frac{105}{140}-\frac{154}{140}\\=\frac{-60-105-154}{140}\\=\frac{-319}{140}\)
11. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-7}{-2}\right) +\left(\frac{-10}{9}\right)\\= \frac{-8}{9}+ \frac{7}{2}-\frac{10}{9}\\=\frac{-16}{18}+\frac{63}{18}-\frac{20}{18}\\=\frac{-16+63-20}{18}\\=\frac{27}{18}\\=\frac{3}{2}\)
12. \(-\left(\frac{-9}{8}\right) +\left(\frac{7}{-3}\right) +\left(\frac{10}{9}\right)\\= \frac{9}{8}- \frac{7}{3}+\frac{10}{9}\\=\frac{81}{72}-\frac{168}{72}+\frac{80}{72}\\=\frac{81-168+80}{72}\\=\frac{-7}{72}\)