Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{2}\right) -\left(\frac{5}{-3}\right) -\left(\frac{4}{4}\right)\\= \frac{-9}{2}+ \frac{5}{3}-\frac{4}{4}\\=\frac{-9}{2}+\frac{5}{3}-\frac{1}{1}\\=\frac{-27}{6}+\frac{10}{6}-\frac{6}{6}\\=\frac{-27+10-6}{6}\\=\frac{-23}{6}\)
2. \(-\left(\frac{-4}{5}\right) +\left(\frac{5}{2}\right) -\left(\frac{-3}{2}\right)\\= \frac{4}{5}+ \frac{5}{2}+\frac{3}{2}\\=\frac{8}{10}+\frac{25}{10}+\frac{15}{10}\\=\frac{8+25+15}{10}\\=\frac{48}{10}\\=\frac{24}{5}\)
3. \(+\left(\frac{-8}{3}\right) +\left(\frac{3}{-6}\right) +\left(\frac{4}{3}\right)\\= \frac{-8}{3}- \frac{3}{6}+\frac{4}{3}\\=\frac{-8}{3}-\frac{1}{2}+\frac{4}{3}\\=\frac{-16}{6}-\frac{3}{6}+\frac{8}{6}\\=\frac{-16-3+8}{6}\\=\frac{-11}{6}\)
4. \(+\left(\frac{7}{9}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{11}{8}\right)\\= \frac{7}{9}+ \frac{8}{2}-\frac{11}{8}\\=\frac{7}{9}+\frac{4}{1}-\frac{11}{8}\\=\frac{56}{72}+\frac{288}{72}-\frac{99}{72}\\=\frac{56+288-99}{72}\\=\frac{245}{72}\)
5. \(+\left(\frac{-9}{7}\right) +\left(\frac{-5}{-5}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-9}{7}+ \frac{5}{5}+\frac{10}{8}\\=\frac{-9}{7}+\frac{1}{1}+\frac{5}{4}\\=\frac{-36}{28}+\frac{28}{28}+\frac{35}{28}\\=\frac{-36+28+35}{28}\\=\frac{27}{28}\)
6. \(-\left(\frac{2}{5}\right) +\left(\frac{7}{-8}\right) +\left(\frac{-11}{-9}\right)\\= \frac{-2}{5}- \frac{7}{8}+\frac{11}{9}\\=\frac{-144}{360}-\frac{315}{360}+\frac{440}{360}\\=\frac{-144-315+440}{360}\\=\frac{-19}{360}\)
7. \(+\left(\frac{-6}{5}\right) +\left(\frac{5}{3}\right) -\left(\frac{-3}{8}\right)\\= \frac{-6}{5}+ \frac{5}{3}+\frac{3}{8}\\=\frac{-144}{120}+\frac{200}{120}+\frac{45}{120}\\=\frac{-144+200+45}{120}\\=\frac{101}{120}\)
8. \(+\left(\frac{4}{-9}\right) -\left(\frac{-4}{8}\right) +\left(\frac{-4}{8}\right)\\= \frac{-4}{9}+ \frac{4}{8}-\frac{4}{8}\\=\frac{-4}{9}+\frac{1}{2}-\frac{1}{2}\\=\frac{-8}{18}+\frac{9}{18}-\frac{9}{18}\\=\frac{-8+9-9}{18}\\=\frac{-8}{18}\\=\frac{-4}{9}\)
9. \(+\left(\frac{-2}{3}\right) -\left(\frac{-7}{8}\right) +\left(\frac{-8}{-3}\right)\\= \frac{-2}{3}+ \frac{7}{8}+\frac{8}{3}\\=\frac{-16}{24}+\frac{21}{24}+\frac{64}{24}\\=\frac{-16+21+64}{24}\\=\frac{69}{24}\\=\frac{23}{8}\)
10. \(-\left(\frac{-8}{5}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{-4}{8}\right)\\= \frac{8}{5}+ \frac{2}{6}+\frac{4}{8}\\=\frac{8}{5}+\frac{1}{3}+\frac{1}{2}\\=\frac{48}{30}+\frac{10}{30}+\frac{15}{30}\\=\frac{48+10+15}{30}\\=\frac{73}{30}\)
11. \(+\left(\frac{-7}{-2}\right) +\left(\frac{2}{9}\right) -\left(\frac{-4}{3}\right)\\= \frac{7}{2}+ \frac{2}{9}+\frac{4}{3}\\=\frac{63}{18}+\frac{4}{18}+\frac{24}{18}\\=\frac{63+4+24}{18}\\=\frac{91}{18}\)
12. \(-\left(\frac{8}{-7}\right) -\left(\frac{-6}{5}\right) -\left(\frac{9}{12}\right)\\= \frac{8}{7}+ \frac{6}{5}-\frac{9}{12}\\=\frac{8}{7}+\frac{6}{5}-\frac{3}{4}\\=\frac{160}{140}+\frac{168}{140}-\frac{105}{140}\\=\frac{160+168-105}{140}\\=\frac{223}{140}\)