Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-7}{2}\right) -\left(\frac{-7}{7}\right)\\= \frac{9}{4}+ \frac{7}{2}+\frac{7}{7}\\=\frac{9}{4}+\frac{7}{2}+\frac{1}{1}\\=\frac{9+7+1}{4}\\=\frac{17}{4}\)
2. \(+\left(\frac{10}{9}\right) -\left(\frac{-2}{8}\right) -\left(\frac{-12}{-4}\right)\\= \frac{10}{9}+ \frac{2}{8}-\frac{12}{4}\\=\frac{10}{9}+\frac{1}{4}-\frac{3}{1}\\=\frac{40}{36}+\frac{9}{36}-\frac{108}{36}\\=\frac{40+9-108}{36}\\=\frac{-59}{36}\)
3. \(+\left(\frac{-8}{-7}\right) -\left(\frac{2}{3}\right) -\left(\frac{-11}{10}\right)\\= \frac{8}{7}- \frac{2}{3}+\frac{11}{10}\\=\frac{240}{210}-\frac{140}{210}+\frac{231}{210}\\=\frac{240-140+231}{210}\\=\frac{331}{210}\)
4. \(-\left(\frac{5}{-6}\right) +\left(\frac{-3}{7}\right) -\left(\frac{-10}{8}\right)\\= \frac{5}{6}- \frac{3}{7}+\frac{10}{8}\\=\frac{5}{6}-\frac{3}{7}+\frac{5}{4}\\=\frac{70}{84}-\frac{36}{84}+\frac{105}{84}\\=\frac{70-36+105}{84}\\=\frac{139}{84}\)
5. \(+\left(\frac{-10}{7}\right) -\left(\frac{-10}{3}\right) -\left(\frac{2}{6}\right)\\= \frac{-10}{7}+ \frac{10}{3}-\frac{2}{6}\\=\frac{-10}{7}+\frac{10}{3}-\frac{1}{3}\\=\frac{-30}{21}+\frac{70}{21}-\frac{7}{21}\\=\frac{-30+70-7}{21}\\=\frac{33}{21}\\=\frac{11}{7}\)
6. \(-\left(\frac{-9}{-2}\right) -\left(\frac{2}{-8}\right) -\left(\frac{-12}{-2}\right)\\= \frac{-9}{2}+ \frac{2}{8}-\frac{12}{2}\\=\frac{-9}{2}+\frac{1}{4}-\frac{6}{1}\\=\frac{-18}{4}+\frac{1}{4}-\frac{24}{4}\\=\frac{-18+1-24}{4}\\=\frac{-41}{4}\)
7. \(-\left(\frac{7}{-3}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{12}{10}\right)\\= \frac{7}{3}+ \frac{8}{6}+\frac{12}{10}\\=\frac{7}{3}+\frac{4}{3}+\frac{6}{5}\\=\frac{35}{15}+\frac{20}{15}+\frac{18}{15}\\=\frac{35+20+18}{15}\\=\frac{73}{15}\)
8. \(+\left(\frac{4}{-5}\right) +\left(\frac{9}{7}\right) +\left(\frac{-10}{8}\right)\\= \frac{-4}{5}+ \frac{9}{7}-\frac{10}{8}\\=\frac{-4}{5}+\frac{9}{7}-\frac{5}{4}\\=\frac{-112}{140}+\frac{180}{140}-\frac{175}{140}\\=\frac{-112+180-175}{140}\\=\frac{-107}{140}\)
9. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{-2}{-2}\right)\\= \frac{-5}{6}- \frac{2}{6}-\frac{2}{2}\\=\frac{-5}{6}-\frac{1}{3}-\frac{1}{1}\\=\frac{-5-1-1}{6}\\=\frac{-7}{6}\)
10. \(+\left(\frac{4}{5}\right) +\left(\frac{7}{-9}\right) -\left(\frac{7}{2}\right)\\= \frac{4}{5}- \frac{7}{9}-\frac{7}{2}\\=\frac{72}{90}-\frac{70}{90}-\frac{315}{90}\\=\frac{72-70-315}{90}\\=\frac{-313}{90}\)
11. \(-\left(\frac{10}{-7}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{9}{-8}\right)\\= \frac{10}{7}+ \frac{9}{8}-\frac{9}{8}\\=\frac{80}{56}+\frac{63}{56}-\frac{63}{56}\\=\frac{80+63-63}{56}\\=\frac{80}{56}\\=\frac{10}{7}\)
12. \(-\left(\frac{3}{7}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{12}{4}\right)\\= \frac{-3}{7}- \frac{6}{5}-\frac{12}{4}\\=\frac{-3}{7}-\frac{6}{5}-\frac{3}{1}\\=\frac{-15}{35}-\frac{42}{35}-\frac{105}{35}\\=\frac{-15-42-105}{35}\\=\frac{-162}{35}\)