Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right) -\left(\frac{7}{-2}\right) +\left(\frac{5}{10}\right)\\= \frac{8}{7}+ \frac{7}{2}+\frac{5}{10}\\=\frac{8}{7}+\frac{7}{2}+\frac{1}{2}\\=\frac{16}{14}+\frac{49}{14}+\frac{7}{14}\\=\frac{16+49+7}{14}\\=\frac{72}{14}\\=\frac{36}{7}\)
2. \(+\left(\frac{8}{-3}\right) +\left(\frac{5}{7}\right) +\left(\frac{-12}{7}\right)\\= \frac{-8}{3}+ \frac{5}{7}-\frac{12}{7}\\=\frac{-56}{21}+\frac{15}{21}-\frac{36}{21}\\=\frac{-56+15-36}{21}\\=\frac{-77}{21}\\=\frac{-11}{3}\)
3. \(-\left(\frac{10}{-7}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-3}{5}\right)\\= \frac{10}{7}- \frac{10}{5}+\frac{3}{5}\\=\frac{10}{7}-\frac{2}{1}+\frac{3}{5}\\=\frac{50}{35}-\frac{70}{35}+\frac{21}{35}\\=\frac{50-70+21}{35}\\=\frac{1}{35}\)
4. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{4}{5}\right)\\= \frac{-6}{7}- \frac{10}{10}+\frac{4}{5}\\=\frac{-6}{7}-\frac{1}{1}+\frac{4}{5}\\=\frac{-30}{35}-\frac{35}{35}+\frac{28}{35}\\=\frac{-30-35+28}{35}\\=\frac{-37}{35}\)
5. \(-\left(\frac{7}{9}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{4}{4}\right)\\= \frac{-7}{9}- \frac{10}{6}+\frac{4}{4}\\=\frac{-7}{9}-\frac{5}{3}+\frac{1}{1}\\=\frac{-7-5+1}{9}\\=\frac{-11}{9}\)
6. \(-\left(\frac{9}{-2}\right) -\left(\frac{8}{-8}\right) +\left(\frac{4}{7}\right)\\= \frac{9}{2}+ \frac{8}{8}+\frac{4}{7}\\=\frac{9}{2}+\frac{1}{1}+\frac{4}{7}\\=\frac{63}{14}+\frac{14}{14}+\frac{8}{14}\\=\frac{63+14+8}{14}\\=\frac{85}{14}\)
7. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{12}{-9}\right)\\= \frac{2}{3}+ \frac{7}{5}-\frac{12}{9}\\=\frac{2}{3}+\frac{7}{5}-\frac{4}{3}\\=\frac{10}{15}+\frac{21}{15}-\frac{20}{15}\\=\frac{10+21-20}{15}\\=\frac{11}{15}\)
8. \(-\left(\frac{-7}{2}\right) +\left(\frac{2}{5}\right) +\left(\frac{-12}{-12}\right)\\= \frac{7}{2}+ \frac{2}{5}+\frac{12}{12}\\=\frac{7}{2}+\frac{2}{5}+\frac{1}{1}\\=\frac{35}{10}+\frac{4}{10}+\frac{10}{10}\\=\frac{35+4+10}{10}\\=\frac{49}{10}\)
9. \(+\left(\frac{-6}{-5}\right) -\left(\frac{7}{-4}\right) -\left(\frac{-5}{-4}\right)\\= \frac{6}{5}+ \frac{7}{4}-\frac{5}{4}\\=\frac{24}{20}+\frac{35}{20}-\frac{25}{20}\\=\frac{24+35-25}{20}\\=\frac{34}{20}\\=\frac{17}{10}\)
10. \(-\left(\frac{-7}{-5}\right) +\left(\frac{-7}{-3}\right) +\left(\frac{7}{4}\right)\\= \frac{-7}{5}+ \frac{7}{3}+\frac{7}{4}\\=\frac{-84}{60}+\frac{140}{60}+\frac{105}{60}\\=\frac{-84+140+105}{60}\\=\frac{161}{60}\)
11. \(-\left(\frac{-2}{-3}\right) +\left(\frac{-8}{-6}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-2}{3}+ \frac{8}{6}-\frac{10}{10}\\=\frac{-2}{3}+\frac{4}{3}-\frac{1}{1}\\=\frac{-2+4-1}{3}\\=\frac{1}{3}\)
12. \(+\left(\frac{-8}{9}\right) -\left(\frac{2}{-9}\right) +\left(\frac{9}{3}\right)\\= \frac{-8}{9}+ \frac{2}{9}+\frac{9}{3}\\=\frac{-8}{9}+\frac{2}{9}+\frac{3}{1}\\=\frac{-8+2+3}{9}\\=\frac{-3}{9}\\=\frac{-1}{3}\)