Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-5}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{9}{-8}\right)\\= \frac{-6}{5}+ \frac{7}{9}-\frac{9}{8}\\=\frac{-432}{360}+\frac{280}{360}-\frac{405}{360}\\=\frac{-432+280-405}{360}\\=\frac{-557}{360}\)
2. \(+\left(\frac{-3}{-4}\right) -\left(\frac{-9}{6}\right) -\left(\frac{11}{2}\right)\\= \frac{3}{4}+ \frac{9}{6}-\frac{11}{2}\\=\frac{3}{4}+\frac{3}{2}-\frac{11}{2}\\=\frac{3+3-11}{4}\\=\frac{-5}{4}\)
3. \(-\left(\frac{5}{7}\right) -\left(\frac{8}{-5}\right) -\left(\frac{11}{-12}\right)\\= \frac{-5}{7}+ \frac{8}{5}+\frac{11}{12}\\=\frac{-300}{420}+\frac{672}{420}+\frac{385}{420}\\=\frac{-300+672+385}{420}\\=\frac{757}{420}\)
4. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-5}{-6}\right)\\= \frac{3}{2}- \frac{10}{3}+\frac{5}{6}\\=\frac{9}{6}-\frac{20}{6}+\frac{5}{6}\\=\frac{9-20+5}{6}\\=\frac{-6}{6}\\=\frac{-1}{1}\)
5. \(-\left(\frac{9}{2}\right) +\left(\frac{-6}{5}\right) -\left(\frac{-11}{5}\right)\\= \frac{-9}{2}- \frac{6}{5}+\frac{11}{5}\\=\frac{-45}{10}-\frac{12}{10}+\frac{22}{10}\\=\frac{-45-12+22}{10}\\=\frac{-35}{10}\\=\frac{-7}{2}\)
6. \(-\left(\frac{-3}{4}\right) +\left(\frac{5}{-10}\right) -\left(\frac{-11}{3}\right)\\= \frac{3}{4}- \frac{5}{10}+\frac{11}{3}\\=\frac{3}{4}-\frac{1}{2}+\frac{11}{3}\\=\frac{9}{12}-\frac{6}{12}+\frac{44}{12}\\=\frac{9-6+44}{12}\\=\frac{47}{12}\)
7. \(-\left(\frac{-3}{-8}\right) -\left(\frac{8}{3}\right) +\left(\frac{-11}{6}\right)\\= \frac{-3}{8}- \frac{8}{3}-\frac{11}{6}\\=\frac{-9}{24}-\frac{64}{24}-\frac{44}{24}\\=\frac{-9-64-44}{24}\\=\frac{-117}{24}\\=\frac{-39}{8}\)
8. \(-\left(\frac{5}{7}\right) +\left(\frac{6}{-6}\right) +\left(\frac{10}{-10}\right)\\= \frac{-5}{7}- \frac{6}{6}-\frac{10}{10}\\=\frac{-5}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{-5-1-1}{7}\\=\frac{-7}{7}\\=\frac{-1}{1}\)
9. \(+\left(\frac{9}{7}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{12}{-8}\right)\\= \frac{9}{7}- \frac{9}{10}-\frac{12}{8}\\=\frac{9}{7}-\frac{9}{10}-\frac{3}{2}\\=\frac{90}{70}-\frac{63}{70}-\frac{105}{70}\\=\frac{90-63-105}{70}\\=\frac{-78}{70}\\=\frac{-39}{35}\)
10. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-6}{5}\right) +\left(\frac{6}{2}\right)\\= \frac{-10}{7}- \frac{6}{5}+\frac{6}{2}\\=\frac{-10}{7}-\frac{6}{5}+\frac{3}{1}\\=\frac{-50}{35}-\frac{42}{35}+\frac{105}{35}\\=\frac{-50-42+105}{35}\\=\frac{13}{35}\)
11. \(-\left(\frac{-3}{-7}\right) -\left(\frac{9}{8}\right) -\left(\frac{-9}{-3}\right)\\= \frac{-3}{7}- \frac{9}{8}-\frac{9}{3}\\=\frac{-3}{7}-\frac{9}{8}-\frac{3}{1}\\=\frac{-24}{56}-\frac{63}{56}-\frac{168}{56}\\=\frac{-24-63-168}{56}\\=\frac{-255}{56}\)
12. \(+\left(\frac{9}{-2}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{8}{-5}\right)\\= \frac{-9}{2}- \frac{6}{6}+\frac{8}{5}\\=\frac{-9}{2}-\frac{1}{1}+\frac{8}{5}\\=\frac{-45}{10}-\frac{10}{10}+\frac{16}{10}\\=\frac{-45-10+16}{10}\\=\frac{-39}{10}\)