Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-2}\right) +\left(\frac{-5}{10}\right) +\left(\frac{12}{-4}\right)\\= \frac{7}{2}- \frac{5}{10}-\frac{12}{4}\\=\frac{7}{2}-\frac{1}{2}-\frac{3}{1}\\=\frac{7-1-3}{2}\\=\frac{3}{2}\)
2. \(-\left(\frac{-4}{7}\right) -\left(\frac{10}{-8}\right) +\left(\frac{-9}{2}\right)\\= \frac{4}{7}+ \frac{10}{8}-\frac{9}{2}\\=\frac{4}{7}+\frac{5}{4}-\frac{9}{2}\\=\frac{16}{28}+\frac{35}{28}-\frac{126}{28}\\=\frac{16+35-126}{28}\\=\frac{-75}{28}\)
3. \(+\left(\frac{-8}{-3}\right) +\left(\frac{7}{8}\right) +\left(\frac{-3}{10}\right)\\= \frac{8}{3}+ \frac{7}{8}-\frac{3}{10}\\=\frac{320}{120}+\frac{105}{120}-\frac{36}{120}\\=\frac{320+105-36}{120}\\=\frac{389}{120}\)
4. \(-\left(\frac{4}{7}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{3}{-9}\right)\\= \frac{-4}{7}- \frac{5}{5}-\frac{3}{9}\\=\frac{-4}{7}-\frac{1}{1}-\frac{1}{3}\\=\frac{-12}{21}-\frac{21}{21}-\frac{7}{21}\\=\frac{-12-21-7}{21}\\=\frac{-40}{21}\)
5. \(-\left(\frac{4}{3}\right) -\left(\frac{-8}{3}\right) -\left(\frac{2}{4}\right)\\= \frac{-4}{3}+ \frac{8}{3}-\frac{2}{4}\\=\frac{-4}{3}+\frac{8}{3}-\frac{1}{2}\\=\frac{-8}{6}+\frac{16}{6}-\frac{3}{6}\\=\frac{-8+16-3}{6}\\=\frac{5}{6}\)
6. \(+\left(\frac{-9}{4}\right) +\left(\frac{2}{8}\right) -\left(\frac{-10}{-8}\right)\\= \frac{-9}{4}+ \frac{2}{8}-\frac{10}{8}\\=\frac{-9}{4}+\frac{1}{4}-\frac{5}{4}\\=\frac{-9+1-5}{4}\\=\frac{-13}{4}\)
7. \(-\left(\frac{3}{-2}\right) +\left(\frac{5}{6}\right) -\left(\frac{11}{-3}\right)\\= \frac{3}{2}+ \frac{5}{6}+\frac{11}{3}\\=\frac{9}{6}+\frac{5}{6}+\frac{22}{6}\\=\frac{9+5+22}{6}\\=\frac{36}{6}\\=\frac{6}{1}\)
8. \(+\left(\frac{-5}{3}\right) +\left(\frac{3}{8}\right) -\left(\frac{7}{-2}\right)\\= \frac{-5}{3}+ \frac{3}{8}+\frac{7}{2}\\=\frac{-40}{24}+\frac{9}{24}+\frac{84}{24}\\=\frac{-40+9+84}{24}\\=\frac{53}{24}\)
9. \(+\left(\frac{-7}{2}\right) +\left(\frac{8}{10}\right) -\left(\frac{-8}{7}\right)\\= \frac{-7}{2}+ \frac{8}{10}+\frac{8}{7}\\=\frac{-7}{2}+\frac{4}{5}+\frac{8}{7}\\=\frac{-245}{70}+\frac{56}{70}+\frac{80}{70}\\=\frac{-245+56+80}{70}\\=\frac{-109}{70}\)
10. \(+\left(\frac{10}{-7}\right) +\left(\frac{3}{5}\right) +\left(\frac{10}{4}\right)\\= \frac{-10}{7}+ \frac{3}{5}+\frac{10}{4}\\=\frac{-10}{7}+\frac{3}{5}+\frac{5}{2}\\=\frac{-100}{70}+\frac{42}{70}+\frac{175}{70}\\=\frac{-100+42+175}{70}\\=\frac{117}{70}\)
11. \(-\left(\frac{-8}{-7}\right) +\left(\frac{2}{-10}\right) +\left(\frac{8}{-9}\right)\\= \frac{-8}{7}- \frac{2}{10}-\frac{8}{9}\\=\frac{-8}{7}-\frac{1}{5}-\frac{8}{9}\\=\frac{-360}{315}-\frac{63}{315}-\frac{280}{315}\\=\frac{-360-63-280}{315}\\=\frac{-703}{315}\)
12. \(-\left(\frac{4}{-7}\right) -\left(\frac{9}{-5}\right) -\left(\frac{8}{6}\right)\\= \frac{4}{7}+ \frac{9}{5}-\frac{8}{6}\\=\frac{4}{7}+\frac{9}{5}-\frac{4}{3}\\=\frac{60}{105}+\frac{189}{105}-\frac{140}{105}\\=\frac{60+189-140}{105}\\=\frac{109}{105}\)