Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{9}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{-12}{3}\right)\\= \frac{2}{9}- \frac{9}{8}-\frac{12}{3}\\=\frac{2}{9}-\frac{9}{8}-\frac{4}{1}\\=\frac{16}{72}-\frac{81}{72}-\frac{288}{72}\\=\frac{16-81-288}{72}\\=\frac{-353}{72}\)
2. \(+\left(\frac{8}{3}\right) +\left(\frac{-4}{7}\right) -\left(\frac{11}{12}\right)\\= \frac{8}{3}- \frac{4}{7}-\frac{11}{12}\\=\frac{224}{84}-\frac{48}{84}-\frac{77}{84}\\=\frac{224-48-77}{84}\\=\frac{99}{84}\\=\frac{33}{28}\)
3. \(+\left(\frac{-7}{-4}\right) -\left(\frac{-5}{8}\right) -\left(\frac{-2}{3}\right)\\= \frac{7}{4}+ \frac{5}{8}+\frac{2}{3}\\=\frac{42}{24}+\frac{15}{24}+\frac{16}{24}\\=\frac{42+15+16}{24}\\=\frac{73}{24}\)
4. \(-\left(\frac{-9}{4}\right) -\left(\frac{10}{-8}\right) +\left(\frac{8}{12}\right)\\= \frac{9}{4}+ \frac{10}{8}+\frac{8}{12}\\=\frac{9}{4}+\frac{5}{4}+\frac{2}{3}\\=\frac{27}{12}+\frac{15}{12}+\frac{8}{12}\\=\frac{27+15+8}{12}\\=\frac{50}{12}\\=\frac{25}{6}\)
5. \(-\left(\frac{-4}{-7}\right) -\left(\frac{-6}{6}\right) -\left(\frac{9}{10}\right)\\= \frac{-4}{7}+ \frac{6}{6}-\frac{9}{10}\\=\frac{-4}{7}+\frac{1}{1}-\frac{9}{10}\\=\frac{-40}{70}+\frac{70}{70}-\frac{63}{70}\\=\frac{-40+70-63}{70}\\=\frac{-33}{70}\)
6. \(+\left(\frac{8}{-5}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-8}{5}+ \frac{2}{9}-\frac{11}{6}\\=\frac{-144}{90}+\frac{20}{90}-\frac{165}{90}\\=\frac{-144+20-165}{90}\\=\frac{-289}{90}\)
7. \(+\left(\frac{9}{-2}\right) +\left(\frac{2}{-4}\right) +\left(\frac{4}{-6}\right)\\= \frac{-9}{2}- \frac{2}{4}-\frac{4}{6}\\=\frac{-9}{2}-\frac{1}{2}-\frac{2}{3}\\=\frac{-27}{6}-\frac{3}{6}-\frac{4}{6}\\=\frac{-27-3-4}{6}\\=\frac{-34}{6}\\=\frac{-17}{3}\)
8. \(+\left(\frac{-8}{7}\right) +\left(\frac{10}{4}\right) +\left(\frac{-11}{-10}\right)\\= \frac{-8}{7}+ \frac{10}{4}+\frac{11}{10}\\=\frac{-8}{7}+\frac{5}{2}+\frac{11}{10}\\=\frac{-80}{70}+\frac{175}{70}+\frac{77}{70}\\=\frac{-80+175+77}{70}\\=\frac{172}{70}\\=\frac{86}{35}\)
9. \(+\left(\frac{10}{-9}\right) -\left(\frac{2}{5}\right) -\left(\frac{12}{10}\right)\\= \frac{-10}{9}- \frac{2}{5}-\frac{12}{10}\\=\frac{-10}{9}-\frac{2}{5}-\frac{6}{5}\\=\frac{-50}{45}-\frac{18}{45}-\frac{54}{45}\\=\frac{-50-18-54}{45}\\=\frac{-122}{45}\)
10. \(-\left(\frac{4}{3}\right) -\left(\frac{-10}{6}\right) -\left(\frac{11}{11}\right)\\= \frac{-4}{3}+ \frac{10}{6}-\frac{11}{11}\\=\frac{-4}{3}+\frac{5}{3}-\frac{1}{1}\\=\frac{-4+5-1}{3}\\=\frac{0}{3}\\=\frac{0}{1}\)
11. \(-\left(\frac{-3}{5}\right) -\left(\frac{3}{-2}\right) -\left(\frac{4}{-7}\right)\\= \frac{3}{5}+ \frac{3}{2}+\frac{4}{7}\\=\frac{42}{70}+\frac{105}{70}+\frac{40}{70}\\=\frac{42+105+40}{70}\\=\frac{187}{70}\)
12. \(-\left(\frac{-2}{-7}\right) +\left(\frac{10}{-3}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-2}{7}- \frac{10}{3}-\frac{2}{3}\\=\frac{-6}{21}-\frac{70}{21}-\frac{14}{21}\\=\frac{-6-70-14}{21}\\=\frac{-90}{21}\\=\frac{-30}{7}\)