Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-2}\right) +\left(\frac{10}{9}\right) +\left(\frac{-3}{2}\right)\\= \frac{-3}{2}+ \frac{10}{9}-\frac{3}{2}\\=\frac{-27}{18}+\frac{20}{18}-\frac{27}{18}\\=\frac{-27+20-27}{18}\\=\frac{-34}{18}\\=\frac{-17}{9}\)
2. \(+\left(\frac{6}{-5}\right) +\left(\frac{-8}{-3}\right) -\left(\frac{-11}{-2}\right)\\= \frac{-6}{5}+ \frac{8}{3}-\frac{11}{2}\\=\frac{-36}{30}+\frac{80}{30}-\frac{165}{30}\\=\frac{-36+80-165}{30}\\=\frac{-121}{30}\)
3. \(-\left(\frac{-7}{-5}\right) -\left(\frac{7}{-4}\right) -\left(\frac{4}{-2}\right)\\= \frac{-7}{5}+ \frac{7}{4}+\frac{4}{2}\\=\frac{-7}{5}+\frac{7}{4}+\frac{2}{1}\\=\frac{-28}{20}+\frac{35}{20}+\frac{40}{20}\\=\frac{-28+35+40}{20}\\=\frac{47}{20}\)
4. \(+\left(\frac{7}{-4}\right) -\left(\frac{-2}{-7}\right) -\left(\frac{-3}{-10}\right)\\= \frac{-7}{4}- \frac{2}{7}-\frac{3}{10}\\=\frac{-245}{140}-\frac{40}{140}-\frac{42}{140}\\=\frac{-245-40-42}{140}\\=\frac{-327}{140}\)
5. \(+\left(\frac{10}{-3}\right) -\left(\frac{-8}{-5}\right) +\left(\frac{2}{2}\right)\\= \frac{-10}{3}- \frac{8}{5}+\frac{2}{2}\\=\frac{-10}{3}-\frac{8}{5}+\frac{1}{1}\\=\frac{-50}{15}-\frac{24}{15}+\frac{15}{15}\\=\frac{-50-24+15}{15}\\=\frac{-59}{15}\)
6. \(+\left(\frac{-7}{-8}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{2}{-9}\right)\\= \frac{7}{8}+ \frac{8}{2}+\frac{2}{9}\\=\frac{7}{8}+\frac{4}{1}+\frac{2}{9}\\=\frac{63}{72}+\frac{288}{72}+\frac{16}{72}\\=\frac{63+288+16}{72}\\=\frac{367}{72}\)
7. \(-\left(\frac{-6}{-7}\right) +\left(\frac{6}{-5}\right) +\left(\frac{-6}{7}\right)\\= \frac{-6}{7}- \frac{6}{5}-\frac{6}{7}\\=\frac{-30}{35}-\frac{42}{35}-\frac{30}{35}\\=\frac{-30-42-30}{35}\\=\frac{-102}{35}\)
8. \(+\left(\frac{6}{-5}\right) -\left(\frac{2}{-6}\right) +\left(\frac{-8}{-8}\right)\\= \frac{-6}{5}+ \frac{2}{6}+\frac{8}{8}\\=\frac{-6}{5}+\frac{1}{3}+\frac{1}{1}\\=\frac{-18}{15}+\frac{5}{15}+\frac{15}{15}\\=\frac{-18+5+15}{15}\\=\frac{2}{15}\)
9. \(-\left(\frac{8}{9}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{7}{-4}\right)\\= \frac{-8}{9}- \frac{3}{10}-\frac{7}{4}\\=\frac{-160}{180}-\frac{54}{180}-\frac{315}{180}\\=\frac{-160-54-315}{180}\\=\frac{-529}{180}\)
10. \(-\left(\frac{-6}{5}\right) +\left(\frac{-5}{7}\right) +\left(\frac{-7}{-3}\right)\\= \frac{6}{5}- \frac{5}{7}+\frac{7}{3}\\=\frac{126}{105}-\frac{75}{105}+\frac{245}{105}\\=\frac{126-75+245}{105}\\=\frac{296}{105}\)
11. \(-\left(\frac{6}{-5}\right) -\left(\frac{5}{7}\right) +\left(\frac{10}{9}\right)\\= \frac{6}{5}- \frac{5}{7}+\frac{10}{9}\\=\frac{378}{315}-\frac{225}{315}+\frac{350}{315}\\=\frac{378-225+350}{315}\\=\frac{503}{315}\)
12. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{4}\right) -\left(\frac{-3}{-8}\right)\\= \frac{-6}{5}+ \frac{3}{4}-\frac{3}{8}\\=\frac{-48}{40}+\frac{30}{40}-\frac{15}{40}\\=\frac{-48+30-15}{40}\\=\frac{-33}{40}\)