Breuken haakjesregel (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bereken

1. \(+\left(\frac{10}{-11}\right)-\left(\frac{-10}{9}\right)\)
2. \(+\left(\frac{13}{10}\right)+\left(\frac{10}{9}\right)\)
3. \(-\left(\frac{-14}{3}\right)-\left(\frac{4}{-11}\right)\)
4. \(-\left(\frac{-11}{9}\right)-\left(\frac{3}{-5}\right)\)
5. \(+\left(\frac{4}{-3}\right)+\left(\frac{-12}{5}\right)\)
6. \(-\left(\frac{10}{9}\right)+\left(\frac{7}{-2}\right)\)
7. \(-\left(\frac{-5}{3}\right)-\left(\frac{-7}{-9}\right)\)
8. \(+\left(\frac{-5}{-7}\right)-\left(\frac{-15}{2}\right)\)
9. \(+\left(\frac{-5}{11}\right)+\left(\frac{-2}{7}\right)\)
10. \(-\left(\frac{5}{-2}\right)-\left(\frac{-12}{-5}\right)\)
11. \(-\left(\frac{-13}{10}\right)-\left(\frac{-9}{2}\right)\)
12. \(+\left(\frac{10}{13}\right)-\left(\frac{14}{11}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-11}\right)-\left(\frac{-10}{9}\right)\\= \frac{-10}{11}+\frac{10}{9}\\=\frac{-90}{99}+\frac{110}{99}\\=\frac{-90+110}{99}\\=\frac{20}{99}\)
2. \(+\left(\frac{13}{10}\right)+\left(\frac{10}{9}\right)\\= \frac{13}{10}+\frac{10}{9}\\=\frac{117}{90}+\frac{100}{90}\\=\frac{117+100}{90}\\=\frac{217}{90}\)
3. \(-\left(\frac{-14}{3}\right)-\left(\frac{4}{-11}\right)\\= \frac{14}{3}+\frac{4}{11}\\=\frac{154}{33}+\frac{12}{33}\\=\frac{154+12}{33}\\=\frac{166}{33}\)
4. \(-\left(\frac{-11}{9}\right)-\left(\frac{3}{-5}\right)\\= \frac{11}{9}+\frac{3}{5}\\=\frac{55}{45}+\frac{27}{45}\\=\frac{55+27}{45}\\=\frac{82}{45}\)
5. \(+\left(\frac{4}{-3}\right)+\left(\frac{-12}{5}\right)\\= \frac{-4}{3}-\frac{12}{5}\\=\frac{-20}{15}-\frac{36}{15}\\=\frac{-20-36}{15}\\=\frac{-56}{15}\)
6. \(-\left(\frac{10}{9}\right)+\left(\frac{7}{-2}\right)\\= \frac{-10}{9}-\frac{7}{2}\\=\frac{-20}{18}-\frac{63}{18}\\=\frac{-20-63}{18}\\=\frac{-83}{18}\)
7. \(-\left(\frac{-5}{3}\right)-\left(\frac{-7}{-9}\right)\\= \frac{5}{3}-\frac{7}{9}\\=\frac{15}{9}-\frac{7}{9}\\=\frac{15-7}{9}\\=\frac{8}{9}\)
8. \(+\left(\frac{-5}{-7}\right)-\left(\frac{-15}{2}\right)\\= \frac{5}{7}+\frac{15}{2}\\=\frac{10}{14}+\frac{105}{14}\\=\frac{10+105}{14}\\=\frac{115}{14}\)
9. \(+\left(\frac{-5}{11}\right)+\left(\frac{-2}{7}\right)\\= \frac{-5}{11}-\frac{2}{7}\\=\frac{-35}{77}-\frac{22}{77}\\=\frac{-35-22}{77}\\=\frac{-57}{77}\)
10. \(-\left(\frac{5}{-2}\right)-\left(\frac{-12}{-5}\right)\\= \frac{5}{2}-\frac{12}{5}\\=\frac{25}{10}-\frac{24}{10}\\=\frac{25-24}{10}\\=\frac{1}{10}\)
11. \(-\left(\frac{-13}{10}\right)-\left(\frac{-9}{2}\right)\\= \frac{13}{10}+\frac{9}{2}\\=\frac{13+9}{10}\\=\frac{22}{10}\\=\frac{11}{5}\)
12. \(+\left(\frac{10}{13}\right)-\left(\frac{14}{11}\right)\\= \frac{10}{13}-\frac{14}{11}\\=\frac{110}{143}-\frac{182}{143}\\=\frac{110-182}{143}\\=\frac{-72}{143}\)