Breuken haakjesregel (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{15}{-11}\right)-\left(\frac{-4}{7}\right)\\= \frac{15}{11}+\frac{4}{7}\\=\frac{105}{77}+\frac{44}{77}\\=\frac{105+44}{77}\\=\frac{149}{77}\)
2. \(+\left(\frac{5}{-6}\right)-\left(\frac{-7}{-9}\right)\\= \frac{-5}{6}-\frac{7}{9}\\=\frac{-15}{18}-\frac{14}{18}\\=\frac{-15-14}{18}\\=\frac{-29}{18}\)
3. \(+\left(\frac{6}{13}\right)-\left(\frac{13}{14}\right)\\= \frac{6}{13}-\frac{13}{14}\\=\frac{84}{182}-\frac{169}{182}\\=\frac{84-169}{182}\\=\frac{-85}{182}\)
4. \(+\left(\frac{-9}{10}\right)+\left(\frac{13}{2}\right)\\= \frac{-9}{10}+\frac{13}{2}\\=\frac{-9+13}{10}\\=\frac{4}{10}\\=\frac{2}{5}\)
5. \(-\left(\frac{-4}{3}\right)-\left(\frac{-8}{5}\right)\\= \frac{4}{3}+\frac{8}{5}\\=\frac{20}{15}+\frac{24}{15}\\=\frac{20+24}{15}\\=\frac{44}{15}\)
6. \(+\left(\frac{9}{4}\right)+\left(\frac{-6}{5}\right)\\= \frac{9}{4}-\frac{6}{5}\\=\frac{45}{20}-\frac{24}{20}\\=\frac{45-24}{20}\\=\frac{21}{20}\)
7. \(+\left(\frac{-3}{-7}\right)-\left(\frac{10}{13}\right)\\= \frac{3}{7}-\frac{10}{13}\\=\frac{39}{91}-\frac{70}{91}\\=\frac{39-70}{91}\\=\frac{-31}{91}\)
8. \(-\left(\frac{-9}{-7}\right)-\left(\frac{-12}{-5}\right)\\= \frac{-9}{7}-\frac{12}{5}\\=\frac{-45}{35}-\frac{84}{35}\\=\frac{-45-84}{35}\\=\frac{-129}{35}\)
9. \(-\left(\frac{5}{6}\right)-\left(\frac{11}{-14}\right)\\= \frac{-5}{6}+\frac{11}{14}\\=\frac{-35}{42}+\frac{33}{42}\\=\frac{-35+33}{42}\\=\frac{-2}{42}\\=\frac{-1}{21}\)
10. \(-\left(\frac{-12}{-13}\right)-\left(\frac{-6}{5}\right)\\= \frac{-12}{13}+\frac{6}{5}\\=\frac{-60}{65}+\frac{78}{65}\\=\frac{-60+78}{65}\\=\frac{18}{65}\)
11. \(+\left(\frac{13}{4}\right)-\left(\frac{13}{-4}\right)\\= \frac{13}{4}+\frac{13}{4}\\=\frac{13+13}{4}\\=\frac{26}{4}\\=\frac{13}{2}\)
12. \(+\left(\frac{-4}{7}\right)-\left(\frac{7}{-2}\right)\\= \frac{-4}{7}+\frac{7}{2}\\=\frac{-8}{14}+\frac{49}{14}\\=\frac{-8+49}{14}\\=\frac{41}{14}\)