Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-15}{4}\right)-\left(\frac{-15}{11}\right)\\= \frac{-15}{4}+\frac{15}{11}\\=\frac{-165}{44}+\frac{60}{44}\\=\frac{-165+60}{44}\\=\frac{-105}{44}\)
2. \(+\left(\frac{-5}{-4}\right)-\left(\frac{-10}{-7}\right)\\= \frac{5}{4}-\frac{10}{7}\\=\frac{35}{28}-\frac{40}{28}\\=\frac{35-40}{28}\\=\frac{-5}{28}\)
3. \(-\left(\frac{-3}{-8}\right)-\left(\frac{-13}{11}\right)\\= \frac{-3}{8}+\frac{13}{11}\\=\frac{-33}{88}+\frac{104}{88}\\=\frac{-33+104}{88}\\=\frac{71}{88}\)
4. \(-\left(\frac{15}{8}\right)-\left(\frac{-10}{-3}\right)\\= \frac{-15}{8}-\frac{10}{3}\\=\frac{-45}{24}-\frac{80}{24}\\=\frac{-45-80}{24}\\=\frac{-125}{24}\)
5. \(+\left(\frac{-3}{-2}\right)-\left(\frac{6}{-13}\right)\\= \frac{3}{2}+\frac{6}{13}\\=\frac{39}{26}+\frac{12}{26}\\=\frac{39+12}{26}\\=\frac{51}{26}\)
6. \(+\left(\frac{5}{2}\right)-\left(\frac{-12}{11}\right)\\= \frac{5}{2}+\frac{12}{11}\\=\frac{55}{22}+\frac{24}{22}\\=\frac{55+24}{22}\\=\frac{79}{22}\)
7. \(-\left(\frac{15}{-7}\right)-\left(\frac{3}{-4}\right)\\= \frac{15}{7}+\frac{3}{4}\\=\frac{60}{28}+\frac{21}{28}\\=\frac{60+21}{28}\\=\frac{81}{28}\)
8. \(+\left(\frac{3}{-2}\right)-\left(\frac{8}{11}\right)\\= \frac{-3}{2}-\frac{8}{11}\\=\frac{-33}{22}-\frac{16}{22}\\=\frac{-33-16}{22}\\=\frac{-49}{22}\)
9. \(-\left(\frac{12}{5}\right)+\left(\frac{-15}{-4}\right)\\= \frac{-12}{5}+\frac{15}{4}\\=\frac{-48}{20}+\frac{75}{20}\\=\frac{-48+75}{20}\\=\frac{27}{20}\)
10. \(+\left(\frac{-7}{8}\right)-\left(\frac{-8}{-7}\right)\\= \frac{-7}{8}-\frac{8}{7}\\=\frac{-49}{56}-\frac{64}{56}\\=\frac{-49-64}{56}\\=\frac{-113}{56}\)
11. \(+\left(\frac{-9}{7}\right)+\left(\frac{12}{13}\right)\\= \frac{-9}{7}+\frac{12}{13}\\=\frac{-117}{91}+\frac{84}{91}\\=\frac{-117+84}{91}\\=\frac{-33}{91}\)
12. \(-\left(\frac{-6}{5}\right)-\left(\frac{6}{-5}\right)\\= \frac{6}{5}+\frac{6}{5}\\=\frac{6+6}{5}\\=\frac{12}{5}\)