Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-14}{-3}\right)+\left(\frac{5}{-3}\right)\\= \frac{14}{3}-\frac{5}{3}\\=\frac{14-5}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
2. \(+\left(\frac{-11}{12}\right)-\left(\frac{-12}{5}\right)\\= \frac{-11}{12}+\frac{12}{5}\\=\frac{-55}{60}+\frac{144}{60}\\=\frac{-55+144}{60}\\=\frac{89}{60}\)
3. \(+\left(\frac{3}{-10}\right)-\left(\frac{-5}{-11}\right)\\= \frac{-3}{10}-\frac{5}{11}\\=\frac{-33}{110}-\frac{50}{110}\\=\frac{-33-50}{110}\\=\frac{-83}{110}\)
4. \(-\left(\frac{4}{-7}\right)-\left(\frac{9}{-7}\right)\\= \frac{4}{7}+\frac{9}{7}\\=\frac{4+9}{7}\\=\frac{13}{7}\)
5. \(+\left(\frac{13}{4}\right)+\left(\frac{-2}{-11}\right)\\= \frac{13}{4}+\frac{2}{11}\\=\frac{143}{44}+\frac{8}{44}\\=\frac{143+8}{44}\\=\frac{151}{44}\)
6. \(-\left(\frac{-12}{5}\right)-\left(\frac{14}{-3}\right)\\= \frac{12}{5}+\frac{14}{3}\\=\frac{36}{15}+\frac{70}{15}\\=\frac{36+70}{15}\\=\frac{106}{15}\)
7. \(-\left(\frac{4}{9}\right)+\left(\frac{7}{2}\right)\\= \frac{-4}{9}+\frac{7}{2}\\=\frac{-8}{18}+\frac{63}{18}\\=\frac{-8+63}{18}\\=\frac{55}{18}\)
8. \(-\left(\frac{11}{4}\right)+\left(\frac{6}{-5}\right)\\= \frac{-11}{4}-\frac{6}{5}\\=\frac{-55}{20}-\frac{24}{20}\\=\frac{-55-24}{20}\\=\frac{-79}{20}\)
9. \(-\left(\frac{-14}{9}\right)+\left(\frac{-10}{3}\right)\\= \frac{14}{9}-\frac{10}{3}\\=\frac{14-10}{9}\\=\frac{4}{9}\)
10. \(+\left(\frac{-15}{2}\right)-\left(\frac{-15}{8}\right)\\= \frac{-15}{2}+\frac{15}{8}\\=\frac{-60}{8}+\frac{15}{8}\\=\frac{-60+15}{8}\\=\frac{-45}{8}\)
11. \(+\left(\frac{2}{-13}\right)+\left(\frac{-6}{11}\right)\\= \frac{-2}{13}-\frac{6}{11}\\=\frac{-22}{143}-\frac{78}{143}\\=\frac{-22-78}{143}\\=\frac{-100}{143}\)
12. \(+\left(\frac{-7}{-8}\right)-\left(\frac{4}{3}\right)\\= \frac{7}{8}-\frac{4}{3}\\=\frac{21}{24}-\frac{32}{24}\\=\frac{21-32}{24}\\=\frac{-11}{24}\)