Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{14}{-13}\right)-\left(\frac{3}{10}\right)\\= \frac{14}{13}-\frac{3}{10}\\=\frac{140}{130}-\frac{39}{130}\\=\frac{140-39}{130}\\=\frac{101}{130}\)
2. \(+\left(\frac{13}{-10}\right)-\left(\frac{14}{9}\right)\\= \frac{-13}{10}-\frac{14}{9}\\=\frac{-117}{90}-\frac{140}{90}\\=\frac{-117-140}{90}\\=\frac{-257}{90}\)
3. \(+\left(\frac{-9}{5}\right)-\left(\frac{15}{7}\right)\\= \frac{-9}{5}-\frac{15}{7}\\=\frac{-63}{35}-\frac{75}{35}\\=\frac{-63-75}{35}\\=\frac{-138}{35}\)
4. \(-\left(\frac{-5}{-11}\right)+\left(\frac{9}{-4}\right)\\= \frac{-5}{11}-\frac{9}{4}\\=\frac{-20}{44}-\frac{99}{44}\\=\frac{-20-99}{44}\\=\frac{-119}{44}\)
5. \(-\left(\frac{15}{13}\right)+\left(\frac{-3}{7}\right)\\= \frac{-15}{13}-\frac{3}{7}\\=\frac{-105}{91}-\frac{39}{91}\\=\frac{-105-39}{91}\\=\frac{-144}{91}\)
6. \(-\left(\frac{-11}{4}\right)+\left(\frac{2}{-5}\right)\\= \frac{11}{4}-\frac{2}{5}\\=\frac{55}{20}-\frac{8}{20}\\=\frac{55-8}{20}\\=\frac{47}{20}\)
7. \(-\left(\frac{13}{-9}\right)+\left(\frac{4}{11}\right)\\= \frac{13}{9}+\frac{4}{11}\\=\frac{143}{99}+\frac{36}{99}\\=\frac{143+36}{99}\\=\frac{179}{99}\)
8. \(-\left(\frac{13}{14}\right)+\left(\frac{-7}{-12}\right)\\= \frac{-13}{14}+\frac{7}{12}\\=\frac{-78}{84}+\frac{49}{84}\\=\frac{-78+49}{84}\\=\frac{-29}{84}\)
9. \(-\left(\frac{5}{-6}\right)+\left(\frac{6}{-11}\right)\\= \frac{5}{6}-\frac{6}{11}\\=\frac{55}{66}-\frac{36}{66}\\=\frac{55-36}{66}\\=\frac{19}{66}\)
10. \(+\left(\frac{-12}{5}\right)-\left(\frac{-8}{-3}\right)\\= \frac{-12}{5}-\frac{8}{3}\\=\frac{-36}{15}-\frac{40}{15}\\=\frac{-36-40}{15}\\=\frac{-76}{15}\)
11. \(+\left(\frac{-5}{6}\right)+\left(\frac{-15}{-13}\right)\\= \frac{-5}{6}+\frac{15}{13}\\=\frac{-65}{78}+\frac{90}{78}\\=\frac{-65+90}{78}\\=\frac{25}{78}\)
12. \(+\left(\frac{-10}{-7}\right)+\left(\frac{-8}{9}\right)\\= \frac{10}{7}-\frac{8}{9}\\=\frac{90}{63}-\frac{56}{63}\\=\frac{90-56}{63}\\=\frac{34}{63}\)