Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{15}{11}\right)+\left(\frac{9}{4}\right)\\= \frac{-15}{11}+\frac{9}{4}\\=\frac{-60}{44}+\frac{99}{44}\\=\frac{-60+99}{44}\\=\frac{39}{44}\)
2. \(+\left(\frac{14}{-9}\right)+\left(\frac{12}{7}\right)\\= \frac{-14}{9}+\frac{12}{7}\\=\frac{-98}{63}+\frac{108}{63}\\=\frac{-98+108}{63}\\=\frac{10}{63}\)
3. \(-\left(\frac{6}{-7}\right)+\left(\frac{-13}{-10}\right)\\= \frac{6}{7}+\frac{13}{10}\\=\frac{60}{70}+\frac{91}{70}\\=\frac{60+91}{70}\\=\frac{151}{70}\)
4. \(+\left(\frac{15}{-13}\right)+\left(\frac{8}{3}\right)\\= \frac{-15}{13}+\frac{8}{3}\\=\frac{-45}{39}+\frac{104}{39}\\=\frac{-45+104}{39}\\=\frac{59}{39}\)
5. \(+\left(\frac{15}{11}\right)+\left(\frac{-12}{7}\right)\\= \frac{15}{11}-\frac{12}{7}\\=\frac{105}{77}-\frac{132}{77}\\=\frac{105-132}{77}\\=\frac{-27}{77}\)
6. \(+\left(\frac{8}{9}\right)-\left(\frac{-2}{13}\right)\\= \frac{8}{9}+\frac{2}{13}\\=\frac{104}{117}+\frac{18}{117}\\=\frac{104+18}{117}\\=\frac{122}{117}\)
7. \(-\left(\frac{15}{-13}\right)+\left(\frac{15}{13}\right)\\= \frac{15}{13}+\frac{15}{13}\\=\frac{15+15}{13}\\=\frac{30}{13}\)
8. \(+\left(\frac{6}{13}\right)-\left(\frac{6}{-11}\right)\\= \frac{6}{13}+\frac{6}{11}\\=\frac{66}{143}+\frac{78}{143}\\=\frac{66+78}{143}\\=\frac{144}{143}\)
9. \(+\left(\frac{10}{-9}\right)+\left(\frac{12}{-11}\right)\\= \frac{-10}{9}-\frac{12}{11}\\=\frac{-110}{99}-\frac{108}{99}\\=\frac{-110-108}{99}\\=\frac{-218}{99}\)
10. \(+\left(\frac{-6}{13}\right)+\left(\frac{14}{-5}\right)\\= \frac{-6}{13}-\frac{14}{5}\\=\frac{-30}{65}-\frac{182}{65}\\=\frac{-30-182}{65}\\=\frac{-212}{65}\)
11. \(+\left(\frac{11}{2}\right)+\left(\frac{-13}{4}\right)\\= \frac{11}{2}-\frac{13}{4}\\=\frac{22}{4}-\frac{13}{4}\\=\frac{22-13}{4}\\=\frac{9}{4}\)
12. \(-\left(\frac{12}{-11}\right)+\left(\frac{-8}{7}\right)\\= \frac{12}{11}-\frac{8}{7}\\=\frac{84}{77}-\frac{88}{77}\\=\frac{84-88}{77}\\=\frac{-4}{77}\)