Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{10}{7}\right) -\left(\frac{5}{9}\right) +\left(\frac{3}{3}\right)\\= \frac{10}{7}- \frac{5}{9}+\frac{3}{3}\\=\frac{10}{7}-\frac{5}{9}+\frac{1}{1}\\=\frac{90}{63}-\frac{35}{63}+\frac{63}{63}\\=\frac{90-35+63}{63}\\=\frac{118}{63}\)
2. \(+\left(\frac{-5}{7}\right) -\left(\frac{6}{-3}\right) +\left(\frac{5}{-11}\right)\\= \frac{-5}{7}+ \frac{6}{3}-\frac{5}{11}\\=\frac{-5}{7}+\frac{2}{1}-\frac{5}{11}\\=\frac{-55}{77}+\frac{154}{77}-\frac{35}{77}\\=\frac{-55+154-35}{77}\\=\frac{64}{77}\)
3. \(+\left(\frac{10}{7}\right) -\left(\frac{7}{-3}\right) -\left(\frac{4}{-6}\right)\\= \frac{10}{7}+ \frac{7}{3}+\frac{4}{6}\\=\frac{10}{7}+\frac{7}{3}+\frac{2}{3}\\=\frac{30}{21}+\frac{49}{21}+\frac{14}{21}\\=\frac{30+49+14}{21}\\=\frac{93}{21}\\=\frac{31}{7}\)
4. \(-\left(\frac{2}{7}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-7}{5}\right)\\= \frac{-2}{7}+ \frac{10}{4}+\frac{7}{5}\\=\frac{-2}{7}+\frac{5}{2}+\frac{7}{5}\\=\frac{-20}{70}+\frac{175}{70}+\frac{98}{70}\\=\frac{-20+175+98}{70}\\=\frac{253}{70}\)
5. \(-\left(\frac{5}{-8}\right) +\left(\frac{-6}{-4}\right) +\left(\frac{-8}{11}\right)\\= \frac{5}{8}+ \frac{6}{4}-\frac{8}{11}\\=\frac{5}{8}+\frac{3}{2}-\frac{8}{11}\\=\frac{55}{88}+\frac{132}{88}-\frac{64}{88}\\=\frac{55+132-64}{88}\\=\frac{123}{88}\)
6. \(-\left(\frac{-10}{-7}\right) -\left(\frac{5}{3}\right) -\left(\frac{10}{-12}\right)\\= \frac{-10}{7}- \frac{5}{3}+\frac{10}{12}\\=\frac{-10}{7}-\frac{5}{3}+\frac{5}{6}\\=\frac{-60}{42}-\frac{70}{42}+\frac{35}{42}\\=\frac{-60-70+35}{42}\\=\frac{-95}{42}\)
7. \(-\left(\frac{5}{3}\right) -\left(\frac{7}{-4}\right) +\left(\frac{2}{8}\right)\\= \frac{-5}{3}+ \frac{7}{4}+\frac{2}{8}\\=\frac{-5}{3}+\frac{7}{4}+\frac{1}{4}\\=\frac{-20}{12}+\frac{21}{12}+\frac{3}{12}\\=\frac{-20+21+3}{12}\\=\frac{4}{12}\\=\frac{1}{3}\)
8. \(-\left(\frac{-8}{-7}\right) +\left(\frac{2}{6}\right) +\left(\frac{10}{-8}\right)\\= \frac{-8}{7}+ \frac{2}{6}-\frac{10}{8}\\=\frac{-8}{7}+\frac{1}{3}-\frac{5}{4}\\=\frac{-96}{84}+\frac{28}{84}-\frac{105}{84}\\=\frac{-96+28-105}{84}\\=\frac{-173}{84}\)
9. \(-\left(\frac{-9}{2}\right) -\left(\frac{-6}{-8}\right) +\left(\frac{-2}{-5}\right)\\= \frac{9}{2}- \frac{6}{8}+\frac{2}{5}\\=\frac{9}{2}-\frac{3}{4}+\frac{2}{5}\\=\frac{90}{20}-\frac{15}{20}+\frac{8}{20}\\=\frac{90-15+8}{20}\\=\frac{83}{20}\)
10. \(+\left(\frac{-10}{7}\right) +\left(\frac{10}{-5}\right) +\left(\frac{8}{3}\right)\\= \frac{-10}{7}- \frac{10}{5}+\frac{8}{3}\\=\frac{-10}{7}-\frac{2}{1}+\frac{8}{3}\\=\frac{-30}{21}-\frac{42}{21}+\frac{56}{21}\\=\frac{-30-42+56}{21}\\=\frac{-16}{21}\)
11. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{10}{8}\right)\\= \frac{-4}{3}+ \frac{3}{4}+\frac{10}{8}\\=\frac{-4}{3}+\frac{3}{4}+\frac{5}{4}\\=\frac{-16}{12}+\frac{9}{12}+\frac{15}{12}\\=\frac{-16+9+15}{12}\\=\frac{8}{12}\\=\frac{2}{3}\)
12. \(+\left(\frac{8}{-9}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{3}{7}\right)\\= \frac{-8}{9}- \frac{6}{10}+\frac{3}{7}\\=\frac{-8}{9}-\frac{3}{5}+\frac{3}{7}\\=\frac{-280}{315}-\frac{189}{315}+\frac{135}{315}\\=\frac{-280-189+135}{315}\\=\frac{-334}{315}\)