Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{3}\right) -\left(\frac{5}{-7}\right) -\left(\frac{5}{11}\right)\\= \frac{-10}{3}+ \frac{5}{7}-\frac{5}{11}\\=\frac{-770}{231}+\frac{165}{231}-\frac{105}{231}\\=\frac{-770+165-105}{231}\\=\frac{-710}{231}\)
2. \(-\left(\frac{-6}{5}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{-8}{2}\right)\\= \frac{6}{5}- \frac{8}{3}-\frac{8}{2}\\=\frac{6}{5}-\frac{8}{3}-\frac{4}{1}\\=\frac{18}{15}-\frac{40}{15}-\frac{60}{15}\\=\frac{18-40-60}{15}\\=\frac{-82}{15}\)
3. \(-\left(\frac{10}{-7}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{-11}{2}\right)\\= \frac{10}{7}- \frac{4}{10}+\frac{11}{2}\\=\frac{10}{7}-\frac{2}{5}+\frac{11}{2}\\=\frac{100}{70}-\frac{28}{70}+\frac{385}{70}\\=\frac{100-28+385}{70}\\=\frac{457}{70}\)
4. \(-\left(\frac{-7}{-5}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{4}{-5}\right)\\= \frac{-7}{5}+ \frac{9}{9}+\frac{4}{5}\\=\frac{-7}{5}+\frac{1}{1}+\frac{4}{5}\\=\frac{-7+1+4}{5}\\=\frac{-2}{5}\)
5. \(+\left(\frac{-2}{-7}\right) +\left(\frac{5}{6}\right) -\left(\frac{12}{4}\right)\\= \frac{2}{7}+ \frac{5}{6}-\frac{12}{4}\\=\frac{2}{7}+\frac{5}{6}-\frac{3}{1}\\=\frac{12}{42}+\frac{35}{42}-\frac{126}{42}\\=\frac{12+35-126}{42}\\=\frac{-79}{42}\)
6. \(-\left(\frac{4}{-3}\right) +\left(\frac{-5}{-5}\right) +\left(\frac{11}{-12}\right)\\= \frac{4}{3}+ \frac{5}{5}-\frac{11}{12}\\=\frac{4}{3}+\frac{1}{1}-\frac{11}{12}\\=\frac{16}{12}+\frac{12}{12}-\frac{11}{12}\\=\frac{16+12-11}{12}\\=\frac{17}{12}\)
7. \(-\left(\frac{-10}{3}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{-6}{-3}\right)\\= \frac{10}{3}+ \frac{8}{5}+\frac{6}{3}\\=\frac{10}{3}+\frac{8}{5}+\frac{2}{1}\\=\frac{50}{15}+\frac{24}{15}+\frac{30}{15}\\=\frac{50+24+30}{15}\\=\frac{104}{15}\)
8. \(+\left(\frac{3}{-4}\right) -\left(\frac{5}{6}\right) -\left(\frac{12}{-7}\right)\\= \frac{-3}{4}- \frac{5}{6}+\frac{12}{7}\\=\frac{-63}{84}-\frac{70}{84}+\frac{144}{84}\\=\frac{-63-70+144}{84}\\=\frac{11}{84}\)
9. \(-\left(\frac{-2}{3}\right) +\left(\frac{2}{-7}\right) +\left(\frac{4}{9}\right)\\= \frac{2}{3}- \frac{2}{7}+\frac{4}{9}\\=\frac{42}{63}-\frac{18}{63}+\frac{28}{63}\\=\frac{42-18+28}{63}\\=\frac{52}{63}\)
10. \(+\left(\frac{4}{5}\right) +\left(\frac{8}{9}\right) +\left(\frac{9}{-7}\right)\\= \frac{4}{5}+ \frac{8}{9}-\frac{9}{7}\\=\frac{252}{315}+\frac{280}{315}-\frac{405}{315}\\=\frac{252+280-405}{315}\\=\frac{127}{315}\)
11. \(-\left(\frac{-9}{-4}\right) +\left(\frac{-5}{5}\right) -\left(\frac{-4}{-9}\right)\\= \frac{-9}{4}- \frac{5}{5}-\frac{4}{9}\\=\frac{-9}{4}-\frac{1}{1}-\frac{4}{9}\\=\frac{-81}{36}-\frac{36}{36}-\frac{16}{36}\\=\frac{-81-36-16}{36}\\=\frac{-133}{36}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{-3}{8}\right) -\left(\frac{7}{-9}\right)\\= \frac{-6}{5}+ \frac{3}{8}+\frac{7}{9}\\=\frac{-432}{360}+\frac{135}{360}+\frac{280}{360}\\=\frac{-432+135+280}{360}\\=\frac{-17}{360}\)