Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{7}\right) -\left(\frac{4}{-2}\right) -\left(\frac{10}{-3}\right)\\= \frac{6}{7}+ \frac{4}{2}+\frac{10}{3}\\=\frac{6}{7}+\frac{2}{1}+\frac{10}{3}\\=\frac{18}{21}+\frac{42}{21}+\frac{70}{21}\\=\frac{18+42+70}{21}\\=\frac{130}{21}\)
2. \(-\left(\frac{4}{3}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{7}{2}\right)\\= \frac{-4}{3}+ \frac{4}{3}+\frac{7}{2}\\=\frac{-8}{6}+\frac{8}{6}+\frac{21}{6}\\=\frac{-8+8+21}{6}\\=\frac{21}{6}\\=\frac{7}{2}\)
3. \(-\left(\frac{-10}{3}\right) -\left(\frac{6}{8}\right) -\left(\frac{4}{-2}\right)\\= \frac{10}{3}- \frac{6}{8}+\frac{4}{2}\\=\frac{10}{3}-\frac{3}{4}+\frac{2}{1}\\=\frac{40}{12}-\frac{9}{12}+\frac{24}{12}\\=\frac{40-9+24}{12}\\=\frac{55}{12}\)
4. \(-\left(\frac{3}{4}\right) +\left(\frac{7}{-5}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-3}{4}- \frac{7}{5}+\frac{5}{9}\\=\frac{-135}{180}-\frac{252}{180}+\frac{100}{180}\\=\frac{-135-252+100}{180}\\=\frac{-287}{180}\)
5. \(+\left(\frac{6}{7}\right) +\left(\frac{-10}{10}\right) -\left(\frac{-3}{10}\right)\\= \frac{6}{7}- \frac{10}{10}+\frac{3}{10}\\=\frac{6}{7}-\frac{1}{1}+\frac{3}{10}\\=\frac{60}{70}-\frac{70}{70}+\frac{21}{70}\\=\frac{60-70+21}{70}\\=\frac{11}{70}\)
6. \(-\left(\frac{-3}{7}\right) +\left(\frac{-3}{5}\right) -\left(\frac{-7}{6}\right)\\= \frac{3}{7}- \frac{3}{5}+\frac{7}{6}\\=\frac{90}{210}-\frac{126}{210}+\frac{245}{210}\\=\frac{90-126+245}{210}\\=\frac{209}{210}\)
7. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-10}{6}\right) +\left(\frac{7}{-5}\right)\\= \frac{6}{5}+ \frac{10}{6}-\frac{7}{5}\\=\frac{6}{5}+\frac{5}{3}-\frac{7}{5}\\=\frac{18}{15}+\frac{25}{15}-\frac{21}{15}\\=\frac{18+25-21}{15}\\=\frac{22}{15}\)
8. \(-\left(\frac{6}{5}\right) +\left(\frac{6}{-8}\right) +\left(\frac{-8}{-11}\right)\\= \frac{-6}{5}- \frac{6}{8}+\frac{8}{11}\\=\frac{-6}{5}-\frac{3}{4}+\frac{8}{11}\\=\frac{-264}{220}-\frac{165}{220}+\frac{160}{220}\\=\frac{-264-165+160}{220}\\=\frac{-269}{220}\)
9. \(+\left(\frac{4}{-5}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{-9}{-12}\right)\\= \frac{-4}{5}+ \frac{6}{2}-\frac{9}{12}\\=\frac{-4}{5}+\frac{3}{1}-\frac{3}{4}\\=\frac{-16}{20}+\frac{60}{20}-\frac{15}{20}\\=\frac{-16+60-15}{20}\\=\frac{29}{20}\)
10. \(+\left(\frac{-9}{-8}\right) +\left(\frac{7}{8}\right) -\left(\frac{4}{-2}\right)\\= \frac{9}{8}+ \frac{7}{8}+\frac{4}{2}\\=\frac{9}{8}+\frac{7}{8}+\frac{2}{1}\\=\frac{9+7+2}{8}\\=\frac{18}{8}\\=\frac{9}{4}\)
11. \(+\left(\frac{7}{3}\right) -\left(\frac{-6}{-10}\right) -\left(\frac{-12}{-10}\right)\\= \frac{7}{3}- \frac{6}{10}-\frac{12}{10}\\=\frac{7}{3}-\frac{3}{5}-\frac{6}{5}\\=\frac{35}{15}-\frac{9}{15}-\frac{18}{15}\\=\frac{35-9-18}{15}\\=\frac{8}{15}\)
12. \(+\left(\frac{-10}{7}\right) +\left(\frac{-4}{2}\right) -\left(\frac{6}{-10}\right)\\= \frac{-10}{7}- \frac{4}{2}+\frac{6}{10}\\=\frac{-10}{7}-\frac{2}{1}+\frac{3}{5}\\=\frac{-50}{35}-\frac{70}{35}+\frac{21}{35}\\=\frac{-50-70+21}{35}\\=\frac{-99}{35}\)