Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-3}\right) -\left(\frac{2}{-10}\right) +\left(\frac{-3}{7}\right)\\= \frac{4}{3}+ \frac{2}{10}-\frac{3}{7}\\=\frac{4}{3}+\frac{1}{5}-\frac{3}{7}\\=\frac{140}{105}+\frac{21}{105}-\frac{45}{105}\\=\frac{140+21-45}{105}\\=\frac{116}{105}\)
2. \(+\left(\frac{9}{2}\right) +\left(\frac{-2}{8}\right) +\left(\frac{-6}{-6}\right)\\= \frac{9}{2}- \frac{2}{8}+\frac{6}{6}\\=\frac{9}{2}-\frac{1}{4}+\frac{1}{1}\\=\frac{18}{4}-\frac{1}{4}+\frac{4}{4}\\=\frac{18-1+4}{4}\\=\frac{21}{4}\)
3. \(+\left(\frac{-5}{-4}\right) +\left(\frac{6}{9}\right) +\left(\frac{10}{-2}\right)\\= \frac{5}{4}+ \frac{6}{9}-\frac{10}{2}\\=\frac{5}{4}+\frac{2}{3}-\frac{5}{1}\\=\frac{15}{12}+\frac{8}{12}-\frac{60}{12}\\=\frac{15+8-60}{12}\\=\frac{-37}{12}\)
4. \(+\left(\frac{6}{5}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{-7}{11}\right)\\= \frac{6}{5}- \frac{9}{9}+\frac{7}{11}\\=\frac{6}{5}-\frac{1}{1}+\frac{7}{11}\\=\frac{66}{55}-\frac{55}{55}+\frac{35}{55}\\=\frac{66-55+35}{55}\\=\frac{46}{55}\)
5. \(-\left(\frac{-4}{3}\right) +\left(\frac{6}{-4}\right) +\left(\frac{-6}{-4}\right)\\= \frac{4}{3}- \frac{6}{4}+\frac{6}{4}\\=\frac{4}{3}-\frac{3}{2}+\frac{3}{2}\\=\frac{8}{6}-\frac{9}{6}+\frac{9}{6}\\=\frac{8-9+9}{6}\\=\frac{8}{6}\\=\frac{4}{3}\)
6. \(+\left(\frac{8}{3}\right) +\left(\frac{2}{3}\right) -\left(\frac{12}{10}\right)\\= \frac{8}{3}+ \frac{2}{3}-\frac{12}{10}\\=\frac{8}{3}+\frac{2}{3}-\frac{6}{5}\\=\frac{40}{15}+\frac{10}{15}-\frac{18}{15}\\=\frac{40+10-18}{15}\\=\frac{32}{15}\)
7. \(-\left(\frac{6}{-7}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{-5}{-3}\right)\\= \frac{6}{7}- \frac{8}{10}+\frac{5}{3}\\=\frac{6}{7}-\frac{4}{5}+\frac{5}{3}\\=\frac{90}{105}-\frac{84}{105}+\frac{175}{105}\\=\frac{90-84+175}{105}\\=\frac{181}{105}\)
8. \(-\left(\frac{9}{7}\right) -\left(\frac{-4}{5}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-9}{7}+ \frac{4}{5}-\frac{4}{11}\\=\frac{-495}{385}+\frac{308}{385}-\frac{140}{385}\\=\frac{-495+308-140}{385}\\=\frac{-327}{385}\)
9. \(+\left(\frac{-5}{7}\right) +\left(\frac{9}{2}\right) +\left(\frac{-12}{10}\right)\\= \frac{-5}{7}+ \frac{9}{2}-\frac{12}{10}\\=\frac{-5}{7}+\frac{9}{2}-\frac{6}{5}\\=\frac{-50}{70}+\frac{315}{70}-\frac{84}{70}\\=\frac{-50+315-84}{70}\\=\frac{181}{70}\)
10. \(-\left(\frac{-3}{2}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{12}{12}\right)\\= \frac{3}{2}- \frac{6}{6}-\frac{12}{12}\\=\frac{3}{2}-\frac{1}{1}-\frac{1}{1}\\=\frac{3-1-1}{2}\\=\frac{1}{2}\)
11. \(-\left(\frac{2}{7}\right) -\left(\frac{10}{8}\right) -\left(\frac{5}{-6}\right)\\= \frac{-2}{7}- \frac{10}{8}+\frac{5}{6}\\=\frac{-2}{7}-\frac{5}{4}+\frac{5}{6}\\=\frac{-24}{84}-\frac{105}{84}+\frac{70}{84}\\=\frac{-24-105+70}{84}\\=\frac{-59}{84}\)
12. \(+\left(\frac{-10}{-9}\right) +\left(\frac{6}{3}\right) -\left(\frac{-8}{7}\right)\\= \frac{10}{9}+ \frac{6}{3}+\frac{8}{7}\\=\frac{10}{9}+\frac{2}{1}+\frac{8}{7}\\=\frac{70}{63}+\frac{126}{63}+\frac{72}{63}\\=\frac{70+126+72}{63}\\=\frac{268}{63}\)