Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) -\left(\frac{-4}{6}\right) +\left(\frac{-6}{6}\right)\\= \frac{6}{5}+ \frac{4}{6}-\frac{6}{6}\\=\frac{6}{5}+\frac{2}{3}-\frac{1}{1}\\=\frac{18}{15}+\frac{10}{15}-\frac{15}{15}\\=\frac{18+10-15}{15}\\=\frac{13}{15}\)
2. \(+\left(\frac{-3}{-7}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-12}{4}\right)\\= \frac{3}{7}+ \frac{3}{7}-\frac{12}{4}\\=\frac{3}{7}+\frac{3}{7}-\frac{3}{1}\\=\frac{3+3-3}{7}\\=\frac{3}{7}\)
3. \(-\left(\frac{-4}{-7}\right) +\left(\frac{-4}{-6}\right) -\left(\frac{10}{-11}\right)\\= \frac{-4}{7}+ \frac{4}{6}+\frac{10}{11}\\=\frac{-4}{7}+\frac{2}{3}+\frac{10}{11}\\=\frac{-132}{231}+\frac{154}{231}+\frac{210}{231}\\=\frac{-132+154+210}{231}\\=\frac{232}{231}\)
4. \(-\left(\frac{-6}{5}\right) +\left(\frac{-3}{3}\right) -\left(\frac{11}{-6}\right)\\= \frac{6}{5}- \frac{3}{3}+\frac{11}{6}\\=\frac{6}{5}-\frac{1}{1}+\frac{11}{6}\\=\frac{36}{30}-\frac{30}{30}+\frac{55}{30}\\=\frac{36-30+55}{30}\\=\frac{61}{30}\)
5. \(+\left(\frac{-4}{5}\right) -\left(\frac{-3}{8}\right) -\left(\frac{-12}{10}\right)\\= \frac{-4}{5}+ \frac{3}{8}+\frac{12}{10}\\=\frac{-4}{5}+\frac{3}{8}+\frac{6}{5}\\=\frac{-32}{40}+\frac{15}{40}+\frac{48}{40}\\=\frac{-32+15+48}{40}\\=\frac{31}{40}\)
6. \(-\left(\frac{5}{-4}\right) +\left(\frac{-3}{9}\right) -\left(\frac{9}{-7}\right)\\= \frac{5}{4}- \frac{3}{9}+\frac{9}{7}\\=\frac{5}{4}-\frac{1}{3}+\frac{9}{7}\\=\frac{105}{84}-\frac{28}{84}+\frac{108}{84}\\=\frac{105-28+108}{84}\\=\frac{185}{84}\)
7. \(-\left(\frac{8}{3}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-8}{3}- \frac{7}{10}+\frac{10}{6}\\=\frac{-8}{3}-\frac{7}{10}+\frac{5}{3}\\=\frac{-80}{30}-\frac{21}{30}+\frac{50}{30}\\=\frac{-80-21+50}{30}\\=\frac{-51}{30}\\=\frac{-17}{10}\)
8. \(+\left(\frac{6}{5}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{-3}{-9}\right)\\= \frac{6}{5}+ \frac{9}{9}-\frac{3}{9}\\=\frac{6}{5}+\frac{1}{1}-\frac{1}{3}\\=\frac{18}{15}+\frac{15}{15}-\frac{5}{15}\\=\frac{18+15-5}{15}\\=\frac{28}{15}\)
9. \(-\left(\frac{2}{3}\right) -\left(\frac{4}{-3}\right) +\left(\frac{4}{-2}\right)\\= \frac{-2}{3}+ \frac{4}{3}-\frac{4}{2}\\=\frac{-2}{3}+\frac{4}{3}-\frac{2}{1}\\=\frac{-2+4-2}{3}\\=\frac{0}{3}\\=\frac{0}{1}\)
10. \(+\left(\frac{-2}{-5}\right) +\left(\frac{9}{7}\right) -\left(\frac{7}{-3}\right)\\= \frac{2}{5}+ \frac{9}{7}+\frac{7}{3}\\=\frac{42}{105}+\frac{135}{105}+\frac{245}{105}\\=\frac{42+135+245}{105}\\=\frac{422}{105}\)
11. \(+\left(\frac{2}{-3}\right) +\left(\frac{7}{-9}\right) -\left(\frac{-9}{8}\right)\\= \frac{-2}{3}- \frac{7}{9}+\frac{9}{8}\\=\frac{-48}{72}-\frac{56}{72}+\frac{81}{72}\\=\frac{-48-56+81}{72}\\=\frac{-23}{72}\)
12. \(+\left(\frac{-9}{2}\right) -\left(\frac{3}{-7}\right) -\left(\frac{-8}{5}\right)\\= \frac{-9}{2}+ \frac{3}{7}+\frac{8}{5}\\=\frac{-315}{70}+\frac{30}{70}+\frac{112}{70}\\=\frac{-315+30+112}{70}\\=\frac{-173}{70}\)