Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{5}\right) -\left(\frac{4}{8}\right) -\left(\frac{-12}{7}\right)\\= \frac{2}{5}- \frac{4}{8}+\frac{12}{7}\\=\frac{2}{5}-\frac{1}{2}+\frac{12}{7}\\=\frac{28}{70}-\frac{35}{70}+\frac{120}{70}\\=\frac{28-35+120}{70}\\=\frac{113}{70}\)
2. \(+\left(\frac{3}{-5}\right) -\left(\frac{9}{-7}\right) +\left(\frac{-10}{-3}\right)\\= \frac{-3}{5}+ \frac{9}{7}+\frac{10}{3}\\=\frac{-63}{105}+\frac{135}{105}+\frac{350}{105}\\=\frac{-63+135+350}{105}\\=\frac{422}{105}\)
3. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{-6}{10}\right)\\= \frac{4}{9}+ \frac{9}{10}-\frac{6}{10}\\=\frac{4}{9}+\frac{9}{10}-\frac{3}{5}\\=\frac{40}{90}+\frac{81}{90}-\frac{54}{90}\\=\frac{40+81-54}{90}\\=\frac{67}{90}\)
4. \(+\left(\frac{9}{2}\right) +\left(\frac{8}{6}\right) +\left(\frac{9}{-12}\right)\\= \frac{9}{2}+ \frac{8}{6}-\frac{9}{12}\\=\frac{9}{2}+\frac{4}{3}-\frac{3}{4}\\=\frac{54}{12}+\frac{16}{12}-\frac{9}{12}\\=\frac{54+16-9}{12}\\=\frac{61}{12}\)
5. \(-\left(\frac{-5}{-8}\right) +\left(\frac{2}{-8}\right) -\left(\frac{10}{2}\right)\\= \frac{-5}{8}- \frac{2}{8}-\frac{10}{2}\\=\frac{-5}{8}-\frac{1}{4}-\frac{5}{1}\\=\frac{-5-1-5}{8}\\=\frac{-11}{8}\)
6. \(-\left(\frac{-4}{5}\right) +\left(\frac{-3}{-4}\right) -\left(\frac{10}{-7}\right)\\= \frac{4}{5}+ \frac{3}{4}+\frac{10}{7}\\=\frac{112}{140}+\frac{105}{140}+\frac{200}{140}\\=\frac{112+105+200}{140}\\=\frac{417}{140}\)
7. \(+\left(\frac{-9}{8}\right) +\left(\frac{9}{-5}\right) +\left(\frac{-5}{9}\right)\\= \frac{-9}{8}- \frac{9}{5}-\frac{5}{9}\\=\frac{-405}{360}-\frac{648}{360}-\frac{200}{360}\\=\frac{-405-648-200}{360}\\=\frac{-1253}{360}\)
8. \(+\left(\frac{2}{-9}\right) +\left(\frac{7}{-3}\right) -\left(\frac{9}{-2}\right)\\= \frac{-2}{9}- \frac{7}{3}+\frac{9}{2}\\=\frac{-4}{18}-\frac{42}{18}+\frac{81}{18}\\=\frac{-4-42+81}{18}\\=\frac{35}{18}\)
9. \(+\left(\frac{4}{9}\right) -\left(\frac{10}{8}\right) +\left(\frac{8}{9}\right)\\= \frac{4}{9}- \frac{10}{8}+\frac{8}{9}\\=\frac{4}{9}-\frac{5}{4}+\frac{8}{9}\\=\frac{16}{36}-\frac{45}{36}+\frac{32}{36}\\=\frac{16-45+32}{36}\\=\frac{3}{36}\\=\frac{1}{12}\)
10. \(+\left(\frac{-9}{-2}\right) -\left(\frac{7}{8}\right) -\left(\frac{9}{-9}\right)\\= \frac{9}{2}- \frac{7}{8}+\frac{9}{9}\\=\frac{9}{2}-\frac{7}{8}+\frac{1}{1}\\=\frac{36}{8}-\frac{7}{8}+\frac{8}{8}\\=\frac{36-7+8}{8}\\=\frac{37}{8}\)
11. \(+\left(\frac{-5}{-3}\right) +\left(\frac{-7}{6}\right) +\left(\frac{-10}{5}\right)\\= \frac{5}{3}- \frac{7}{6}-\frac{10}{5}\\=\frac{5}{3}-\frac{7}{6}-\frac{2}{1}\\=\frac{10}{6}-\frac{7}{6}-\frac{12}{6}\\=\frac{10-7-12}{6}\\=\frac{-9}{6}\\=\frac{-3}{2}\)
12. \(-\left(\frac{10}{7}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{11}{8}\right)\\= \frac{-10}{7}- \frac{7}{9}+\frac{11}{8}\\=\frac{-720}{504}-\frac{392}{504}+\frac{693}{504}\\=\frac{-720-392+693}{504}\\=\frac{-419}{504}\)