Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-9}\right) +\left(\frac{-5}{9}\right) +\left(\frac{8}{-7}\right)\\= \frac{-5}{9}- \frac{5}{9}-\frac{8}{7}\\=\frac{-35}{63}-\frac{35}{63}-\frac{72}{63}\\=\frac{-35-35-72}{63}\\=\frac{-142}{63}\)
2. \(+\left(\frac{10}{7}\right) +\left(\frac{4}{-5}\right) -\left(\frac{-2}{8}\right)\\= \frac{10}{7}- \frac{4}{5}+\frac{2}{8}\\=\frac{10}{7}-\frac{4}{5}+\frac{1}{4}\\=\frac{200}{140}-\frac{112}{140}+\frac{35}{140}\\=\frac{200-112+35}{140}\\=\frac{123}{140}\)
3. \(+\left(\frac{-8}{-5}\right) +\left(\frac{3}{-7}\right) -\left(\frac{-4}{-4}\right)\\= \frac{8}{5}- \frac{3}{7}-\frac{4}{4}\\=\frac{8}{5}-\frac{3}{7}-\frac{1}{1}\\=\frac{56}{35}-\frac{15}{35}-\frac{35}{35}\\=\frac{56-15-35}{35}\\=\frac{6}{35}\)
4. \(+\left(\frac{6}{-7}\right) +\left(\frac{7}{4}\right) -\left(\frac{-12}{2}\right)\\= \frac{-6}{7}+ \frac{7}{4}+\frac{12}{2}\\=\frac{-6}{7}+\frac{7}{4}+\frac{6}{1}\\=\frac{-24}{28}+\frac{49}{28}+\frac{168}{28}\\=\frac{-24+49+168}{28}\\=\frac{193}{28}\)
5. \(+\left(\frac{10}{-3}\right) +\left(\frac{-8}{5}\right) +\left(\frac{-7}{-3}\right)\\= \frac{-10}{3}- \frac{8}{5}+\frac{7}{3}\\=\frac{-50}{15}-\frac{24}{15}+\frac{35}{15}\\=\frac{-50-24+35}{15}\\=\frac{-39}{15}\\=\frac{-13}{5}\)
6. \(-\left(\frac{-2}{9}\right) -\left(\frac{3}{10}\right) +\left(\frac{4}{2}\right)\\= \frac{2}{9}- \frac{3}{10}+\frac{4}{2}\\=\frac{2}{9}-\frac{3}{10}+\frac{2}{1}\\=\frac{20}{90}-\frac{27}{90}+\frac{180}{90}\\=\frac{20-27+180}{90}\\=\frac{173}{90}\)
7. \(-\left(\frac{4}{-3}\right) +\left(\frac{-3}{4}\right) -\left(\frac{9}{-11}\right)\\= \frac{4}{3}- \frac{3}{4}+\frac{9}{11}\\=\frac{176}{132}-\frac{99}{132}+\frac{108}{132}\\=\frac{176-99+108}{132}\\=\frac{185}{132}\)
8. \(-\left(\frac{6}{-5}\right) -\left(\frac{9}{-6}\right) -\left(\frac{2}{7}\right)\\= \frac{6}{5}+ \frac{9}{6}-\frac{2}{7}\\=\frac{6}{5}+\frac{3}{2}-\frac{2}{7}\\=\frac{84}{70}+\frac{105}{70}-\frac{20}{70}\\=\frac{84+105-20}{70}\\=\frac{169}{70}\)
9. \(+\left(\frac{6}{5}\right) +\left(\frac{10}{-7}\right) +\left(\frac{11}{3}\right)\\= \frac{6}{5}- \frac{10}{7}+\frac{11}{3}\\=\frac{126}{105}-\frac{150}{105}+\frac{385}{105}\\=\frac{126-150+385}{105}\\=\frac{361}{105}\)
10. \(-\left(\frac{6}{-5}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{3}{-8}\right)\\= \frac{6}{5}+ \frac{7}{4}+\frac{3}{8}\\=\frac{48}{40}+\frac{70}{40}+\frac{15}{40}\\=\frac{48+70+15}{40}\\=\frac{133}{40}\)
11. \(-\left(\frac{8}{3}\right) -\left(\frac{4}{-5}\right) -\left(\frac{-4}{3}\right)\\= \frac{-8}{3}+ \frac{4}{5}+\frac{4}{3}\\=\frac{-40}{15}+\frac{12}{15}+\frac{20}{15}\\=\frac{-40+12+20}{15}\\=\frac{-8}{15}\)
12. \(-\left(\frac{4}{-5}\right) +\left(\frac{-4}{6}\right) +\left(\frac{-3}{8}\right)\\= \frac{4}{5}- \frac{4}{6}-\frac{3}{8}\\=\frac{4}{5}-\frac{2}{3}-\frac{3}{8}\\=\frac{96}{120}-\frac{80}{120}-\frac{45}{120}\\=\frac{96-80-45}{120}\\=\frac{-29}{120}\)