Breuken haakjesregel (reeks 1)

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Bereken

1. \(+\left(\frac{-14}{9}\right)-\left(\frac{5}{-2}\right)\)
2. \(-\left(\frac{10}{3}\right)-\left(\frac{-6}{13}\right)\)
3. \(-\left(\frac{-10}{-7}\right)+\left(\frac{10}{-7}\right)\)
4. \(-\left(\frac{5}{4}\right)+\left(\frac{9}{-7}\right)\)
5. \(+\left(\frac{3}{-2}\right)-\left(\frac{5}{-11}\right)\)
6. \(-\left(\frac{-7}{-10}\right)+\left(\frac{10}{-7}\right)\)
7. \(+\left(\frac{2}{-11}\right)-\left(\frac{-14}{-9}\right)\)
8. \(+\left(\frac{-8}{3}\right)-\left(\frac{-2}{3}\right)\)
9. \(-\left(\frac{7}{12}\right)+\left(\frac{-8}{3}\right)\)
10. \(+\left(\frac{-9}{4}\right)+\left(\frac{-11}{-10}\right)\)
11. \(+\left(\frac{-14}{-3}\right)+\left(\frac{6}{-13}\right)\)
12. \(+\left(\frac{10}{7}\right)-\left(\frac{12}{5}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{-14}{9}\right)-\left(\frac{5}{-2}\right)\\= \frac{-14}{9}+\frac{5}{2}\\=\frac{-28}{18}+\frac{45}{18}\\=\frac{-28+45}{18}\\=\frac{17}{18}\)
2. \(-\left(\frac{10}{3}\right)-\left(\frac{-6}{13}\right)\\= \frac{-10}{3}+\frac{6}{13}\\=\frac{-130}{39}+\frac{18}{39}\\=\frac{-130+18}{39}\\=\frac{-112}{39}\)
3. \(-\left(\frac{-10}{-7}\right)+\left(\frac{10}{-7}\right)\\= \frac{-10}{7}-\frac{10}{7}\\=\frac{-10-10}{7}\\=\frac{-20}{7}\)
4. \(-\left(\frac{5}{4}\right)+\left(\frac{9}{-7}\right)\\= \frac{-5}{4}-\frac{9}{7}\\=\frac{-35}{28}-\frac{36}{28}\\=\frac{-35-36}{28}\\=\frac{-71}{28}\)
5. \(+\left(\frac{3}{-2}\right)-\left(\frac{5}{-11}\right)\\= \frac{-3}{2}+\frac{5}{11}\\=\frac{-33}{22}+\frac{10}{22}\\=\frac{-33+10}{22}\\=\frac{-23}{22}\)
6. \(-\left(\frac{-7}{-10}\right)+\left(\frac{10}{-7}\right)\\= \frac{-7}{10}-\frac{10}{7}\\=\frac{-49}{70}-\frac{100}{70}\\=\frac{-49-100}{70}\\=\frac{-149}{70}\)
7. \(+\left(\frac{2}{-11}\right)-\left(\frac{-14}{-9}\right)\\= \frac{-2}{11}-\frac{14}{9}\\=\frac{-18}{99}-\frac{154}{99}\\=\frac{-18-154}{99}\\=\frac{-172}{99}\)
8. \(+\left(\frac{-8}{3}\right)-\left(\frac{-2}{3}\right)\\= \frac{-8}{3}+\frac{2}{3}\\=\frac{-8+2}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
9. \(-\left(\frac{7}{12}\right)+\left(\frac{-8}{3}\right)\\= \frac{-7}{12}-\frac{8}{3}\\=\frac{-7-8}{12}\\=\frac{-15}{12}\\=\frac{-5}{4}\)
10. \(+\left(\frac{-9}{4}\right)+\left(\frac{-11}{-10}\right)\\= \frac{-9}{4}+\frac{11}{10}\\=\frac{-45}{20}+\frac{22}{20}\\=\frac{-45+22}{20}\\=\frac{-23}{20}\)
11. \(+\left(\frac{-14}{-3}\right)+\left(\frac{6}{-13}\right)\\= \frac{14}{3}-\frac{6}{13}\\=\frac{182}{39}-\frac{18}{39}\\=\frac{182-18}{39}\\=\frac{164}{39}\)
12. \(+\left(\frac{10}{7}\right)-\left(\frac{12}{5}\right)\\= \frac{10}{7}-\frac{12}{5}\\=\frac{50}{35}-\frac{84}{35}\\=\frac{50-84}{35}\\=\frac{-34}{35}\)