تمارين الأعداد الكسرية والقيم المطلقة

\(A = \frac{-7}{5} + \frac{4}{5}\)
\(\frac{-7}{5} + \frac{4}{5}\)
\(= \frac{-7 + 4}{5}\)
\(= \frac{-3}{5}\)
\(B = \frac{24}{42} \div \frac{25}{35}\)
\(\frac{24}{42} \div \frac{25}{35}\)
\(= \frac{24}{42} \times \frac{35}{25}\)
\(= \frac{4 \times 6}{6 \times 7} \times \frac{5 \times 7}{5 \times 5}\)
\(= \frac{4}{7} \times \frac{7}{5}\)
\(= \frac{4 \times 7}{7 \times 5}\)
\(= \frac{28}{35}\)
\(= \frac{4}{5}\)
\(C = \left( -\frac{1}{6} + \frac{3}{7} \right)\left( \frac{5}{6} + \frac{9}{21} \right)\)
\(-\frac{1}{6} + \frac{3}{7}\)
\(= \frac{-7 + 18}{42}\)
\(= \frac{11}{42}\)
\(\frac{5}{6} + \frac{9}{21}\)
\(= \frac{35 + 18}{42}\)
\(= \frac{53}{42}\)
\(C = \frac{11}{42} \times \frac{53}{42}\)
\(= \frac{583}{1764}\)
\(D = \left| \frac{3}{2} - \frac{5}{3} \right| - \left( -\frac{5}{3} \right)\)
\(\frac{3}{2} - \frac{5}{3}\)
\(= \frac{9 - 10}{6}\)
\(= \frac{-1}{6}\)
\(\left| \frac{-1}{6} \right| = \frac{1}{6}\)
\(-(-\frac{5}{3}) = \frac{5}{3}\)
\(D = \frac{1}{6} + \frac{5}{3}\)
\(= \frac{1 + 10}{6}\)
\(= \frac{11}{6}\)
\(|x| = \frac{2}{3}\)
\(|x| = \frac{2}{3}\)
\(\Rightarrow x = \frac{2}{3}\) أو \(x = -\frac{2}{3}\)
\(|x| = \frac{5}{2} - \frac{7}{2}\)
\(\frac{5}{2} - \frac{7}{2}\)
\(= \frac{-2}{2}\)
\(= -1\)
\(|x| = -1\)
المعادلة مستحيلة لأن القيمة المطلقة دائماً موجبة
\(|x| + \left( -\frac{7}{12} \right) = 0\)
\(|x| - \frac{7}{12} = 0\)
\(|x| = \frac{7}{12}\)
\(\Rightarrow x = \frac{7}{12}\) أو \(x = -\frac{7}{12}\)
\(|x| + \frac{3}{7} = 0\)
\(|x| = -\frac{3}{7}\)
المعادلة مستحيلة لأن القيمة المطلقة دائماً موجبة
\(x + \frac{13}{4} = 0\)
\(x = -\frac{13}{4}\)
\(|x| = -\frac{4}{5}\)
\(|x| = -\frac{4}{5}\)
المعادلة مستحيلة لأن القيمة المطلقة دائماً موجبة