5.51 Упростите выражение и подчеркните его коэффициент: a) \(\frac{5}{6}\)x \(\cdot\) (-\(\frac{1}{5}\)y); в) -\(\frac{20}{9}\)x \(\cdot\) (-\(\frac{9}{4}\)z); д) \(\frac{3}{8}\)n \(\cdot\) (-\(\frac{7}{6}\)b) \(\cdot\) \(\frac{2}{7}\)z; б) -\(\frac{4}{7}\)a \(\cdot\) (-\(\frac{7}{8}\)a); г) \(\frac{5}{12}\)x \(\cdot\) (-\(\frac{4}{15}\)y); e) \(\frac{5}{9}\)a \(\cdot\) \(\frac{9}{20}\)b \(\cdot\) 3z.

Ответ:

1. a) \(\frac{5}{6}\)x \(\cdot\) (-\(\frac{1}{5}\)y)

   Упрощаем выражение: \(\frac{5}{6}\)x \(\cdot\) (-\(\frac{1}{5}\)y) = -\(\frac{5}{30}\)xy = -\(\frac{1}{6}\)xy

   Коэффициент: -\(\frac{1}{6}\)

2. б) -\(\frac{4}{7}\)a \(\cdot\) (-\(\frac{7}{8}\)a)

   Упрощаем выражение: -\(\frac{4}{7}\)a \(\cdot\) (-\(\frac{7}{8}\)a) = \(\frac{28}{56}\)a² = \(\frac{1}{2}\)a²

   Коэффициент: \(\frac{1}{2}\)

3. в) -\(\frac{20}{9}\)x \(\cdot\) (-\(\frac{9}{4}\)z)

   Упрощаем выражение: -\(\frac{20}{9}\)x \(\cdot\) (-\(\frac{9}{4}\)z) = \(\frac{180}{36}\)xz = 5xz

   Коэффициент: 5

4. г) \(\frac{5}{12}\)x \(\cdot\) (-\(\frac{4}{15}\)y)

   Упрощаем выражение: \(\frac{5}{12}\)x \(\cdot\) (-\(\frac{4}{15}\)y) = -\(\frac{20}{180}\)xy = -\(\frac{1}{9}\)xy

   Коэффициент: -\(\frac{1}{9}\)

5. д) \(\frac{3}{8}\)n \(\cdot\) (-\(\frac{7}{6}\)b) \(\cdot\) \(\frac{2}{7}\)z

   Упрощаем выражение: \(\frac{3}{8}\)n \(\cdot\) (-\(\frac{7}{6}\)b) \(\cdot\) \(\frac{2}{7}\)z = -\(\frac{42}{336}\)bnz = -\(\frac{1}{8}\)bnz

   Коэффициент: -\(\frac{1}{8}\)

6. e) \(\frac{5}{9}\)a \(\cdot\) \(\frac{9}{20}\)b \(\cdot\) 3z

   Упрощаем выражение: \(\frac{5}{9}\)a \(\cdot\) \(\frac{9}{20}\)b \(\cdot\) 3z = \(\frac{135}{180}\)abz = \(\frac{3}{4}\)abz

   Коэффициент: \(\frac{3}{4}\)

Ответ: