12. Приведите дроби к знаменателю 40xy²: a) \(\frac{1}{10y^2}\) б) \(\frac{3}{x}\) в) \(\frac{7}{20}\) г) \(\frac{13}{2y}\) д) \(\frac{5}{8xy}\) e) \(\frac{x}{4}\)

Решение:

а)

\(\frac{1}{10y^2} = \frac{1 \cdot 4x}{10y^2 \cdot 4x} = \frac{4x}{40xy^2}\)б)\(\frac{3}{x} = \frac{3 \cdot 40y^2}{x \cdot 40y^2} = \frac{120y^2}{40xy^2}\)в)\(\frac{7}{20} = \frac{7 \cdot 2xy^2}{20 \cdot 2xy^2} = \frac{14xy^2}{40xy^2}\)г)\(\frac{13}{2y} = \frac{13 \cdot 20xy}{2y \cdot 20xy} = \frac{260xy}{40xy^2}\)д)\(\frac{5}{8xy} = \frac{5 \cdot 5y}{8xy \cdot 5y} = \frac{25y}{40xy^2}\)е)\(\frac{x}{4} = \frac{x \cdot 10xy^2}{4 \cdot 10xy^2} = \frac{10x^2y^2}{40xy^2}\)

Ответ: а) \(\frac{4x}{40xy^2}\), б) \(\frac{120y^2}{40xy^2}\), в) \(\frac{14xy^2}{40xy^2}\), г) \(\frac{260xy}{40xy^2}\), д) \(\frac{25y}{40xy^2}\), е) \(\frac{10x^2y^2}{40xy^2}\).