№3 Сравните дроби: а) \(\frac{7}{12}\) и \(\frac{3}{4}\); б) \(\frac{2}{3}\) и \(\frac{5}{8}\); в) \(\frac{9}{25}\) и \(\frac{7}{20}\)

Чтобы сравнить дроби, нужно привести их к общему знаменателю и сравнить числители.

а) \(\frac{7}{12}\) и \(\frac{3}{4}\)
НОК(12, 4) = 12
\(\frac{3}{4}\) = \(\frac{3 \cdot 3}{4 \cdot 3}\) = \(\frac{9}{12}\)
\(\frac{7}{12}\) < \(\frac{9}{12}\), значит, \(\frac{7}{12}\) < \(\frac{3}{4}\)

б) \(\frac{2}{3}\) и \(\frac{5}{8}\)
НОК(3, 8) = 24
\(\frac{2}{3}\) = \(\frac{2 \cdot 8}{3 \cdot 8}\) = \(\frac{16}{24}\)
\(\frac{5}{8}\) = \(\frac{5 \cdot 3}{8 \cdot 3}\) = \(\frac{15}{24}\)
\(\frac{16}{24}\) > \(\frac{15}{24}\), значит, \(\frac{2}{3}\) > \(\frac{5}{8}\)

в) \(\frac{9}{25}\) и \(\frac{7}{20}\)
НОК(25, 20) = 100
\(\frac{9}{25}\) = \(\frac{9 \cdot 4}{25 \cdot 4}\) = \(\frac{36}{100}\)
\(\frac{7}{20}\) = \(\frac{7 \cdot 5}{20 \cdot 5}\) = \(\frac{35}{100}\)
\(\frac{36}{100}\) > \(\frac{35}{100}\), значит, \(\frac{9}{25}\) > \(\frac{7}{20}\)

Ответ:
а) \(\frac{7}{12}\) < \(\frac{3}{4}\); б) \(\frac{2}{3}\) > \(\frac{5}{8}\); в) \(\frac{9}{25}\) > \(\frac{7}{20}\)