Solve the following fraction simplification problems.

Решение:

Упростим предложенные дроби, найдя наибольший общий делитель (НОД) числителя и знаменателя.

Колонка Д:

• \(\frac{3}{15} = \frac{3\div3}{15\div3} = \frac{1}{5}\)
• \(\frac{6}{36} = \frac{6\div6}{36\div6} = \frac{1}{6}\)
• \(\frac{4}{26} = \frac{4\div2}{26\div2} = \frac{2}{13}\)
• \(\frac{5}{70} = \frac{5\div5}{70\div5} = \frac{1}{14}\)
• \(\frac{4}{52} = \frac{4\div4}{52\div4} = \frac{1}{13}\)
• \(\frac{2}{30} = \frac{2\div2}{30\div2} = \frac{1}{15}\)
• \(\frac{8}{28} = \frac{8\div4}{28\div4} = \frac{2}{7}\)
• \(\frac{6}{90} = \frac{6\div6}{90\div6} = \frac{1}{15}\)
• \(\frac{5}{10} = \frac{5\div5}{10\div5} = \frac{1}{2}\)
• \(\frac{3}{27} = \frac{3\div3}{27\div3} = \frac{1}{9}\)
• \(\frac{4}{8} = \frac{4\div4}{8\div4} = \frac{1}{2}\)
• \(\frac{6}{20} = \frac{6\div2}{20\div2} = \frac{3}{10}\)
• \(\frac{6}{78} = \frac{6\div6}{78\div6} = \frac{1}{13}\)
• \(\frac{3}{48} = \frac{3\div3}{48\div3} = \frac{1}{16}\)
• \(\frac{5}{55} = \frac{5\div5}{55\div5} = \frac{1}{11}\)

Колонка Е:

• \(\frac{5}{60} = \frac{5\div5}{60\div5} = \frac{1}{12}\)
• \(\frac{3}{36} = \frac{3\div3}{36\div3} = \frac{1}{12}\)
• \(\frac{4}{48} = \frac{4\div4}{48\div4} = \frac{1}{12}\)
• \(\frac{6}{96} = \frac{6\div6}{96\div6} = \frac{1}{16}\)
• \(\frac{6}{72} = \frac{6\div6}{72\div6} = \frac{1}{12}\)
• \(\frac{3}{51} = \frac{3\div3}{51\div3} = \frac{1}{17}\)
• \(\frac{2}{24} = \frac{2\div2}{24\div2} = \frac{1}{12}\)
• \(\frac{5}{65} = \frac{5\div5}{65\div5} = \frac{1}{13}\)
• \(\frac{12}{32} = \frac{12\div4}{32\div4} = \frac{3}{8}\)
• \(\frac{3}{6} = \frac{3\div3}{6\div3} = \frac{1}{2}\)
• \(\frac{5}{75} = \frac{5\div5}{75\div5} = \frac{1}{15}\)
• \(\frac{4}{56} = \frac{4\div4}{56\div4} = \frac{1}{14}\)
• \(\frac{10}{28} = \frac{10\div2}{28\div2} = \frac{5}{14}\)
• \(\frac{7}{56} = \frac{7\div7}{56\div7} = \frac{1}{8}\)

Колонка Ж:

• \(\frac{9}{27} = \frac{9\div9}{27\div9} = \frac{1}{3}\)
• \(\frac{4}{72} = \frac{4\div4}{72\div4} = \frac{1}{18}\)
• \(\frac{50}{80} = \frac{50\div10}{80\div10} = \frac{5}{8}\)
• \(\frac{15}{45} = \frac{15\div15}{45\div15} = \frac{1}{3}\)
• \(\frac{25}{75} = \frac{25\div25}{75\div25} = \frac{1}{3}\)
• \(\frac{33}{44} = \frac{33\div11}{44\div11} = \frac{3}{4}\)
• \(\frac{10}{65} = \frac{10\div5}{65\div5} = \frac{2}{13}\)
• \(\frac{12}{72} = \frac{12\div12}{72\div12} = \frac{1}{6}\)
• \(\frac{25}{100} = \frac{25\div25}{100\div25} = \frac{1}{4}\)

Колонка З:

• \(\frac{5}{20} = \frac{5\div5}{20\div5} = \frac{1}{4}\)
• \(\frac{8}{68} = \frac{8\div4}{68\div4} = \frac{2}{17}\)
• \(\frac{13}{65} = \frac{13\div13}{65\div13} = \frac{1}{5}\)
• \(\frac{16}{80} = \frac{16\div16}{80\div16} = \frac{1}{5}\)
• \(\frac{4}{24} = \frac{4\div4}{24\div4} = \frac{1}{6}\)
• \(\frac{3}{90} = \frac{3\div3}{90\div3} = \frac{1}{30}\)
• \(\frac{15}{60} = \frac{15\div15}{60\div15} = \frac{1}{4}\)
• \(\frac{8}{52} = \frac{8\div4}{52\div4} = \frac{2}{13}\)
• \(\frac{18}{54} = \frac{18\div18}{54\div18} = \frac{1}{3}\)
• \(\frac{14}{77} = \frac{14\div7}{77\div7} = \frac{2}{11}\)
• \(\frac{10}{60} = \frac{10\div10}{60\div10} = \frac{1}{6}\)
• \(\frac{12}{78} = \frac{12\div6}{78\div6} = \frac{2}{13}\)
• \(\frac{6}{102} = \frac{6\div6}{102\div6} = \frac{1}{17}\)
• \(\frac{12}{42} = \frac{12\div6}{42\div6} = \frac{2}{7}\)
• \(\frac{3}{12} = \frac{3\div3}{12\div3} = \frac{1}{4}\)

Ответ: Соответствующие упрощенные дроби указаны в решении.