Решебник по математике 5 класс Ерина Виленкин рабочая тетрадь Часть 1, 2 Часть 2 | Страница 42

\[Стр.\ 42.\]

\[\boxed{\mathbf{7.}}\]

\[\textbf{а)}\ \frac{7}{30}\ и\ \frac{29}{84}\]

\[НОК(30;84) = 420\]

\[\frac{7}{30} = \frac{7 \cdot 14}{30 \cdot 14} = \frac{98}{420};\]

\[\frac{29}{84} = \frac{29 \cdot 5}{84 \cdot 5} = \frac{145}{420}.\]

\[\textbf{б)}\ \frac{1}{6}\ и\ \frac{3}{8}\]

\[НОК(6;8) = 24\]

\[\frac{1}{6} = \frac{4}{24};\]

\[\frac{3}{8} = \frac{9}{24}.\]

\[\textbf{в)}\ \frac{11}{35}\ и\ \frac{7}{45}\]

\[НОК(35;45) = 35 \cdot 9 = 315\]

\[\frac{11}{35} = \frac{11 \cdot 9}{35 \cdot 9} = \frac{99}{315};\]

\[\frac{7}{45} = \frac{7 \cdot 7}{45 \cdot 7} = \frac{49}{315}.\]

\[\textbf{г)}\ \frac{7}{10}\ и\ \frac{5}{11}\]

\[НОК(10;11) = 10 \cdot 11 = 110\]

\[\frac{7}{10} = \frac{77}{110};\]

\[\frac{5}{11} = \frac{50}{110}.\]

\[\textbf{д)}\ \frac{3}{20}\ и\ \frac{1}{16}\]

\[НОК(20;16) = 4 \cdot 5 \cdot 4 = 80\]

\[\frac{3}{20} = \frac{12}{80};\]

\[\frac{1}{16} = \frac{5}{80}.\]

\[\textbf{е)}\ \frac{2}{15}\ \ и\ \frac{4}{27}\]

\[НОК(15;27) = 9 \cdot 3 \cdot 5 = 135\]

\[\frac{2}{15} = \frac{2 \cdot 9}{15 \cdot 9} = \frac{18}{135};\]

\[\frac{4}{27} = \frac{4 \cdot 5}{27 \cdot 5} = \frac{20}{135}.\]

\[\textbf{ж)}\ \frac{5}{42}\ и\ \frac{3}{56}\]

\[НОК(42;56) = 6 \cdot 7 \cdot 4 = 168\]

\[\frac{5}{42} = \frac{5 \cdot 4}{42 \cdot 4} = \frac{20}{168};\]

\[\frac{3}{56} = \frac{3 \cdot 3}{56 \cdot 3} = \frac{9}{168}.\]

\[\textbf{з)}\ \frac{29}{60}\ и\ \frac{109}{126}\]

\[НОК(60;126) = 6 \cdot 10 \cdot 21 =\]

\[= 1260\]

\[\frac{29}{60} = \frac{29 \cdot 21}{60 \cdot 21} = \frac{609}{1260};\]

\[\frac{109}{126} = \frac{109 \cdot 10}{126 \cdot 10} = \frac{1090}{1260}.\]

\[\textbf{и)}\ \frac{139}{270}\ и\ \frac{71}{450}\]

\[НОК(270;450) = 90 \cdot 3 \cdot 5 =\]

\[= 1350\]

\[\frac{139}{270} = \frac{139 \cdot 5}{270 \cdot 5} = \frac{695}{1350};\]

\[\frac{71}{450} = \frac{71 \cdot 3}{450 \cdot 3} = \frac{213}{1350}.\]

\[к)\ \frac{17}{104}\ и\ \frac{59}{338}\]

\[НОК(104;338) = 8 \cdot 13 \cdot 13 =\]

\[= 1352\]

\[\frac{17}{104} = \frac{17 \cdot 13}{104 \cdot 13} = \frac{221}{1352};\]

\[\frac{59}{338} = \frac{59 \cdot 4}{338 \cdot 4} = \frac{256}{1352}.\]