Question

inpartire rumerelor rationale

Answer 1

$a) \frac{17}{150} : \frac{34}{300} = \frac{17}{150} \times \frac{300}{34} = \frac{17 \times 300}{150 \times 34} = \frac{5100}{5100} = 1 \\ \\ b) \frac{3}{8} : \frac{5}{4} = \frac{3}{8} \times \frac{4}{5} = \frac{3 \times 4}{8 \times 5} = \frac{12}{40} = \frac{3}{10} \\ \\ c)3 \frac{1}{3} : 1 \frac{1}{9} = \frac{3 \times 3 + 1}{3} : 1 \frac{1}{9} = \frac{9 + 1}{3} : 1 \frac{1}{9} = \frac{10}{3} : 1 \frac{1}{9} = \frac{10}{3} : \frac{1 \times 9 + 1}{3} = \frac{10}{3} + \frac{9 + 1}{9} = \frac{10}{3} : \frac{10}{9} = \frac{10}{3} \times \frac{9}{10} = \frac{10 \times 9}{3 \times 10} = \frac{90}{30} = 3 \\ \\ d)4 \frac{1}{5} : 2 \frac{1}{10} = \frac{4 \times 5 + 1 }{5} : 2 \frac{1}{10} = \frac{20 + 1}{5} : 2 \frac{1}{10} = \frac{21}{5} : 2 \frac{1}{10} = \frac{21}{5} : \frac{2 \times 10 + 1}{10} = \frac{21}{5} : \frac{20 + 1}{10} = \frac{21}{5} : \frac{21}{10} = \frac{21}{5} \times \frac{10}{21} = \frac{21 \times 10}{5 \times 21} = \frac{210}{105} = 2$