Explicație pas cu pas:
3. c.m.m.m.c. al numerelor: 3, 5, 12 (=2²×3), 2, 6 (=2×3), 4 (=2²) este 60
[tex] \frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60} [/tex]
[tex] \frac{1}{5} = \frac{1 \times 12}{5 \times 12} = \frac{12}{60} [/tex]
[tex] \frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60} [/tex]
[tex] \frac{7}{3} = \frac{7 \times 20}{3 \times 20} = \frac{140}{60} [/tex]
[tex] \frac{9}{2} = \frac{9 \times 30}{2 \times 30} = \frac{270}{60} [/tex]
[tex] \frac{11}{6} = \frac{11 \times 10}{6 \times 10} = \frac{110}{60} [/tex]
[tex]\frac{5}{4} = \frac{5 \times 15}{4 \times 15} = \frac{75}{60} [/tex]
4. a)
[tex] \frac{12}{50} = \frac{ {2}^{2} \times 3}{2 \times {5}^{2} } = \frac{6}{25} [/tex]
b)
[tex] \frac{24}{36} = \frac{ {2}^{3} \times 3 }{ {2}^{2} \times {3}^{2}} = \frac{2}{3} [/tex]
c)
[tex] \frac{48}{64} = \frac{ {2}^{4} \times 3}{ {2}^{6} } = \frac{3}{4} [/tex]
d)
[tex] \frac{39}{63} = \frac{3 \times 13}{ {3}^{2} \times 7} = \frac{13}{21} [/tex]
e)
[tex] \frac{63}{96} = \frac{ {3}^{2} \times 7}{ {2}^{5} \times 3} = \frac{21}{32} [/tex]
f)
[tex] \frac{300}{1500} = \frac{ {2}^{2} \times 3 \times {5}^{2}}{{2}^{2} \times 3 \times {5}^{3}} = \frac{1}{5} [/tex]
g)
[tex] \frac{245000}{452000} = \frac{ {2}^{3} \times {5}^{4} \times {7}^{2} }{ {2}^{5} \times {5}^{3} \times 113} = \frac{245}{452} [/tex]
h)
[tex] \frac{xx}{x} = \frac{11x}{x} = 11 [/tex]
i)
[tex] \frac{212121}{2121} = \frac{{3}^{2} \times {7}^{2} \times 13 \times 37}{3 \times 7 \times 101} = \frac{10101}{101} [/tex]
j)
[tex] \frac{ {2}^{n + 1} + {2}^{n}}{{4}^{n + 2} + {4}^{n}} = \frac{ {2}^{n} (2 + 1)}{ {4}^{n}( {4}^{2} + 1)} = \frac{{2}^{n} \times 3}{({2}^{2})^{n} \times 17} = \frac{{2}^{n} \times 3}{{2}^{n} \times {2}^{n}\times 17} = \frac{3}{17 \times {2}^{n} } [/tex]
