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Bài 2. > , < , = ?
5/7 < 4/3 2/5 < 6/10 1/4 = 3/12 27/36 >
2/9 7/6 > 7/9
7/2 = 2/7 15/23 < 1 27/9 > 2 14/15 < 1 51/17 < 4
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\(a,\frac{2}{3}+\frac{1}{2}+\frac{1}{6}=\frac{4}{6}+\frac{3}{6}+\frac{1}{6}=\frac{8}{6}=\frac{4}{3}\)
\(b,\frac{5}{12}+\frac{5}{6}-\frac{3}{4}=\frac{5}{12}+\frac{10}{12}-\frac{9}{12}=\frac{6}{12}=\frac{1}{2}\)
a) 2/3 + 1/2 + 1/6 = 4/6 + 3/6 + 1/6 = 7/6 + 1/6 = 8/6 = 4/3
b) 5/12 + 5/6 - 3/4 = 5/12 + 10/12 - 9/12 = 15/12 - 9/12 = 6/12 = 1/2
c) 1/3 x 3/5 x 2/5 = 3/15 x 2/5 = 6/75 = 2/25
d) 15/16 : 3/8 x 3/4 = 15/16 x 8/3 x 3/4 = 1/10 x 3/4 = 3/40
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\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha
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Bài 7: Tính
a) \(4\dfrac{2}{5}\times8\dfrac{3}{4}-2\dfrac{3}{4}\)
\(=\dfrac{22}{5}\times\dfrac{35}{4}-\dfrac{11}{4}\)
\(=\dfrac{77}{2}-\dfrac{11}{4}\)
\(=\dfrac{143}{4}\)
b) \(2\dfrac{2}{3}+1\dfrac{2}{5}-\dfrac{2}{15}\)
\(=\dfrac{8}{3}+\dfrac{7}{5}-\dfrac{2}{15}\)
\(=\dfrac{47}{15}-\dfrac{2}{15}\)
\(=\dfrac{45}{15}=3\)
c) \(3\dfrac{1}{3}-2\dfrac{2}{3}+1\dfrac{5}{6}\)
\(=\dfrac{10}{3}-\dfrac{8}{3}+\dfrac{11}{6}\)
\(=\dfrac{2}{3}+\dfrac{11}{6}\)
\(=\dfrac{15}{6}\)
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a) 6 giờ 45 phút
b) 10 ngày 30 giờ
c) 17 phút
d) 9 giờ
e) 3,75 phút
f) 2 giây
a 6 giờ 45 phút
b 11 ngày 6 giờ
c 17 phút
d 9 giờ
e 3.75 phút
f 2 giây
\(3\dfrac{4}{5}+5\dfrac{6}{15}+4,5\)
\(=3\dfrac{4}{5}+5\dfrac{6}{15}+\dfrac{9}{2}\)
\(=\dfrac{19}{5}+\dfrac{27}{5}+\dfrac{9}{2}\)
`=46/5 + 9/2`
`=92/10 + 45/10`
`=137/10`
\(=\dfrac{3.4+5}{5}+\dfrac{5.15+6}{15}+\dfrac{9}{2}=\dfrac{19}{5}+\dfrac{27}{5}+\dfrac{9}{2}=\dfrac{19+27}{5}+\dfrac{9}{2}=\dfrac{46}{5}+\dfrac{9}{2}=\dfrac{46.2+9.5}{10}=\dfrac{137}{10}\)