tính nhanh : 2/1*3+2/3*5+2/5*7+.......+2/23*25
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A = 2/1*5 + 2/5*9 + ... + 2/101*105
= 1/2(4/1*5 + 4/5*9 + ... + 4/101*105)
= 1/2(1 - 1/5 + 1/5 - 1/9 + ... + 1/101 - 1/105)
= 1/2(1 - 1/105)
= 1/2 * 104/105 = 52/105
Sửa câu b. Phân số thứ 2 phải là 4/5*8
B = 4/2*5 + 4/5*8 + ... + 4/47*50
= 4/3(3/2*5 + 3/5*8 + ... + 3/47*50)
= 4/3(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/47 - 1/50)
= 4/3(1/2 - 1/50)
= 4/3 * 24/50 = 16/25
a, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
= ( 1 + 9 ) + ( 2 + 8 ) + ( 3 + 7 ) + ( 4 + 6 ) + 5
= 10 + 10 + 10 + 10 + 5
= 45
b, 25 + 25 + 28 + 23 + 22 + 27
= ( 25 + 25 ) + ( 28 + 22 ) + ( 23 + 27 )
= 50 + 50 + 50
= 150
\(\dfrac{7}{2}+\dfrac{2}{25}=\dfrac{7\times25}{2\times25}+\dfrac{2\times2}{25\times2}=\dfrac{175}{50}+\dfrac{4}{50}=\dfrac{179}{50}\)
\(\dfrac{23}{5}-\dfrac{11}{3}=\dfrac{23\times3}{5\times3}-\dfrac{11\times5}{3\times5}=\dfrac{69}{15}-\dfrac{55}{15}=\dfrac{14}{15}\)
\(\dfrac{3}{7}-\dfrac{1}{14}=\dfrac{3\times2}{7\times2}-\dfrac{1}{14}=\dfrac{6}{14}-\dfrac{1}{14}=\dfrac{5}{14}\)
\(\dfrac{8}{5}:\dfrac{1}{3}=\dfrac{8}{5}\times3=\dfrac{8\times3}{5}=\dfrac{24}{5}\)
\(2:\dfrac{5}{3}=2\times\dfrac{3}{5}=\dfrac{2\times3}{5}=\dfrac{6}{5}\)
\(\dfrac{4}{5}\times\dfrac{7}{15}=\dfrac{4\times7}{5\times15}=\dfrac{28}{75}\)
Lời giải:
\(\frac{7}{2}+\frac{2}{25}=\frac{7\times 25+2\times 2}{2\times 25}=\frac{179}{50}\)
\(\frac{23}{5}-\frac{11}{3}=\frac{23\times 3-5\times 11}{5\times 3}=\frac{14}{15}\)
\(\frac{3}{7}-\frac{1}{14}=\frac{6}{14}-\frac{1}{14}=\frac{6-1}{14}=\frac{5}{14}\)
\(\frac{8}{5}: \frac{1}{3}=\frac{8}{5}\times 3=\frac{24}{5}\)
$2: \frac{5}{3}=\frac{2\times 3}{5}=\frac{6}{5}$
$\frac{4}{5}\times \frac{7}{15}=\frac{28}{75}$