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10 tháng 8 2022
1.3.77−1+3.7.99−3+7.9.1313−7+9.13.1515−9+\frac{19-13}{13.15.19}+13.15.1919−13
=\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}=1.31−3.71+3.71−7.91+7.91−9.131+9.131−13.151+13.151−15.191
=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31−15.191=28595−2851=28594
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)b,=61.(1.3.76+3.7.96+7.9.136+9.13.156+13.15.196)
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)c,=81.(1.2.31+2.3.41+3.4.51+...+48.49.501)
=\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)=161.(1.2.32+2.3.42+3.4.52+...+48.49.502)
=\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)=161.(1.2.33−1+2.3.44−2+3.4.55−3+...+48.49.5050−48)
=\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)=161.(1.21−2.31+2.31−3.41+3.41−4.51+...+48.491−49.501)
=\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}=161.(21−24501)=161.(24501225−24501)=4900153
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)d,=75.(1.5.87+5.8.127+8.12.157+...+33.36.407)
=\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)=75.(1.5.88−1+5.8.1212−5+8.12.1515−8+...+33.36.4040−33)
=\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)=75.(1.51−5.81+5.81−8.121+8.121−12.151+...+33.361−36.401)
=\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}=75.(51−14401)=75.(1440288−14401)=28841
P/S: . là nhân nha
VT
20 tháng 8 2017
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
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
AD
1
22 tháng 9 2021
Bài 4
35/85 = 7/17
36/108 = 1/3
25/100 = 1/4
39/52 = 3/4
Bài 8
a) 9/8 và 7/12
= 8×3=24 ; 12×2=24
=>9/8 =27/24
=> 7/12 ; 14/24
b) 3/20 và 4/15
=20×3=60 ; 15×4=60
=> 9/60 ; 16/60
Bài 9
a) \(\frac{3}{8},\frac{15}{8},\frac{9}{8},\frac{7}{8}\)
Từ lớn -> bé:
=>\(\frac{15}{8},\frac{9}{8},\frac{7}{8},\frac{3}{8}\)
b) \(\frac{4}{15},\frac{3}{5},\frac{8}{45},\frac{7}{15}=\frac{12}{45},\frac{27}{45},\frac{8}{45},\frac{21}{45}\)
Từ lớn -> bé:
=> \(\frac{3}{5},\frac{7}{15},\frac{4}{15},\frac{8}{45}\)
c) \(\frac{3}{8},\frac{4}{5},\frac{47}{40},\frac{9}{4}=\frac{15}{40},\frac{32}{40},\frac{47}{40},\frac{90}{40}\)
Từ lớn -> bé:
=>\(\frac{9}{4},\frac{47}{40},\frac{4}{5},\frac{3}{8}\)
Bài 10
a, Ta có
`x/15 < 4/15`
` <=> x < 4`
` <=> x ∈ {1 ; 2 ; 3}`
b, Ta có
`5/9 > x/9`
` <=> 5 > x`
` <=> x ∈ {1 ; 2 ; 3 ; 4}`
c, Ta có
`1 <x/8 < 11/8`
` <=> 8/8 < x/8 < 11/8`
` <=> 8 < x <11`
` <=> x ∈ {9 ; 10}`
G
20 tháng 2 2020
\(\frac{5}{6}\times\frac{7}{12}+\frac{5}{12}\times\frac{5}{6}+\frac{1}{6}\)
= \(\frac{35}{72}+\frac{25}{36}+\frac{1}{6}\)
= \(\frac{97}{72}\)
\(\left(\frac{8}{15}\times\frac{3}{4}\times\frac{5}{4}\right):\frac{7}{8}\)
= \(\frac{1}{2}:\frac{7}{8}\)
=\(\frac{4}{7}\)
HOK TỐT ^^
26 tháng 3 2017
1a)\(\frac{5}{3}\)=\(\frac{5x4}{3x4}\)=\(\frac{20}{12}\); \(\frac{1}{4}\)=\(\frac{1x3}{4x3}\)=\(\frac{3}{12}\)
b)\(\frac{3}{8}\)=\(\frac{3x3}{8x3}\)=\(\frac{9}{24}\); \(\frac{7}{24}\)
c)\(\frac{1}{2}\)=\(\frac{1x15}{2x15}\)=\(\frac{15}{30}\); \(\frac{2}{3}\)=\(\frac{2x10}{3x10}\)=\(\frac{20}{30}\); \(\frac{3}{5}\)=\(\frac{3x6}{5x6}\)=\(\frac{18}{30}\)
2a)\(\frac{11}{8}\)>\(\frac{11}{9}\)
b)\(\frac{4}{9}\)<\(\frac{3}{5}\)
c)\(\frac{6}{5}\)>\(\frac{5}{6}\)
6/8>5/7
9/15=3/5
24/36<75/100