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7 tháng 9 2019
Câu hỏi của Lê Tiến Cường - Toán lớp 6 - Học toán với OnlineMath
7 tháng 9 2019
\(A=\frac{3}{2}+\frac{7}{6}+\frac{13}{12}+...+\frac{10101}{10100}=\frac{2+1}{2}+\frac{6+1}{6}+\frac{12+1}{12}+...+\frac{10100+1}{10100}\)
\(A=\left(1+\frac{1}{2}\right)+\left(1+\frac{1}{6}\right)+\left(1+\frac{1}{12}\right)+....+\left(1+\frac{1}{10100}\right)\)
\(A=\left(1+\frac{1}{1\times2}\right)+\left(1+\frac{1}{2\times3}\right)+\left(1+\frac{1}{3\times4}\right)+...+\left(1+\frac{1}{100\times101}\right)\)
\(A=\left(1+1+1+....+1\right)+\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{100\times101}\right)\)
\(A=100+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{100}-\frac{1}{101}\right)\)
\(A=100+1-\frac{1}{101}=101-\frac{1}{101}< 101=B\)
\(\Rightarrow A< B\)
So easy
10 tháng 5 2018
\(\frac{x-12}{3}=\frac{x+1}{4}\)
=>(x-12).4=(x+1)*3
4x-48=3x+3
4x-3x=48+3
x=51
10 tháng 5 2018
(x-12)/3=(x+1)/4
(x-12)*4=(x+1)*3
x*4-12*4=x*3+1*3
4x-48=3x+3
4x-3x=3+48
x=51
11 tháng 5 2021
=(1975/1976+2010/2011+1963/1968)x(4/12-3/12-1/12)
=(1975/1976+2010/2011+1963/1968)x0
=0
TM
24 tháng 4 2016
\(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}:\frac{3+\frac{3}{13}+\frac{3}{169}+\frac{3}{91}}{7+\frac{7}{13}+\frac{7}{169}+\frac{1}{91}}=\frac{12\left(\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}{4\left(\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}:\frac{3\left(\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}{7\left(\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}\)
\(=\frac{12}{4}:\frac{3}{7}\)
\(=3:\frac{3}{7}\)
\(=3.\frac{7}{3}\)
\(=7\)
mk nha bạn
AK
9 tháng 4 2018
\(4\frac{3}{4}+\left(-0,37\right)+\frac{1}{8}+\left(-1,28\right)+\left(-2,5\right)+3\frac{1}{12}\)
\(=\frac{19}{4}+-\frac{37}{100}+\frac{1}{8}+-\frac{128}{100}+-\frac{250}{100}+\frac{37}{12}\)
\(=\left(\frac{19}{4}+\frac{1}{8}+\frac{37}{12}\right)-\left(\frac{37}{100}+\frac{128}{100}+\frac{250}{100}\right)\)
\(=\left(\frac{114}{24}+\frac{3}{24}+\frac{74}{24}\right)-\frac{415}{100}\)
\(=\frac{191}{24}-\frac{415}{100}\)
\(=\frac{457}{120}\)
Tham khảo nha !!!
9 tháng 4 2018
\(4\frac{3}{4}+\left(-0,37\right)+\frac{1}{8}+\left(-1,28\right)+\left(-2,5\right)+3\frac{1}{12}\)
\(=\frac{19}{4}+\frac{-37}{100}+\frac{1}{8}+\frac{-32}{25}+\frac{-5}{2}+\frac{37}{12}\)
\(=\left(\frac{19}{4}+\frac{1}{8}+\frac{-5}{2}\right)+\left(\frac{-37}{100}+\frac{-32}{25}\right)+\frac{37}{12}\)
\(=\frac{19}{8}+\frac{-33}{20}+\frac{37}{12}\)
\(=\frac{29}{40}+\frac{37}{12}\)
\(=\frac{457}{120}\)
KN
31 tháng 8 2020
\(B=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^9.33+3^9.15}{3^9.2^4}\)
\(=\frac{3^9\left(33+15\right)}{3^9.2^4}=\frac{3^9.48}{3^9.16}\)
\(=\frac{48}{16}=3\)
31 tháng 8 2020
\(B=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
\(=\frac{3^{10}.\left(11+5\right)}{3^9.8}\)
\(=\frac{3^{10}.16}{3^9.8}\)
\(=\frac{3.2}{1}\)
\(=6\)
5 tháng 3 2020
\(B=81.\left(\frac{12-\frac{12}{7}-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right).\frac{158158158}{711711711}\)
\(\Leftrightarrow B=81.\left(\frac{12\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}{4\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}:\frac{5\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}{6\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}\right).\frac{158\left(1001001\right)}{711\left(1001001\right)}\)
\(\Leftrightarrow B=81\left(\frac{12}{3}:\frac{5}{6}\right).\frac{158}{711}\)
\(\Leftrightarrow B=81\left(3.\frac{6}{5}\right).\frac{2}{9}\)
\(\Leftrightarrow B=81.\frac{18}{5}.\frac{2}{9}\)
\(\Leftrightarrow B=\frac{324}{5}\)
Hok tốt!!
9 tháng 8 2017
A) \(\frac{1}{2}\cdot\left(\frac{2}{9}+\frac{3}{7}-\frac{5}{27}\right)\)
\(=\frac{1}{2}\cdot\frac{1}{2}\)
\(=\frac{1}{4}\)
B) \(\left(\frac{-5}{28}+1.75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right)\)
\(=\left(\frac{-5}{28}+\frac{7}{4}+\frac{8}{35}\right):\frac{-69}{20}\)
\(=\frac{14}{5}:\frac{-69}{20}\)
\(=\frac{-56}{69}\)
\(\frac{4^8.3^{12}.27^2}{6^{12}.9^3}\)
= \(\frac{\left(2^2\right)^8.3^{12}.27^2}{\left(2.3\right)^{12}.\left(3^2\right)^3}\)
= \(\frac{2^{16}.3^{12}.27^2}{2^{12}.3^{12}.27^2}\)
= \(\frac{2^{16}}{2^{12}}\)= 24 = 16