Tinh hop ly gia tri cac bieu thuc sau
c) \(6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{5}\right)\)
d) \(\left(\frac{3}{5}+0,415-\frac{3}{200}\right).2\frac{2}{3}.0,25\)
Tinh hop ly gia tri cac bieu thuc sau
a) \(\left(19\frac{5}{8}:\frac{7}{12}-13\frac{1}{2}:\frac{7}{12}\right).\frac{4}{5}\)
b) \(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
Tinh hop ly gia tri bieu thuc sau
\(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{2}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{8}\right)\left(1-\frac{1}{10}\right)\)
(1-1/3)x(1-1/5)x(1-1/7)x(1-1/9)x(1-1/2)x(1-1/4)x(1-1/6)x(1-1/8)x(1-1/10)
=2/3x4/5x6/7x8/9x1/2x3/4x5/6x7/8x9/10
=2x4x6x8x1x3x5x7x9 /3x5x7x9x2x4x6x8x10
=1/10
Tinh hop ly gia tri cua cac bieu thuc sau
c)\(\frac{-5}{7}.\frac{3}{9}+\frac{4}{9}:\frac{-7}{3}\)
d) \(8\frac{2}{7}-\left(3\frac{4}{9}+4\frac{2}{7}\right)\)
c) =-5/7x3/9+4/9x3/-7
=-5/7x3/9+3/9x4/-7
=3/9x(-5/7+4/-7)
=3/9x-9/7
=-3/7
d) =58/7 - (31/9+30/7)
=58/7-31/9-30/7
=(58/7-30/7)-(31/9)
=4-31/9
=5/9
1) Tinh gia tri cua bieu thuc:
A=\(\frac{\left(1+2+...+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-\frac{1}{5}\right)\left(2,4.42-21.4,8\right)}{1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
B=\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}}\)
\(A=\frac{\left(1+2+...+100\right)\left(\frac{1}{2}^2-...-\frac{1}{5}\right)\left(2,4.42-21.4,8\right)}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
=> \(A=\frac{\left(1+2+...+100\right)\left(\frac{1}{2}-...-\frac{1}{5}\right).0}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)= 0
\(a,1\frac{13}{15}.0,75-\left(\frac{8}{15}+0,25\right).\frac{24}{47}\)
\(b,5:\left(4\frac{3}{4}-1\frac{25}{28}\right)-1\frac{3}{8}:\left(\frac{3}{8}+\frac{9}{20}\right)\)
\(c,6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{5}\right)\)
\(d,\left(\frac{3}{5}+0,415-\frac{3}{200}\right).2\frac{2}{3}.0,25\)
\(e,\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
\(g,1\frac{13}{15}.0,75-\left(\frac{11}{20}+25\%\right);\frac{7}{3}\)
\(\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
\(\frac{1}{2}+\frac{3}{4}-\left(\frac{3}{4}-\frac{4}{5}\right)\)
\(6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}\left(\frac{1}{3}-\frac{1}{5}\right)\)
\(\left(\frac{7}{8}-\frac{3}{4}\right)1\frac{1}{3}-\frac{2}{7}\left(3,5\right)^2\)
\(\left(\frac{3}{5}+0,415-\frac{3}{200}\right)2\frac{2}{3}.0,25\)
Thực hiện các phép tính
cảm ơn
\(\left(\frac{3}{8}+-\frac{3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
\(=\left(\frac{9}{24}+-\frac{18}{24}+\frac{14}{24}\right):\frac{5}{6}+\frac{1}{2}\)
\(=\frac{5}{24}:\frac{5}{6}+\frac{1}{2}\)
\(=\frac{5}{24}.\frac{6}{5}+\frac{1}{2}\)
\(=\frac{1}{4}+\frac{1}{2}\)
\(=\frac{1}{4}+\frac{2}{4}\)
\(=\frac{3}{4}\)
\(\frac{1}{2}+\frac{3}{4}-\left(\frac{3}{4}-\frac{4}{5}\right)\)
\(=\frac{1}{2}+\frac{3}{4}-\left(\frac{15}{20}-\frac{16}{20}\right)\)
\(=\frac{1}{2}+\frac{3}{4}-\frac{-1}{20}\)
\(=\frac{10}{20}+\frac{15}{20}-\frac{-1}{20}\)
\(=\frac{25}{20}-\frac{-1}{20}\)
\(=\frac{26}{20}\)
\(=\frac{13}{10}\)
1/2+3/4-(3/4-4/5)
1/2+3/4+3/4+4/5
1/2+6/4+4/5
10/20+30/20+16/20
56/20=14/5
Tinh hop ly cac bieu thuc sau
a)\(\left(1-\frac{1}{7}\right)\left(1-\frac{2}{7}\right)\left(1-\frac{3}{7}\right)...\left(1-\frac{2014}{7}\right)\)
b) \(\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}+1\right)...\left(\frac{1}{99}+1\right)\)
\(b,\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}+1\right)...\left(\frac{1}{99}+1\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\)
\(=\frac{100}{2}\)
\(=50\)
Tinh gia tri bieu thuc:
\(D=\left(\frac{3}{2}\right)^2+\left(\frac{1}{4}\right)^2-\left(\frac{1}{2}\right)^3\)
D = \(\frac{9}{4}+\frac{1}{16}-\frac{1}{8}\)
D = \(\frac{35}{16}\)
\(D=\left(\frac{3}{2}\right)^2+\left(\frac{1}{4}\right)^2-\left(\frac{1}{2}\right)^3\)
\(D=\frac{9}{4}+\frac{1}{16}-\frac{1}{8}\)
\(D=\frac{37}{16}-\frac{1}{8}\)
\(D=\frac{35}{16}.\)
Chúc bạn học tốt!
1) A= \(\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
b) Cho 3 so x,y,z la 3 so khac 0 thoa man dieu kien :
\(\frac{y+z-x}{x}=\frac{z+x-y}{y}=\frac{x+y-z}{z}\)
Hay tinh gia tri bieu thuc:\(B=\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)\)
Bài 1 :
Ta có :
\(A=\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
\(A=\frac{3\left(\frac{1}{4}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{2}\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}\)
\(A=\frac{3}{5}+\frac{1}{\frac{5}{2}}\)
\(A=\frac{3}{5}+\frac{2}{5}\)
\(A=1\)
\(b)\) Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{y+z-x}{x}=\frac{z+x-y}{y}=\frac{x+y-z}{z}=\frac{y+z-x+z+x-y+x+y-z}{x+y+z}=\frac{2\left(x+y+z\right)}{x+y+z}=2\)
Đo đó :
\(\frac{y+z-x}{x}=2\)\(\Rightarrow\)\(y+z=3x\)\(\left(1\right)\)
\(\frac{z+x-y}{y}=2\)\(\Rightarrow\)\(x+z=3y\)\(\left(2\right)\)
\(\frac{x+y-z}{z}=2\)\(\Rightarrow\)\(x+y=3z\)\(\left(3\right)\)
Lại có : \(B=\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)=\frac{x+y}{y}.\frac{y+z}{z}.\frac{x+z}{x}\)
Thay (1), (2) và (3) vào \(B=\frac{x+y}{y}.\frac{y+z}{z}.\frac{x+z}{x}\) ta được :
\(B=\frac{2z}{y}.\frac{2x}{z}.\frac{2y}{x}=\frac{8xyz}{xyz}=8\)
Vậy \(B=8\)
Chúc bạn học tốt ~
bạn phùng minh quân câu 1 a tại sao lại rút gọn được \(\frac{3.\left(\frac{1}{4}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}=\frac{3}{5}\) vậy nó không cùng nhân tử mà
câu b \(\frac{y+z-x+z+x-y+x+y-z}{x+y+z}=\frac{\left(y-y+y\right)+\left(-x+x+x\right)+\left(z+z-z\right)}{x+y+z}=\frac{x+y+z}{x+y+z}=1\)sao lại ra bằng 2
(mình chỉ góp ý thôi nha tại mình làm thấy nó sai sai)