a] \(5\times5\times3\times15\times25\times9=\)
b] \(9\times21\times7\times3\times49=\)
c] \(8\times4\times10\times25=\)
Tính nhanh:\(\frac{1\times2\times3+2\times4\times6+3\times6\times9+4\times8\times12+5\times10\times15}{1\times3\times5+2\times6\times10+3\times9\times15+4\times12\times20+5\times15\times25}-\frac{1+2+3+2+4+6+3+6+9+4+8+12+5+10+15}{1+3+5+2+6+10+3+9+15+4+12+20+5+15+25}\)
Bài 2: Tính
a) \(\dfrac{30\times25\times7\times8}{75\times8\times12\times14}\)
b)\(\dfrac{8\times3\times4}{16\times3}\)
c)\(\dfrac{4\times5\times6}{3\times10\times8}\)
(Các bạn tách các số ra rồi gạch, gạch xong thì nhân lại và ra kết quả) Thanks
a) \(\dfrac{30\times25\times7\times8}{75\times8\times12\times14}=\dfrac{3\times2\times5\times25\times7\times8}{25\times3\times8\times3\times4\times2\times7}=\dfrac{5}{3\times4}=\dfrac{5}{12}\)
b) \(\dfrac{8\times3\times4}{16\times3}=\dfrac{8\times3\times2\times2}{8\times2\times3}=2\)
c) \(\dfrac{4\times5\times6}{3\times10\times8}=\dfrac{4\times5\times3\times2}{3\times5\times2\times4\times2}=\dfrac{1}{2}\)
giúp mik với ạ, mình sẽ tick ạ! Thanks.
tính :\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+\frac{1}{4\times5\times6}+\frac{1}{5\times6\times7}+\frac{1}{6\times7\times8}+\frac{1}{7\times8\times9}+\frac{1}{8\times9\times10}\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)
Tính nhanh giá trị biểu thức :
\(\frac{1\times3\times5+2\times6\times10+4\times10\times12+7\times21\times35}{1\times5\times7+2\times10\times14+4\times20\times28+7\times35\times49}\)
1 x 3 x 5 + 2 x 6 x 10 + 4 x 10 x 12 + 7 x 21 x 35 / 1 x 5 x 7 + 2 x 10 x 14 + 4 x 20 x 28 + 7 x 35 x 49
= 3 / 7 + 6 / 14 + 10 x 2 x 6 / 10 x 2 x 28 + 21 / 49
= 3 / 7 + 6 / 14 + 6 / 28 + 21 / 49
= 3 / 7 + 6 / 14 + 3 / 14 + 3 / 7
= ( 3 / 7 + 3 / 7 ) + ( 6 / 14 + 3 / 14 )
= 6 / 7 + 9 14
= 12 / 14 + 9 / 14
= 21 / 14
nho hem
lm dau tien lun do
dung 100% nha
thực hiện phép tính:\(A=\frac{2^{12}\times4^6\times9^2}{2^{12}\times3^6+8^4\times3^5}-\frac{5^{10}\times7^3-25^2\times49^2}{125^3\times7^3+5^9\times14^3}\)
Tính một cách hợp lí :
\(B=\dfrac{40404}{70707}+\dfrac{244\times395-151}{244+395\times243}+\dfrac{1\times3\times5+2\times6\times10+4\times12\times20+7\times21\times35}{1\times5\times7+2\times10\times14+4\times20\times28+7\times35\times49}\)
\(B=\dfrac{40404}{70707}+\dfrac{244\times395-151}{244+395\times243}+\dfrac{1\times3\times5+2\times6\times10+4\times12\times20+7\times21\times35}{1\times5\times7+2\times10\times14+4\times20\times28+7\times35\times49}\\ =\dfrac{4}{7}+\dfrac{243\times395+395-151}{244+395\times243}+\dfrac{1\times3\times5\left(1+2+4+7\right)}{1\times5\times7\left(1+2+4+7\right)}\\ =\dfrac{4}{7}+\dfrac{243\times395+244}{244+395\times243}+\dfrac{3}{7}\\ =\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+1\\ =1+1=2\)
\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+\frac{1}{9\times10}\)
1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6+1/7-1/7+1/8-1/8+1/9+1/9-1/10
=1/2-1/10
=5/10-1/10
=4/10=2/5
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{8x9}+\frac{1}{9x10}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{2}-\frac{1}{10}\)
\(\frac{2}{5}\)
= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
= 1/2-0-0-0-0-0-0-0-0-1/10
=1/2 - 1/10
=2/5
tớ trước nhé
CHO A = \(\frac{2\times9\times8+3\times12\times10+4\times15\times12+...+98\times297\times200}{2\times3\times4+3\times4\times5+4\times5\times6+...+98\times99\times100}\)
TÍNH A\(^2\)
\(A=\frac{2\cdot9\cdot8+3\cdot12\cdot10+4\cdot15\cdot12+...+98\cdot297\cdot200}{2\cdot3\cdot4+3\cdot4\cdot5+4\cdot5\cdot6+...+98\cdot99\cdot100}\)
\(=\frac{2\cdot1\cdot3\cdot3\cdot4\cdot2+3\cdot1\cdot4\cdot3\cdot5\cdot2+...+98\cdot1+99\cdot3+100\cdot2}{2\cdot3\cdot4+3\cdot4\cdot5+...+98\cdot99\cdot100}\)
\(=\frac{1\cdot3\cdot2\cdot\left(2\cdot3\cdot4+3\cdot4\cdot5+...+98\cdot99\cdot100\right)}{2\cdot3\cdot4+3\cdot4\cdot5+...+98\cdot99\cdot100}\)
\(=1\cdot3\cdot2\)
\(=6\)
\(A^2=6^2=36\)
a.\(\frac{7^3\times5^8}{49\times25^4}\)
b.\(\frac{3^9\times25\times5^3}{15\times625\times3^8}\)
c.\(\frac{2^{50}\times3^{61}+2^{90}\times3^{16}}{2^{51}\times3^{61}+2^{91}\times3^{16}}\)
d.\((\frac{2}{5}-\frac{1}{2})^2+(\frac{1}{2}+\frac{3}{5})^2\)
a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.5^8}=7\)
b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^9.5^2.5^3}{3.5.5^4.3^8}=\frac{3^9.5^5}{3^9.5^5}=1\)
c) \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)
d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2\)
\(=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2\)
\(=\frac{1}{100}+\frac{121}{100}=\frac{122}{100}=\frac{61}{50}\)
a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=\frac{7^3.5^8}{7^2.5^8}=7\)
b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^9.5^2.5^3}{5.3.5^4.3^8}=\frac{3^9.5^5}{5^5.3^9}=1\)
c) \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)
d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(-\frac{1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{122}{100}=1,22\)