a) \(\dfrac{-3}{7}+\dfrac{4}{21}=\dfrac{-3\cdot3}{21}+\dfrac{4}{21}=\dfrac{-9}{21}+\dfrac{4}{21}=\dfrac{-9+4}{21}=-\dfrac{5}{21}\)

b) \(\left(-0,346\right)+\left(-1,2\right)=-1,546\)

a: \(\dfrac{-3}{7}+\dfrac{4}{21}=-\dfrac{9}{21}+\dfrac{4}{21}=-\dfrac{5}{21}\)

b: \(\left(-0,346\right)+\left(-1,2\right)=-\left(1,2+0,346\right)=-1,546\)

a: \(1,2756\simeq1\)

b: \(\dfrac{x-2}{7}=\dfrac{6}{21}\)

=>\(\dfrac{x-2}{7}=\dfrac{2}{7}\)

=>x-2=2

=>x=2+2=4

a) 1,2756 ≃ 1 

b) 

\(\dfrac{x-2}{7}=\dfrac{6}{21}\\ =>x-2=\dfrac{6}{21}\cdot7=\dfrac{6}{3}=2\\ =>x=2+2=4\)

\(\dfrac{3}{5}:1,5+20\%-3\dfrac{1}{4}\)

\(=\dfrac{3}{5}:\dfrac{3}{2}+\dfrac{1}{5}-\dfrac{13}{4}\)

\(=\dfrac{2}{5}+\dfrac{1}{5}-\dfrac{13}{4}=\dfrac{3}{5}-\dfrac{13}{4}=\dfrac{12}{20}-\dfrac{65}{20}=\dfrac{-53}{20}\)

\(\dfrac{3}{5}:1,5+20\%-3\dfrac{1}{4}\\ =\dfrac{3}{5}:\dfrac{3}{2}+\dfrac{1}{5}-\dfrac{13}{4}\\ =\dfrac{3}{5}\cdot\dfrac{2}{3}+\dfrac{1}{5}-\dfrac{13}{4}\\ =\dfrac{2}{5}+\dfrac{1}{5}-\dfrac{13}{4}\\ =\dfrac{3}{5}-\dfrac{13}{4}\\ =\dfrac{12}{20}-\dfrac{65}{20}\\ =\dfrac{-53}{20}\)

\(a.8,2+\left(-3,5\right)+50+3,5+\left(-8,2\right)\\ =\left(8,2-8,2\right)+\left(3,5-3,5\right)+50\\ =0+0+50\\ =50\\ b.\dfrac{8}{15}\cdot\dfrac{-45}{4}\\ =\dfrac{4\cdot2}{15}\cdot\dfrac{15\cdot-3}{4}\\ =2\cdot-3\\ =-6\)

a: \(8,2+\left(-3,5\right)+50+3,5+\left(-8,2\right)\)

\(=\left(8,2-8,2\right)+\left(3,5-3,5\right)+50\)

=0+0+50

=50

b: \(\dfrac{8}{15}\cdot\dfrac{-45}{4}=\dfrac{8}{4}\cdot\dfrac{-45}{15}=2\cdot\left(-3\right)=-6\)

a: x:1,25=-2,4

=>\(x=-2,4\cdot1,25=-3\)

b: \(\dfrac{5}{8}x-\dfrac{7}{24}=-\dfrac{2}{3}\)

=>\(\dfrac{5}{8}x=-\dfrac{2}{3}+\dfrac{7}{24}=-\dfrac{16}{24}+\dfrac{7}{24}=-\dfrac{9}{24}=-\dfrac{3}{8}\)

=>\(x=-\dfrac{3}{8}:\dfrac{5}{8}=-\dfrac{3}{8}\cdot\dfrac{8}{5}=-\dfrac{3}{5}\)

9 gói.

Trong đề có ấy bạn.

\(x+\dfrac{5}{12}=-\dfrac{7}{6}\)

=>\(x=-\dfrac{7}{6}-\dfrac{5}{12}=-\dfrac{14}{12}-\dfrac{5}{12}=-\dfrac{19}{12}\)

\(x+\dfrac{5}{12}=-\dfrac{7}{6}\\ \Rightarrow x=-\dfrac{7}{6}-\dfrac{5}{12}\\ \Rightarrow x=-\dfrac{19}{12}\)

Vậy \(x=-\dfrac{19}{12}\)

\(A=\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot...\cdot\dfrac{9999}{10000}\)

\(=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{10000}\right)\)

\(=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{100}\right)\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1+\dfrac{1}{100}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{99}{100}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{101}{100}\)

\(=\dfrac{1}{100}\cdot\dfrac{101}{2}=\dfrac{101}{200}\)

\(A=\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot...\cdot\dfrac{9999}{10000}\\ \Rightarrow A=\dfrac{3\cdot8\cdot15\cdot...\cdot9999}{4\cdot9\cdot16\cdot...\cdot10000}\\\Rightarrow A=\dfrac{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot99\cdot101}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot100\cdot100}\\ \Rightarrow A=\dfrac{\left(1\cdot2\cdot3\cdot...\cdot99\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot101\right)}{\left(2\cdot3\cdot4\cdot...\cdot100\right)\cdot\left(2\cdot3\cdot4\cdot...\cdot100\right)}\\\Rightarrow A=\dfrac{101}{100\cdot2}\\\Rightarrow A=\dfrac{101}{200}\)

Vậy \(A=\dfrac{101}{200}\)

Để số có 6 chữ số lập được có giá trị nhỏ nhất thì chữ số hàng trăm nghìn phải có giá trị nhỏ nhất

Mà số cần tìm có các chữ số 1 và 7 nằm xen kẽ nên:

Số cần tìm là 171717

Vậy số cần tìm là 171717

Là 171717

Đặt \(A=5+5^3+...+5^{99}\)

=>\(25A=5^3+5^5+...+5^{101}\)

=>\(25A-A=5^5+5^5+...+5^{101}-5-5^3-...-5^{99}\)

=>\(24A=5^{101}-5\)

=>\(A=\dfrac{5^{101}-5}{24}\)