abcd = 1100 * ab + cd mà abcd\(⋮11\) nên 1100 * ab + cd \(⋮11\), 1100 \(⋮\)11 nên ab + cd\(⋮\)11

1. Với $x$ nguyên, để $\frac{12}{3x-1}$ là số nguyên thì:

$3x-1\in Ư(12)$. Mà $3x-1\not\vdots 3$ nên:

$\Rightarrow 3x-1\in \left\{\pm 1; \pm 2; \pm 4\right\}$

$\Rightarrow x\in \left\{0; \frac{2}{3}; 1; \frac{-1}{3}; \frac{5}{3}; -1\right\}$

Vì $x$ nguyên nên $x\in \left\{0; 1; -1\right\}$

2.

Với $x$ nguyên thì $6x-4, 2x+3$ nguyên. Để $\frac{6x-4}{2x+3}$ nguyên thì:

$6x-4\vdots 2x+3$

$\Rightarrow 3(2x+3)-13\vdots 2x+3$

$\Rightarrow 13\vdots 2x+3$
$\Rightarrow 2x+3\in \left\{\pm 1; \pm 13\right\}$

$\Rightarrow x\in \left\{-1; -2; 5; -8\right\}$

Các cặp phân số bằng nhau: \(\dfrac{2}{4}\)=\(\dfrac{4}{8}\)=\(\dfrac{8}{16}\)=\(\dfrac{16}{32}\)

\(\dfrac{2}{8}\)=\(\dfrac{4}{16}=\dfrac{8}{32}\)

\(\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=\dfrac{32}{16}\)

MN trả lời nhanh giúp mik với nhé

Xin cám ơn!

Bài 5:

a. Để $M$ là phân số thì $n-3\neq 0$ hay $n\neq 3$

b. $n=0$ thì $M=\frac{4}{0-3}=\frac{-4}{3}$

$n=9$ thì $M=\frac{4}{9-3}=\frac{2}{3}$

$n=-9$ thì $M=\frac{4}{-9-3}=\frac{-1}{3}$

Bài 9:

\(\frac{13}{25}=\frac{26}{50}=\frac{39}{75}\)

Để phân số \(\dfrac{12}{3x-1}\) mang giá trị nguyên 

Khi \(12⋮3x-1\) hay \(3x-1\inƯ12=\left\{-12;-6;-4;-3;-2;-1;1;2;3;4;6;12\right\}\)

\(\Rightarrow x=\left\{-1;0;1\right\}\)

\(\dfrac{12}{3x-1}\inℤ\)

\(\Rightarrow3x-1\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}\)

\(\Rightarrow3x\in\left\{2;0;3;-1;4;-2;5;-3;7;-5;13;-11\right\}\)

\(\Rightarrow x\in\dfrac{2}{3};\dfrac{0}{1};\dfrac{4}{3};-\dfrac{2}{3};\dfrac{5}{3};-1;\dfrac{7}{3};-\dfrac{5}{3};\dfrac{13}{3};-\dfrac{11}{3}\)

Mà \(x\inℤ\)

Vậy \(x\in\left\{0;1;-1\right\}\)

Vậy \(x\in\left\{1;-1;0\right\}\) để \(\dfrac{12}{3x-1}\) nguyên

\(\left(-2\right)^3-45\)

\(=-8-45\)

\(=-53\)

\(...............\)

\(\left(-3^2\right)+2022^0\cdot\left(-1\right)^{2023}\)

\(=9+1\cdot\left(-1\right)\)

\(=9+\left(-1\right)\)

\(=8\)

Tự tính đê

Theo bn Thái Anh dù t cũng như m

\(\dfrac{116}{15}\)>\(\dfrac{15}{116}\)

So sánh 2 phân số: \(\dfrac{15}{116}\) và \(\dfrac{116}{15}\)

Ta có: \(\dfrac{15}{116}< 1\)

           \(\dfrac{116}{15}>1\)

Từ đó ta có: \(\dfrac{15}{116}< 1< \dfrac{116}{15}\)

\(\Rightarrow\dfrac{15}{116}< \dfrac{116}{15}\) \(\Rightarrow\) Vậy \(\dfrac{15}{116}< \dfrac{116}{15}\)

Bài 6.3 

\(\dfrac{8}{11}\)  = \(\dfrac{16}{22}\) = \(\dfrac{24}{33}\)

\(\dfrac{-5}{9}\)  = \(\dfrac{-10}{18}\) = \(\dfrac{-15}{27}\)

Bài 6.4

\(\dfrac{-12}{-4}\) = \(\dfrac{-12:\left(-4\right)}{-4:\left(-4\right)}\) = \(\dfrac{3}{1}\)

\(\dfrac{7}{-35}\) = \(\dfrac{7:\left(-7\right)}{-35:\left(-7\right)}\) = \(\dfrac{-1}{5}\)

\(\dfrac{-9}{27}\) = \(\dfrac{-9:9}{27:9}\) = \(\dfrac{-1}{3}\)