\(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(\dfrac{5}{3}-\dfrac{3}{2}\right)+\left(\dfrac{7}{3}-\dfrac{5}{2}\right)\\ =\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{5}{3}+\dfrac{3}{2}+\dfrac{7}{3}-\dfrac{5}{2}\\ =\left(\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}\right)+\left(-\dfrac{1}{3}-\dfrac{5}{3}+\dfrac{7}{3}\right)\\ =-\dfrac{1}{2}+\dfrac{1}{3}\\ =-\dfrac{1}{6}\)

\(a)4^7:2^5\\ =\left(2^2\right)^7:2^5\\ =2^{14}:2^5\\ =2^9\\ b)3^{10}:9^3\\ =3^{10}:\left(3^2\right)^3\\ =3^{10}:3^6\\ =3^4\\ c)27^9:3^{10}\\ \left(3^3\right)^9:3^{10}\\ =3^{27}:3^{10}\\ =3^{17}\\ d)25^5:5^3\\ =\left(5^2\right)^5:5^3\\ =5^{10}:5^3\\ =5^7\\ e)36^7:6^4\\ =\left(6^2\right)^7:6^4\\ =6^{14}:6^4\\ =6^{10}\\ g)4^3\cdot8^4\\ =\left(2^2\right)^3\cdot\left(2^3\right)^4\\ =2^6\cdot3^{12}\\ =2^{18}\)

quy đồng nhé

2,153 <  2,741

2 số thập phân thì quy đồng kiểu gì vậy?

Ta có :

\(12=2^2.3\)

\(15=3.5\)

\(=>BCNN\left(12;15\right)=3.5.2^2=3.5.4=60\)

\(=>60:12=5;60:15=4\)

\(\dfrac{5}{12}=\dfrac{5.5}{12.5}=\dfrac{25}{60}\)

\(\dfrac{8}{15}=\dfrac{8.4}{15.4}=\dfrac{32}{60}\)

Vì \(25< 32\) nên

\(=>\dfrac{25}{60}< \dfrac{32}{60}\)

\(=>\dfrac{5}{12}< \dfrac{8}{15}\)

Vậy \(\dfrac{5}{12}< \dfrac{8}{15}\)

Nếu có gì sai sót thì nhớ bảo mình , mình cảm ơn!

Tử số chung: 40

Ta có:    \(\dfrac{5}{12}\)= \(\dfrac{5.8}{12.8}\)= \(\dfrac{40}{96}\);           \(\dfrac{8}{15}\)= \(\dfrac{8.5}{15.5}\)= \(\dfrac{40}{75}\)

Vì  \(\dfrac{40}{96}\) < \(\dfrac{40}{75}\) nên \(\dfrac{5}{12}\) < \(\dfrac{8}{15}\)

2B:

a) C1: \(\dfrac{-7}{12}=\dfrac{-6-1}{12}=\dfrac{-6}{12}+\dfrac{-1}{12}=\dfrac{-1}{2}+\dfrac{-1}{12}\)

C2: \(\dfrac{-7}{12}=\dfrac{-3-4}{12}=\dfrac{-3}{12}+\dfrac{-4}{12}=\dfrac{-1}{4}+\dfrac{-1}{3}\)

C4: \(\dfrac{-7}{12}=\dfrac{-2-5}{12}=\dfrac{-2}{12}+\dfrac{-5}{12}\)

b) C1: \(\dfrac{-7}{12}=\dfrac{4-11}{12}=\dfrac{4}{12}-\dfrac{11}{12}=\dfrac{1}{3}-\dfrac{11}{12}\)

C2: \(\dfrac{-7}{12}=\dfrac{2-9}{12}=\dfrac{2}{12}-\dfrac{9}{12}=\dfrac{1}{6}-\dfrac{3}{4}\)

C3: \(\dfrac{-7}{12}=\dfrac{3-10}{12}=\dfrac{3}{12}-\dfrac{10}{12}=\dfrac{1}{4}-\dfrac{5}{6}\)

Bài 1B:

a) 

\(\dfrac{-1}{16}+\dfrac{-1}{24}\\ =\dfrac{-3}{48}+\dfrac{-2}{48}\\ =\dfrac{-5}{48}\)

b) 

\(\dfrac{-1}{8}-\dfrac{3}{20}\\ =\dfrac{-5}{40}-\dfrac{6}{40}\\ =\dfrac{-11}{40}\)

c) 

\(-\dfrac{18}{10}+0,4\\ =\dfrac{-9}{5}+\dfrac{2}{5}\\ =\dfrac{-7}{5}\)

d) 

\(6,5-\left(-\dfrac{1}{5}\right)\\ =\dfrac{13}{2}+\dfrac{1}{5}\\ =\dfrac{65}{10}+\dfrac{2}{10}\\ =\dfrac{67}{10}\)

Lời giải:

PT $\Leftrightarrow (x-1)\left(\frac{1}{13}+\frac{1}{14}-\frac{1}{15}-\frac{1}{16}\right)=0$

Hiển nhiên $\frac{1}{13}+\frac{1}{14}>\frac{1}{15}+\frac{1}{16}$

$\Rightarrow \frac{1}{13}+\frac{1}{14}-\frac{1}{15}-\frac{1}{16}>0$

$\Rightarrow x-1=0$

$\Rightarrow x=1$

Vậy PT có nghiệm duy nhất $x=1$.

P/s: Bạn lưu ý lần sau gõ đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để mọi người đọc hiểu đề của bạn hơn nhé. 

a,

\(-\frac{9}{11}<\frac 9x<-\frac{9}{13}\\\Rightarrow \frac{-11}{9}>\frac x9 >\frac{-13}{9}\\ \Rightarrow -11>x>-13\)

b, 

\(-\frac35<\frac 9x <-\frac49\\\Rightarrow -\frac53>\frac x9>-\frac 94\\\Rightarrow \frac{-60}{36}>\frac{4x}{36}>\frac{-81}{36}\\\Rightarrow -60>4x>-81\\\Rightarrow -15>x>-\frac{81}{4}\)

a: \(1,25:\left(\dfrac{1}{2}-1\dfrac{1}{2}\right)-1,75\cdot\left(-20\%\right)\)

\(=\dfrac{5}{4}:\left(-1\right)-\dfrac{7}{4}\cdot\dfrac{-1}{5}\)

\(=-\dfrac{5}{4}+\dfrac{7}{20}=\dfrac{-25}{20}+\dfrac{7}{20}=-\dfrac{18}{20}=-\dfrac{9}{10}\)

b: \(\left(2,2+40\%\right):\left(\dfrac{1}{2}-1,25:20\%\right)\)

\(=\left(2,2+0,4\right):\left(0,5-1,25:0,2\right)\)

\(=2,6:\left(-5,75\right)=-\dfrac{52}{115}\)

c: \(\left[\dfrac{3}{4}-1,25:\left(-1\dfrac{1}{2}\right)\right]:\left(3,75-\dfrac{1}{2}:0,25\right)\)

\(=\left(\dfrac{3}{4}-\dfrac{5}{4}:\dfrac{-3}{2}\right):\left(\dfrac{15}{4}-\dfrac{1}{2}:\dfrac{1}{4}\right)\)

\(=\left(\dfrac{3}{4}+\dfrac{5}{4}\cdot\dfrac{2}{3}\right):\left(\dfrac{15}{4}-2\right)\)

\(=\left(\dfrac{3}{4}+\dfrac{5}{6}\right):\dfrac{7}{4}=\left(\dfrac{9}{12}+\dfrac{10}{12}\right):\dfrac{7}{4}\)

\(=\dfrac{19}{12}\cdot\dfrac{4}{7}=\dfrac{19}{21}\)

d: \(0,75\cdot\dfrac{-17}{13}-\dfrac{3}{4}\cdot\dfrac{-4}{13}-1,25\)

\(=0,75\cdot\dfrac{-17}{13}+\dfrac{3}{4}\cdot\dfrac{4}{13}-1,25\)

\(=0,75\cdot\left(-\dfrac{17}{13}+\dfrac{4}{13}\right)-1,25\)

=-0,75-1,25

=-2