a: \(-1,2+\dfrac{2}{3}+x=5\)

=>\(x=5+1,2-\dfrac{2}{3}=6,2-\dfrac{2}{3}\)

=>\(x=\dfrac{31}{5}-\dfrac{2}{3}=\dfrac{93}{15}-\dfrac{10}{15}=\dfrac{83}{15}\)

b: \(2\dfrac{4}{7}-3x=\dfrac{-4}{5}+\dfrac{2}{3}\)

=>\(\dfrac{18}{7}-3x=\dfrac{-12}{15}+\dfrac{10}{15}=\dfrac{-2}{15}\)

=>\(3x=\dfrac{18}{7}+\dfrac{2}{15}=\dfrac{270}{105}+\dfrac{14}{105}=\dfrac{284}{105}\)

=>\(x=\dfrac{284}{315}\)

c: \(\dfrac{1}{6}-\dfrac{3}{8}+1,75=3\dfrac{4}{3}-x\)

=>\(\dfrac{13}{3}-x=\dfrac{4}{24}-\dfrac{9}{24}+\dfrac{42}{24}=\dfrac{37}{24}\)

=>\(x=\dfrac{13}{3}-\dfrac{37}{24}=\dfrac{108}{24}-\dfrac{37}{24}=\dfrac{71}{24}\)

d: \(\dfrac{1}{6}-\dfrac{4}{9}+0,125=2\dfrac{4}{3}-2x\)

=>\(\dfrac{10}{3}-2x=\dfrac{-11}{72}\)

=>\(2x=\dfrac{10}{3}+\dfrac{11}{72}=\dfrac{240}{72}+\dfrac{11}{72}=\dfrac{251}{72}\)

=>\(x=\dfrac{251}{144}\)

e: \(2\dfrac{2}{3}-4x=\dfrac{-7}{5}+\dfrac{2}{3}\)

=>\(2+\dfrac{2}{3}-4x=\dfrac{-7}{5}+\dfrac{2}{3}\)

=>\(2-4x=-\dfrac{7}{5}\)

=>\(4x=2+\dfrac{7}{5}=\dfrac{17}{5}\)

=>\(x=\dfrac{17}{20}\)

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

=>\(x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}=\dfrac{3}{6}-\dfrac{5}{6}=\dfrac{-2}{6}=-\dfrac{1}{3}\)

=>\(x=-\dfrac{1}{3}-\dfrac{1}{3}=-\dfrac{2}{3}\)

g: \(\left(\dfrac{3}{5}-\dfrac{4}{3}\right)+\left(\dfrac{5}{8}-x\right)=\dfrac{9}{7}\)

=>\(\dfrac{-11}{15}+\dfrac{5}{8}-x=\dfrac{9}{7}\)

=>\(\dfrac{-13}{120}-x=\dfrac{9}{7}\)

=>\(x=-\dfrac{13}{120}-\dfrac{9}{7}=\dfrac{-1171}{840}\)

a, \(-1,2+\dfrac{2}{3}+x=5\Leftrightarrow x=5+1,2-\dfrac{2}{3}=\dfrac{83}{15}\)

b, \(2\dfrac{4}{7}-3x=-\dfrac{4}{5}+\dfrac{2}{3}\Leftrightarrow\dfrac{18}{7}-3x=-\dfrac{2}{15}\Leftrightarrow3x=\dfrac{284}{105}\Leftrightarrow x=\dfrac{284}{315}\)

c, \(\dfrac{1}{6}-\dfrac{3}{8}+1,75=3\dfrac{4}{3}-x\Leftrightarrow-x+\dfrac{13}{3}=\dfrac{37}{24}\Leftrightarrow x=\dfrac{13}{3}-\dfrac{37}{24}=\dfrac{67}{24}\)

d, \(\dfrac{1}{6}-\dfrac{4}{9}+0,125=2\dfrac{4}{3}-2x\Leftrightarrow-2x+\dfrac{10}{3}=-\dfrac{-11}{72}\Leftrightarrow2x=\dfrac{251}{72}\Leftrightarrow x=\dfrac{251}{144}\)

e, \(2\dfrac{2}{3}-4x=-\dfrac{7}{5}+\dfrac{2}{7}\Leftrightarrow\dfrac{8}{3}-4x=-\dfrac{39}{35}\Leftrightarrow4x=\dfrac{397}{105}\Leftrightarrow x=\dfrac{397}{420}\)

f, \(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\Leftrightarrow x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}=-\dfrac{1}{3}\Leftrightarrow x=-\dfrac{2}{3}\)

g, \(\left(\dfrac{3}{5}-\dfrac{4}{3}\right)+\left(\dfrac{5}{8}-x\right)=\dfrac{9}{7}\Leftrightarrow\dfrac{-11}{15}+\dfrac{5}{8}-x=\dfrac{9}{7}\Leftrightarrow\left(-\dfrac{13}{120}\right)-x=\dfrac{9}{7}\Leftrightarrow x=-\dfrac{1171}{840}\)

\(\left(\dfrac{7}{6}+\dfrac{5}{12}\right)\times12\)

\(=\left(\dfrac{14}{12}+\dfrac{5}{12}\right)\times12\)

\(=\dfrac{19}{12}\times12=19\)

 ❤

TK ạ

Nếu chỉ có hai lực tác dụng vào cùng một vật mà vật vẫn đứng yên thì hai lực đó là hai lực cân bằng.

→u𝑢→ và →v𝑣→ biểu diễn cho hai vecto cân bằng thì hai vecto này có chung gốc, ngược hướng và có độ lớn (hay độ dài) bằng nhau.

 Hai lực cân bằng là hai lực có cùng phương, ngược chiều, cùng độ lớn và có cùng điểm đặt (tác động vào cùng một điểm).

 Nếu biểu diễn bằng vector thì 2 vector này cùng phương, ngược chiều, có độ dài bằng nhau và có chung điểm gốc.

a: \(\dfrac{-3}{5}+\dfrac{28}{5}\left(\dfrac{13}{56}-\dfrac{5}{24}+\dfrac{1}{7}\right)\)

\(=\dfrac{-3}{5}+\dfrac{28}{5}\left(\dfrac{39}{168}-\dfrac{35}{168}+\dfrac{24}{168}\right)\)

\(=\dfrac{-3}{5}+\dfrac{28}{5}\cdot\dfrac{28}{168}=\dfrac{-3}{5}+\dfrac{28}{5}\cdot\dfrac{1}{6}=\dfrac{-3}{5}+\dfrac{14}{15}\)

\(=\dfrac{-9}{15}+\dfrac{14}{15}=\dfrac{5}{15}=\dfrac{1}{3}\)

b: \(\dfrac{5}{7}\cdot\dfrac{11}{18}+\dfrac{3}{7}\cdot\dfrac{5}{18}+\dfrac{4}{9}\)

\(=\dfrac{5}{18}\left(\dfrac{11}{7}+\dfrac{3}{7}\right)+\dfrac{4}{9}\)

\(=\dfrac{5}{18}\cdot2+\dfrac{4}{9}=\dfrac{5}{9}+\dfrac{4}{9}=\dfrac{9}{9}=1\)

c: \(4\dfrac{5}{9}:\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)

\(=\left(\dfrac{41}{9}+\dfrac{49}{9}\right):\dfrac{-5}{7}=10\cdot\dfrac{-7}{5}=-14\)

d: \(\left(-\dfrac{3}{5}+\dfrac{4}{9}\right):\dfrac{7}{11}+\left(-\dfrac{2}{5}+\dfrac{5}{9}\right):\dfrac{7}{11}\)

\(=\left(-\dfrac{3}{5}+\dfrac{4}{9}+\dfrac{-2}{5}+\dfrac{5}{9}\right)\cdot\dfrac{11}{7}\)

\(=\left(-\dfrac{5}{5}+\dfrac{9}{9}\right)\cdot\dfrac{11}{7}=\left(-1+1\right)\cdot\dfrac{11}{7}=0\)

e: \(\dfrac{-3}{4}\cdot5\dfrac{3}{13}-0,75\cdot\dfrac{36}{13}\)

\(=\dfrac{-3}{4}\left(5+\dfrac{3}{13}+\dfrac{36}{13}\right)\)

\(=\dfrac{-3}{4}\cdot8=-6\)

f: \(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{302\cdot305}\)

\(=\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{302\cdot305}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{302}-\dfrac{1}{305}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{305}\right)=\dfrac{1}{3}\cdot\dfrac{12}{61}=\dfrac{4}{61}\)

g: \(6\dfrac{5}{12}:2\dfrac{3}{4}-11\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\)

\(=\dfrac{77}{12}:\dfrac{11}{4}-\dfrac{45}{4}\cdot\dfrac{2}{15}=\dfrac{77}{12}\cdot\dfrac{4}{11}-\dfrac{3}{2}\)

\(=\dfrac{7}{3}-\dfrac{3}{2}=\dfrac{14}{6}-\dfrac{9}{6}=\dfrac{5}{6}\)

h: \(\left(\dfrac{3}{5}+0,415-\dfrac{3}{200}\right)\cdot2\dfrac{2}{3}\cdot0,25\)

\(=\left(0,6+0,415-0,015\right)\cdot\dfrac{8}{3}\cdot\dfrac{1}{4}\)

\(=1\cdot\dfrac{2}{3}=\dfrac{2}{3}\)

i: \(\dfrac{5}{16}:0,125-\left(2\dfrac{1}{4}-0,6\right)\cdot\dfrac{10}{11}\)

\(=\dfrac{5}{16}:\dfrac{1}{8}-\left(\dfrac{9}{4}-\dfrac{3}{5}\right)\cdot\dfrac{10}{11}\)

\(=\dfrac{5}{2}-\left(\dfrac{45}{20}-\dfrac{12}{20}\right)\cdot\dfrac{10}{11}=\dfrac{5}{2}-\dfrac{33}{20}\cdot\dfrac{10}{11}=\dfrac{5}{2}-\dfrac{3}{2}=\dfrac{2}{2}=1\)

cam on nha

\(C=\left(6-\dfrac{2}{3}+\dfrac{5}{16}\right)-\left(2+\dfrac{4}{3}-\dfrac{7}{8}\right)-\left(6-\dfrac{5}{8}+\dfrac{13}{12}\right)\)

\(=6-\dfrac{2}{3}+\dfrac{5}{16}-2-\dfrac{4}{3}+\dfrac{7}{8}-6+\dfrac{5}{8}-\dfrac{13}{12}\)

\(=\left(6-2-6\right)+\left(-\dfrac{2}{3}-\dfrac{4}{3}\right)+\left(\dfrac{5}{16}+\dfrac{7}{8}+\dfrac{5}{8}\right)-\dfrac{13}{12}\)

\(=-2-2+\left(\dfrac{5}{16}+\dfrac{12}{8}\right)-\dfrac{13}{12}\)

\(=-4-\dfrac{13}{12}+\dfrac{29}{16}=-\dfrac{157}{48}\)

\(C=\left(6-\dfrac{2}{3}-\dfrac{5}{10}\right)-\left(2+\dfrac{4}{3}-\dfrac{7}{8}\right)-\left(6-\dfrac{5}{8}+\dfrac{13}{12}\right)\)

\(=6-\dfrac{2}{3}-\dfrac{5}{10}-2-\dfrac{4}{3}+\dfrac{7}{8}-6+\dfrac{5}{8}-\dfrac{13}{12}\)

\(=\left(6-2-6\right)+\left(-\dfrac{2}{3}-\dfrac{4}{3}\right)+\left(\dfrac{7}{8}+\dfrac{5}{8}\right)+\left(\dfrac{-5}{10}-\dfrac{13}{12}\right)\)

\(=\left(-2\right)+\left(-2\right)+\dfrac{3}{2}+\dfrac{-19}{12}\)
\(=\left(-4\right)+\dfrac{18}{12}+\dfrac{-19}{12}\)

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

\(=\dfrac{-48}{12}+\dfrac{-1}{12}\)

\(=\dfrac{-49}{12}\)

\(B=\left(5-\dfrac{3}{4}+\dfrac{1}{5}\right)-\left(6+\dfrac{7}{4}-\dfrac{8}{5}\right)-\left(2-\dfrac{5}{4}+\dfrac{16}{5}\right)\)

\(=5-\dfrac{3}{4}+\dfrac{1}{5}-6-\dfrac{7}{4}+\dfrac{8}{5}-2+\dfrac{5}{4}-\dfrac{16}{5}\)

\(=\left(5-6-2\right)+\left(-\dfrac{3}{4}-\dfrac{7}{4}+\dfrac{5}{4}\right)+\left(\dfrac{1}{5}+\dfrac{8}{5}-\dfrac{16}{5}\right)\)

\(=-3+\dfrac{-5}{4}+\dfrac{-7}{5}=-3-1,25-1,4=-5,65\)

Olm chào em, em chưa hiểu chỗ nào em nhỉ?

a) \(\dfrac{-3}{100}>\dfrac{-50}{100}=-\dfrac{1}{2}\)

\(\dfrac{-2}{3}< \dfrac{-1,5}{3}=-\dfrac{1}{2}\)

\(\Rightarrow\dfrac{-3}{100}>\dfrac{-2}{3}\)

b) \(\dfrac{-3}{5}=\dfrac{-9}{15}\)

\(\dfrac{-2}{3}=\dfrac{-10}{15}\)

Mà:  - 9 > -10 

\(\Rightarrow-\dfrac{9}{15}>\dfrac{-10}{15}\)

hay `-3/5>-2/3` 

c) \(\dfrac{-5}{4}< \dfrac{-2}{4}=-\dfrac{1}{2}\)

\(-\dfrac{3}{8}>\dfrac{-4}{8}=-\dfrac{1}{2}\)

\(\Rightarrow-\dfrac{5}{4}< \dfrac{-3}{8}\) 

d) \(-\dfrac{2}{3}=\dfrac{1}{3}-1\)

\(-\dfrac{3}{4}=\dfrac{1}{4}-1\)

Vì: `1/3>1/4` 

`=>1/3-1>1/4-1` 

Hay `-2/3>-3/4` 

a: \(\dfrac{-3}{100}=\dfrac{-3\cdot3}{100\cdot3}=\dfrac{-9}{300};\dfrac{2}{-3}=\dfrac{-2}{3}=\dfrac{-2\cdot100}{3\cdot100}=\dfrac{-200}{300}\)

mà -9>-200

nên \(\dfrac{-3}{100}>\dfrac{-2}{3}\)

b: \(\dfrac{-3}{5}=\dfrac{-3\cdot3}{5\cdot3}=\dfrac{-9}{15};\dfrac{2}{-3}=\dfrac{-2}{3}=\dfrac{-2\cdot5}{3\cdot5}=\dfrac{-10}{15}\)

mà -9>-10

nên \(\dfrac{-3}{5}>\dfrac{2}{-3}\)

c: \(\dfrac{-5}{4}=\dfrac{-5\cdot2}{4\cdot2}=\dfrac{-10}{8};\dfrac{-3}{8}=\dfrac{-3}{8}\)

mà -10<-3

nên \(-\dfrac{5}{4}< -\dfrac{3}{8}\)

d: \(\dfrac{-2}{3}=\dfrac{-2\cdot4}{3\cdot4}=\dfrac{-8}{12};\dfrac{3}{-4}=\dfrac{-3}{4}=\dfrac{-3\cdot3}{4\cdot3}=\dfrac{-9}{12}\)

mà -8>-9

nên \(-\dfrac{2}{3}>\dfrac{3}{-4}\)

e: \(\dfrac{267}{-268}=\dfrac{-267}{268}>-1;-1=\dfrac{-1343}{1343}>\dfrac{-1347}{1343}\)

Do đó: \(\dfrac{267}{-268}>\dfrac{-1347}{1343}\)

f: \(\dfrac{2022\cdot2023-1}{2022\cdot2023}=1-\dfrac{1}{2022\cdot2023}\)

\(\dfrac{2023\cdot2024-1}{2023\cdot2024}=1-\dfrac{1}{2023\cdot2024}\)

Ta có: 2022<2024

=>\(2022\cdot2023< 2023\cdot2024\)

=>\(\dfrac{1}{2022\cdot2023}>\dfrac{1}{2023\cdot2024}\)

=>\(-\dfrac{1}{2022\cdot2023}< -\dfrac{1}{2023\cdot2024}\)

=>\(\dfrac{-1}{2022\cdot2023}+1< \dfrac{-1}{2023\cdot2024}+1\)

=>\(\dfrac{2022\cdot2023-1}{2022\cdot2023}< \dfrac{2023\cdot2024-1}{2023\cdot2024}\)

g: \(\dfrac{2022\cdot2023}{2022\cdot2023+1}=1-\dfrac{1}{2022\cdot2023+1}\)

\(\dfrac{2023\cdot2024}{2023\cdot2024+1}=1-\dfrac{1}{2023\cdot2024+1}\)

Vì \(2022\cdot2023+1< 2023\cdot2024+1\)

nên \(\dfrac{1}{2022\cdot2023+1}>\dfrac{1}{2023\cdot2024+1}\)

=>\(\dfrac{-1}{2022\cdot2023+1}< \dfrac{-1}{2023\cdot2024+1}\)

=>\(\dfrac{-1}{2022\cdot2023+1}+1< \dfrac{-1}{2023\cdot2024}+1\)

=>\(\dfrac{2022\cdot2023}{2022\cdot2023+1}< \dfrac{2023\cdot2024}{2023\cdot2024+1}\)

\(\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{12}+\dfrac{1}{35}\\ =\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{7}{45}+\dfrac{5}{9}+\dfrac{1}{12}+\dfrac{1}{35}\\ =\left(\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{1}{12}\right)+\left(\dfrac{3}{5}+\dfrac{5}{9}-\dfrac{7}{45}\right)+\dfrac{1}{35}\\ =\left(\dfrac{8}{12}+\dfrac{3}{12}+\dfrac{1}{12}\right)+\left(\dfrac{27}{45}+\dfrac{25}{45}-\dfrac{7}{45}\right)+\dfrac{1}{35}\\ =\dfrac{12}{12}+\dfrac{45}{45}+\dfrac{1}{35}\\ =1+1+\dfrac{1}{35}\\ =2+\dfrac{1}{35}\\ =\dfrac{70}{35}+\dfrac{1}{35}=\dfrac{71}{35}\)

\(\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{12}+\dfrac{1}{35}\)

\(=\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{7}{45}+\dfrac{5}{9}+\dfrac{1}{12}+\dfrac{1}{35}\)

\(=\left(\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{1}{12}\right)+\left(\dfrac{3}{5}+\dfrac{1}{35}\right)+\left(-\dfrac{7}{45}+\dfrac{5}{9}\right)\)

\(=\left(\dfrac{8}{12}+\dfrac{3}{12}+\dfrac{1}{12}\right)+\left(\dfrac{21}{35}+\dfrac{1}{35}\right)+\left(-\dfrac{7}{45}+\dfrac{25}{45}\right)\)

\(=1+\dfrac{22}{35}+\dfrac{18}{45}\)

\(=\dfrac{315}{315}+\dfrac{198}{315}+\dfrac{126}{315}\)

\(=\dfrac{71}{35}\)