Bài 4: Cộng hai số nguyên cùng dấu

135

5:

a: \(\dfrac{\dfrac{11}{3}+\dfrac{11}{37}-\dfrac{11}{111}}{\dfrac{12}{3}+\dfrac{12}{37}-\dfrac{12}{111}}\)

\(=\dfrac{11\left(\dfrac{1}{3}+\dfrac{1}{37}-\dfrac{1}{111}\right)}{12\left(\dfrac{1}{3}+\dfrac{1}{37}-\dfrac{1}{111}\right)}\)

\(=\dfrac{11}{12}\)

b: \(\dfrac{\dfrac{3}{2}+1-\dfrac{3}{591}}{2+\dfrac{4}{3}-\dfrac{4}{591}}\)

\(=\dfrac{\dfrac{3}{2}+\dfrac{3}{3}-\dfrac{3}{591}}{\dfrac{4}{2}+\dfrac{4}{3}-\dfrac{4}{591}}\)

\(=\dfrac{3\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{591}\right)}{4\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{591}\right)}=\dfrac{3}{4}\)

7:

a: \(\dfrac{17}{1\cdot2}+\dfrac{17}{2\cdot3}+...+\dfrac{17}{50\cdot51}=\dfrac{x+1}{3}\)

=>\(\dfrac{x+1}{3}=17\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{50\cdot51}\right)\)

=>\(x+1=51\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{50}-\dfrac{1}{51}\right)\)

=>\(x+1=51\cdot\dfrac{50}{51}=50\)

=>x=50-1=49

b: \(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{97\cdot99}=\dfrac{49}{x+9}\)

=>\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{97\cdot99}=\dfrac{98}{x+9}\)

=>\(\dfrac{98}{x+9}=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}=1-\dfrac{1}{99}=\dfrac{98}{99}\)

=>x+9=99

=>x=90

`a, 8x=64`

`=>x= 64:8`

`=> x=8`

`b, (-5)x=25`

`=>x=25:(-5)`

`=>x=-5`

`c,4x+1=21`

`=>4x=21-1`

`=>4x=20`

`=>x=20:4`

`=>x=5`

`d, (-3)x-1=8`

`=>(-3)x=8+1`

`=>(-3)x=9`

`=>x=9:(-3)`

`=>x=(-3)`

a: \(\left(-11\right)\cdot\left(-28\right)+\left(-9\right)\cdot13\)

\(=308-117\)

=191

b: \(\left(-69\right)\cdot\left(-31\right)-\left(-15\right)\cdot12\)

\(=2139-\left(-180\right)\)

=2139+180

=2319

c: \(\left[16-\left(-5\right)\right]\cdot\left(-7\right)\)

\(=\left(16+5\right)\cdot\left(-7\right)\)

\(=-7\cdot21=-147\)

d: \(\left[\left(-4\right)\cdot\left(-9\right)-6\right]\left[\left(-12\right)-\left(-7\right)\right]\)

\(=\left[36-6\right]\left[-12+7\right]\)

\(=30\cdot\left(-5\right)=-150\)

a: \(\dfrac{-35}{-7}=\dfrac{35}{7}=5\)

b: \(\dfrac{42}{-21}=-\dfrac{42}{21}=-2\)

c: \(\dfrac{55}{-5}=-\dfrac{55}{5}=-11\)

d: \(\dfrac{46}{-23}=-\dfrac{46}{23}=-2\)

e: \(-30:\left(-2\right)=\dfrac{30}{2}=15\)

f: \(23\cdot\left(-4\right)=-23\cdot4=-92\)

g: \(15\cdot\left(-3\right)\cdot0=15\cdot0=0\)

h: \(-32\cdot14=-32\cdot10-32\cdot4=-320-128=-448\)

a: \(\left(-5\right)\cdot4=-5\cdot4=-20\)

b: \(6\cdot\left(-7\right)=-6\cdot7=-42\)

c: \(\left(-14\right)\cdot20=-14\cdot20=-280\)

d: \(51\cdot\left(-10\right)=-51\cdot10=-510\)

a) \(15+\left(-24\right)\)

\(=15-24\)

\(=-9\)

b) \(\left(-135\right)-\left(-35\right)\)

\(=-135+35\)

\(=-100\)

c) \(3-\left(-15\right)\)

\(=3+15\)

\(=18\)

d) \(\left(45-3756\right)+3756\)

\(=45-3756+3756\)

\(=45\)

e) \(-2023-\left(2022-2023\right)\)

\(=-2023-2022+2023\)

\(=-2022\)

f) \(\left(-17\right)+\left(-23\right)\)

\(=-17-23\)

\(=-40\)

g) \(38-50\)

\(=-12\)

h) \(-6-15\)

\(=-21\)

k) \(-75-\left(-80\right)\)

\(=-75+80\)

\(=5\)

4/5=0,8

7/10=0,7

23/25=0,92

=>0,7<0,8<0,92

=>Bóng đá là môn được yêu thích nhất

Trong 1h vòi chảy được 1/3(bể)

Trong 1,25h vòi chảy được 1,25/3=5/12(bể)

\(\left(-24\right).x=-120\)

\(x=\left(-120\right):\left(-24\right)\)

\(x=5\)