a) Ta có: \(1+\left(-2\right)+3+\left(-4\right)+...+2021\)

\(=\left(1-2\right)+\left(3-4\right)+...+\left(2019-2020\right)+2021\)

\(=\left(-1\right)+\left(-1\right)+...+\left(-1\right)+2021\)

\(=-1010+2021=1011\)

1+(-2)+3+(-4)+....+2021

=(1+3+5+.....+2021)-(2+4+6+....+2020)

=\(\dfrac{\left(1+2021\right)\cdot2021}{2}-\dfrac{\left(2+2020\right)\cdot2020}{2}=1010\cdot2021-1010\cdot2020\\ =1010\cdot\left(2021-2020\right)=1010\cdot1\\ =1010\)

1 + (-2) + 3 + (-4) +......+ 2021

= ( 1 - 2 ) + ( 3 - 4 ) +....+ ( 2019 - 2020 ) + 2021

= (-1) + (-1) +.....+ (-1) + 2021

Từ 1 đến 2020 có số số hạng là : 

( 2020 - 1 ) : 1 + 1 = 2020 ( số hạng ) 

⇒ 1 + 2021 = 2022

8507cm2

32m^2 217dm^2=320217

3/5 giờ 12 phút = 48 phút

\(\dfrac{3}{7}.\left(\dfrac{5-1}{4}\right)=\dfrac{3}{7}.1=\dfrac{3}{7}\)

\(\dfrac{11}{10}-\dfrac{6}{10}=\dfrac{5}{10}=\dfrac{1}{2}\)

a)

= 15/28 - 1/4

= 2/7

b)

= 7/10 : 2/3

= 21/20

85m2 7cm2= 850007    cm2

32m217dm2=  3217  dm2

3/5 giờ 12=  48 phút

Tính

a.3/7x5/4-1/4

= 15/28 - 1/4

- 2/7 

b.11/10-2/5:2/3

= 11/10 - 3/5

= 1/2

a: =20/60+12/60-15/60=17/60

b: =7/8-1/4-2/5=5/8-2/5=25/40-16/40=9/40

\(a,\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{4}=\dfrac{20}{60}+\dfrac{12}{60}-\dfrac{15}{60}=\dfrac{17}{60}\\ b,\dfrac{7}{8}-\left(\dfrac{1}{4}+\dfrac{2}{5}\right)=\dfrac{7}{8}-\dfrac{13}{20}=\dfrac{9}{40}\)

\(a,\dfrac{1}{3}-\left(-1\dfrac{2}{5}\right)+\left(-3\dfrac{1}{4}\right)\\ =\dfrac{1}{3}-\left(-\dfrac{7}{5}\right)-\dfrac{13}{4}\\ =\dfrac{1}{3}+\dfrac{7}{5}-\dfrac{13}{4}\\ =\dfrac{20}{3\times20}+\dfrac{7\times12}{5\times12}-\dfrac{13\times15}{4\times15}\\ =\dfrac{20+84-195}{60}\\ =\dfrac{-91}{60}\)

\(b,\dfrac{5}{4}-\left(-3\dfrac{1}{2}\right)-\dfrac{7}{10}\\ =\dfrac{5}{4}+\dfrac{7}{2}-\dfrac{7}{10}\\ =\dfrac{5\times5}{4\times5}+\dfrac{7\times10}{2\times10}-\dfrac{7\times2}{10\times2}\\ =\dfrac{25+70-14}{20}\\ =\dfrac{81}{20}\)

\(c,\dfrac{3}{2}-\left[\left(-\dfrac{4}{7}-\left(\dfrac{1}{2}+\dfrac{5}{8}\right)\right)\right]\\ =\dfrac{3}{2}-\left[-\dfrac{4}{7}-\left(\dfrac{4}{8}+\dfrac{5}{8}\right)\right]\\ =\dfrac{3}{2}-\left(-\dfrac{4}{7}-\dfrac{9}{8}\right)\\ =\dfrac{3}{2}+\dfrac{4}{7}+\dfrac{9}{8}\\ =\dfrac{3\times28}{2\times28}+\dfrac{4\times8}{8\times7}+\dfrac{9\times7}{8\times7}\\ =\dfrac{84+32+63}{56}\\ =\dfrac{179}{56}\)

`@` `\text {Ans}`

`\downarrow`

`a,`

\(\dfrac{1}{3}-\left(-1\dfrac{2}{5}\right)+\left(-3\dfrac{1}{4}\right)\)

`= 1/3+7/5 - 13/4`

`= 26/15 - 13/4`

`= -91/60`

`b,`

\(\dfrac{5}{4}-\left(-3\dfrac{1}{2}\right)-\dfrac{7}{10}\)

`= 5/4+7/2 - 7/10`

`= 1,25 + 3,5 - 0,7`

`= 4,75 - 0,7`

`= 4,05`

`c,`

\(\dfrac{3}{2}-\left[\left(-\dfrac{4}{7}\right)-\left(\dfrac{1}{2}+\dfrac{5}{8}\right)\right]\)

`= 3/2 - [(-4/7) - 9/8]`

`= 3/2 - (-95/56)`

`= 179/56`

a, \(1+\dfrac{3}{4}=\dfrac{7}{4}\)

b, \(\dfrac{4}{5}-\dfrac{3}{8}=\dfrac{32-15}{40}=\dfrac{17}{40}\)

c, \(1:\dfrac{2}{3}=\dfrac{1.3}{2}=\dfrac{3}{2}\)

d, \(\dfrac{2}{5}.\dfrac{5}{2}=1\)

a)1 + 3/4=7/4

   b)4/5 -3/8=17/40

  c)1 : 2/3=3/2

  d)2/5 x 5/2=1

Đáp án:

a)1 + 3/4=7/4

b)4/5 -3/8=17/40

c)1 : 2/3=3/2

d)2/5 x 5/2=1

`1`

`a, 1/2 +1/3= 3/6 + 2/6 =5/6`

`d, 1/3 +3/5= 5/15 + 9/15=14/15`

`c,4/5 +1/2= 8/10 + 5/10= 13/10`

`2`

`a,1/2 +1/4=2/4 +1/4=3/4`

`b, 2/3 +1/6 = 4/6+1/6=5/6`

`c, 7/12 +1/2=7/12+ 6/12= 13/12`

`3`

Giải

Cả `2` ngày đi tất cả số quãng đường là :

`1/4 +1/2 =1/4+ 2/4= 3/4 ( quãng đường)`

đ/s...

`@ yL`

`@` `\text {Ans}`

`\downarrow`

`1,`

`a)`

`-7/25 + (-8)/25`

`= (-7 - 8)/25`

`= -15/25`

`= -3/5`

`b)`

`6/13 + (-15)/39`

`= 18/39 + (-15)/39`

`= (18 - 15)/39`

`= 3/39`

`= 1/13`

`c)`

`5/7 + 4/(-14)`

`= 10/14 + (-4)/14`

`= (10 - 4)/14`

`= 6/14`

`= 3/7`

`d)`

`-8/18 + (-15)/27`

`= -4/9 + (-5)/9`

`= (-4-5)/9`

`= -9/9 = -1`

`2,`

`a)`

`3/5 + (-7)/4`

`= 12/20 + (-35)/20`

`= (12 - 35)/20`

`=-23/20`

`b)`

`(-2) + (-5)/8`

`= (-16)/8 + (-5)/8`

`= (-16 - 5)/8`

`= -21/8`

`c)`

`1/8 + (-5)/9`

`= 9/72 + (-40)/72`

`= (9-40)/72`

`= -31/72`

`d)`

`6/13 + (-14)/39`

`= 18/39 + (-14)/39`

`= (18 - 14)/39`

`= 4/39`

`e)`

`(-18)/24 + 15/21`

`= (-3)/4 + 5/7`

`= (-21)/28 + 20/28`

`= (-21 + 20)/28`

`= -1/28`

a) 3/4+1/12 =5/6

b)11/4-6/7=53/28

c)2/9x8=16/9

d)8/21:4/7=2/3

a) 3/4+1/12 = 9/12 + 1/12= 10/12= 5/6

b)11/4-6/7 = 77/28 - 24/28 = 53/28

c)2/9x8= 16/9

d)8/21:4/7 = 8/21 x 7/4 = 2/3

a)5/6

b)53/28

c)16/9

d)2/3

\(\left(\dfrac{1}{6}+4\right)\times\dfrac{3}{10}=\left(\dfrac{1}{6}+\dfrac{24}{6}\right)=\dfrac{25}{6}\times\dfrac{3}{10}=\dfrac{5}{4}\)

\(\left(\dfrac{1}{8}-\dfrac{1}{9}\right)\times\dfrac{3}{2}=\left(\dfrac{9}{72}-\dfrac{8}{72}\right)\times\dfrac{3}{2}=\dfrac{1}{72}\times\dfrac{3}{2}=\dfrac{1}{48}\)

a) = 25/6 x 3/10

= 5/4

b) = 1/72 x 3/2 

= 1/48