Đáp án:

Giải thích các bước giải:

 BÀI TẬP 1:

Câu 1:

`(1)/(3)+0,25+(3)/(-4)`

`=(1)/(3)+((1)/(4)+(-3)/(4))`

`=(1)/(3)+(-1)/(2)`

`=(2-3)/(3*2)`

`=(-1)/(6)`

Câu 2:

`1 (2)/(3)+1 (3)/(5)-2`

`=(1+1)-2+((2)/(3)+(3)/(5))`

`=2-2+(10+9)/(3*5)`

`=(19)/(15)`

Câu 3:

`(-2)/(3)+(3)/(8)-(1)/(6)`

`=(-16+9-4)/(3*2*4)`

`=(-11)/(24)`

Câu 4: 

`(1)/(2)-(-1)/(3)-(1)/(10)+(1)/(5)`

`=((1)/(2)+(1)/(5)-(1)/(10))+(1)/(3)`

`=(5+2-1)/(2*5)+(1)/(3)`

`=(6)/(2*5)+(1)/(3)`

`=(3)/(5)+(1)/(3)`

`=(9+5)/(5*3)`

`=(14)/(15)`

Câu 5:

`(1)/(4)+(3)/(4):(-6)/(7)`

`=(1)/(4)+(3)/(4)*(-7)/(6)`

`=(1)/(4)+(-7)/(4*2)`

`=(2-7)/(4*2)`

`=(-5)/(8)`

Câu 6:

`3-1 (4)/(5):(-3)/(4)`

`=3-(9)/(5)*(-4)/(3)`

`=3-(3*(-4))/(5)`

`=3-(-12)/(5)`

`=(15+12)/(5)`

`=(27)/(5)`

Câu 7:

`((1)/(5)-0,4)*(3-1 (4)/(5))`

`=((1)/(5)-(2)/(5))*(3-(9)/(5))`

`=(-1)/(5)*(6)/(5)`

`=(-6)/(25)`

Câu 8:

`(3)/(5)*17 (1)/(3)-32 (1)/(3)*(3)/(5)`

`=(3)/(5)*(17 (1)/(3) - 32 (1)/(3))`

`=(3)/(5)*((17-32)+((1)/(3)-(1)/(3)))`

`=(3)/(5)*(-15)`

`=3*(-3)`

`=-9`

Câu 9:

`(7)/(21)+(8)/(21):(5)/(6)-(15)/(9)`

`=((7)/(21)-(15)/(9)+(8)/(21)*(6)/(5))`

`=(21-105)/(3*3*7)+(48)/(21*5)`

`=(-84*5)/(3*3*7*5)+(48*3)/(3*7*5*3)`

`=((-84*5)+(48*3))/(3*3*7*5)`

`=(-420+144)/(3*3*5*7)`

`=(-276)/(3*3*5*7)`

`=(-46)/(5*7)`

`=(-46)/(35)`

Câu 10:

`((4)/(9)-(3)/(5)):(6)/(5)+((5)/(9)-(2)/(5))`

`=(20-27)/(9*5)*(5)/(6)+(25-18)/(9*5)`

`=(-7)/(9)*(1)/(6)+(7)/(9*5)`

`=(-7)/(9*6)+(7)/(9*5)`

`=(-7*5)/(9*6*5)+(7*6)/(9*5*6)`

`=(7*6-7*5)/(9*6*5)`

`=(7)/(9*6*5)`

`=(7)/(270)`

...

Giải thích các bước giải:

Bài 1: 

1,  $\frac{1}{3}$ + 0,25 + $\frac{3}{-4}$ 

= $\frac{1}{3}$ +$\frac{1}{4}$ +($\frac{-3}{4}$ )

= $\frac{1}{3}$ + ($\frac{-1}{2}$ )

= $\frac{-1}{6}$ 

2, 1$\frac{2}{3}$ + 1$\frac{3}{5}$ - 2

= $\frac{5}{3}$ + $\frac{8}{5}$ - 2

= $\frac{49}{15}$ - 2

= $\frac{19}{15}$ 

3,  $\frac{-2}{3}$ +$\frac{3}{8}$ -$\frac{1}{6}$ 

= $\frac{-7}{24}$ -$\frac{1}{6}$

= $\frac{-11}{24}$ 

4,  $\frac{1}{2}$ -$\frac{-1}{3}$ -$\frac{1}{10}$ + $\frac{1}{5}$ 

= $\frac{5}{6}$ -$\frac{1}{10}$ +$\frac{1}{5}$ 

= $\frac{11}{15}$ +$\frac{1}{5}$

= $\frac{14}{15}$ 

5,  $\frac{1}{4}$ +$\frac{3}{4}$ : $\frac{-6}{7}$ 

= $\frac{1}{4}$ + $\frac{-7}{8}$

= $\frac{-5}{8}$ 

6,  3 -1$\frac{4}{5}$ : $\frac{-3}{4}$ 

= 3 - $\frac{9}{5}$ : $\frac{-3}{4}$ 

= 3 - ($\frac{-12}{5}$ )

= $\frac{27}{5}$ 

7,  ($\frac{1}{5}$ -0,4) .(3-1$\frac{4}{5}$ )

= ($\frac{1}{5}$ -$\frac{2}{5}$) .( 3 - $\frac{9}{5}$ )

= $\frac{-1}{5}$ .$\frac{6}{5}$ 

= $\frac{-6}{25}$ 

8, $\frac{7}{21}$ + $\frac{8}{21}$ : $\frac{5}{6}$ -$\frac{15}{9}$ 

= $\frac{7}{21}$ + $\frac{16}{35}$ - $\frac{-15}{9}$ 

= $\frac{-92}{105}$ 

10,  ($\frac{4}{9}$ -$\frac{3}{5}$) :$\frac{6}{5}$ +($\frac{5}{9}$ -$\frac{2}{5}$ )

= $\frac{-7}{45}$ :$\frac{6}{5}$ +$\frac{7}{45}$ 

= $\frac{7}{270}$ 

11,  ( $\frac{-13}{10}$ ) : $\frac{3}{5}$ + |$\frac{-2}{5}$ | .$\frac{5}{4}$ 

= $\frac{-13}{6}$ +$\frac{2}{5}$ .$\frac{5}{4}$ 

= $\frac{-13}{6}$ +$\frac{1}{2}$ 

= $\frac{-5}{3}$ 

12,  (0,5-$\frac{3}{4}$ ).($\frac{-1}{2}$ )²

= ($\frac{1}{2}$ -$\frac{3}{4}$ ). $\frac{1}{4}$ 

= $\frac{-1}{4}$ . $\frac{1}{4}$ 

= $\frac{-1}{16}$ 

13,  1$\frac{5}{3}$ .$\frac{2}{7}$ +$\frac{8}{3}$ .$\frac{5}{7}$ -$\frac{2}{3}$ 

= $\frac{8}{3}$ .$\frac{2}{7}$ +$\frac{8}{3}$ .$\frac{5}{7}$ -$\frac{2}{3}$ 

= $\frac{8}{3}$ .($\frac{2}{7}$ +$\frac{5}{7}$ ) -$\frac{2}{3}$ 

= $\frac{8}{3}$ -$\frac{2}{3}$ 

= 2

15, 7$\frac{1}{3}$ .2 $\frac{1}{11}$- 7 $\frac{1}{3}$ .1$\frac{9}{11}$ -$\frac{3}{2}$ 

= $\frac{22}{3}$ . $\frac{23}{11}$ -$\frac{22}{3}$ -$\frac{20}{11}$ -$\frac{3}{2}$ 

= $\frac{22}{3}$ .($\frac{23}{11}$ - $\frac{20}{11}$ ) -$\frac{3}{2}$ 

= $\frac{22}{3}$ .$\frac{3}{11}$ -$\frac{3}{2}$ 

= 2-$\frac{3}{2}$ 

= $\frac{1}{2}$ 

16,  $\frac{2}{5}$ -$\frac{-1}{2}$ +$\frac{3}{-5}$ - $3^{2}$ /20 

= $\frac{2}{5}$ -$\frac{-1}{2}$ +$\frac{-3}{5}$ -$\frac{9}{20}$ 

= $\frac{9}{10}$ +$\frac{-21}{20}$ 

= $\frac{-3}{20}$ 

Bài 2;

a,x+ $\frac{5}{6}$ =$\frac{1}{3}$ 

⇔ x= $\frac{1}{3}$ -$\frac{5}{6}$ 

⇔ x =$\frac{-1}{2}$ 

Vậy x = $\frac{-1}{2}$ 

b,  $\frac{-2}{15}$ - x = $\frac{-3}{4}$ 

⇔ x= $\frac{-2}{15}$ - $\frac{-3}{4}$ 

⇔  x= $\frac{37}{60}$ 

Vậy x = $\frac{37}{60}$ 

c,  $\frac{-5}{4}$ - x = 0,25

⇔ x= $\frac{-5}{4}$ -0,25

⇔ x= $\frac{-3}{2}$ 

Vậy x = $\frac{-3}{2}$ 

d,  $\frac{1}{2}$ x -$\frac{1}{3}$ =$\frac{5}{6}$ 

⇔ $\frac{1}{2}$ x =$\frac{5}{6}$ +$\frac{1}{3}$ 

⇔ $\frac{1}{2 }$ x = $\frac{7}{6}$ 

⇔ x = $\frac{7}{6}$ :$\frac{1}{2}$ 

⇔ x= $\frac{7}{3}$ 

Vậy x = $\frac{7}{3}$ 

$\frac{1}{7}$ +$\frac{6}{7}$ x = $\frac{-3}{2}$

⇔ $\frac{6}{7}$ x= $\frac{-3}{2}$ -$\frac{1}{2}$ 

⇔ $\frac{6}{7}$ x= -2

⇔ x = -2 :$\frac{6}{7}$ 

⇔ x= $\frac{-7}{3}$ 

Vậy x = $\frac{-7}{3}$ 

$\frac{18}{5}$ -$\frac{5}{4}$ x =$\frac{1}{-6}$

⇒ $\frac{18}{5}$ -$\frac{5}{4}$ x = $\frac{-1}{6}$ 

⇔ $\frac{5}{4}$ x = $\frac{18}{5}$ -$\frac{-1}{6}$ 

⇔ $\frac{5}{4}$ x = $\frac{113}{30}$ 

⇔ x= $\frac{113}{30}$ : $\frac{5}{4}$ 

⇔ x= $\frac{226}{75}$ 

Vậy x = $\frac{226}{75}$ 

$\frac{4}{3}$ -x :$\frac{16}{7}$ -$\frac{1}{8}$ =$\frac{1}{3}$

⇔ $\frac{4}{3}$ - x :$\frac{16}{7}$ = $\frac{11}{24}$ 

⇔ $\frac{4}{3}$ -x = $\frac{22}{21}$ 

⇔ x= $\frac{2}{7}$ 

Vậy x = $\frac{2}{7}$ 

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