46.37 + 93.46 + 54.61 + 69.54

= 46.(37+93) + 54.(61+69)

= 46. 130 + 54.130

= 130.(46+54)

= 130.100 = 13 000

46 . 37 + 93 . 46 + 54 . 61 + 69 . 54

= 46 . (37+ 93) + 54 . (61 + 69)

= 46 . 130 + 54 . 130

= (46 + 54) . 130

= 100 . 130

= 13000

   46 . 37 + 93.46+54.61 + 69 . 54

= 46 . (37 + 93) + 54 . ( 61 + 69)

= 46 . 130 + 54 . 130

= ( 46 + 54) . 130

= 100 .130

=13000

Hình vẽ :  

Giải : a) Vì  M nằm giữa A và B(AM < AB) nên AM + MB = AB

=> BM = AB - AM = 12 - 6 = 6 (cm)

b) N là trung điểm của BM => BN = NM = BM/2 = 6/2 = 3 (cm)

Vì M nằm giữa A và N nên AM + NM = AN

=> AN = 6 + 3 = 9 (cm)

6. Ta có : 3n + 13 = 3(n + 2) + 4

Do n + 2 \(⋮\)n + 2 => 3(n + 2) \(⋮\)n + 2

Để 3n + 13 \(⋮\)n + 2 thì 4 \(⋮\)n + 2 => n + 2 \(\in\)Ư(4) = {1; 2; 4}

Lập bảng : 

Vì n là số tự nhiên => n = 0 hoặc 2 thì 3n + 13 \(⋮\)n + 2

\(A=\left\{-3;-2;-1;0;1;2;3;4\right\}\)

\(3n+13⋮n+2\)

\(\Rightarrow3n+6+7⋮n+2\)

\(\Rightarrow n+2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

lập bảng nha

31: (-29)+8-9

\(=\left(-29\right)+\left(8-9\right)\)

\(=-29-1=-30\)

32: \(\left(-14\right)-6-10\)

\(=\left(-14-6\right)-10\)

=-20-10

=-30

33: \(\left(-42\right)+10+2\)

\(=\left(-42\right)+\left(10+2\right)\)

=-42+12

=-30

34: \(\left(-45\right)+25-20\)

\(=\left(-45\right)+\left(25-20\right)\)

=-45+5

=-40

35: \(\left(-60\right)+17+3\)

\(=\left(-60\right)+\left(17+3\right)\)

=-60+20

=-40

36: \(\left(-48\right)+18-10\)

\(=\left(-48+18\right)-10\)

=-30-10

=-40

câu d) 

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

câu e)

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

câu f)

\(\dfrac{8}{3}-\left(-\dfrac{4}{3}+3\right)\\ =\dfrac{8}{3}+\dfrac{4}{3}-3\\ =4-3=1\)

Lời giải:
g.

$=\frac{-5}{11}+\frac{-6}{11}+1=(\frac{-5}{11}+\frac{-6}{11})+1$

$=\frac{-11}{11}+1=(-1)+1=0$

h.

$=\frac{-17}{13}+\frac{4}{13}+\frac{25}{101}$

$=\frac{-13}{13}+\frac{25}{101}=(-1)+\frac{25}{101}=-(1-\frac{25}{101})$

$=\frac{-76}{101}$

i.

$=\frac{6}{7}+\frac{1}{8}-\frac{3}{16}.4=\frac{6}{7}+\frac{1}{8}-\frac{3}{4}$

$=\frac{6}{7}+\frac{1}{8}-\frac{6}{8}=\frac{6}{7}+\frac{-5}{8}$
$=\frac{13}{56}$

CÂU A)

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

CÂI B)

\(-\dfrac{7}{31}+\left(\dfrac{24}{17}+\dfrac{7}{31}\right)\\ =-\dfrac{7}{31}+\dfrac{24}{17}+\dfrac{7}{31}=\dfrac{24}{17}\)

CÂU C)

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

k.

$=\frac{-5}{7}(\frac{2}{11}+\frac{9}{11})+\frac{12}{7}$

$=\frac{-5}{7}.\frac{11}{11}+\frac{12}{7}$

$=\frac{-5}{7}+\frac{12}{7}=\frac{7}{7}=1$

l.

$=(\frac{1}{5}+\frac{4}{5})+(\frac{-2}{9}+\frac{-7}{9})+\frac{16}{17}$

$=\frac{5}{5}+\frac{-9}{9}+\frac{16}{17}$

$=1+(-1)+\frac{16}{17}=\frac{16}{17}$

a.

$=(\frac{-17}{13}+\frac{4}{13})+(\frac{11}{31}+\frac{20}{31})+\frac{2}{135}$

$=\frac{-13}{13}+\frac{31}{31}+\frac{2}{135}=(-1)+1+\frac{2}{135}=\frac{2}{135}$

b.

$=(\frac{3}{17}+\frac{20}{-17})+(\frac{4}{18}+\frac{-2}{9})+(\frac{5}{8}+\frac{21}{56})$

$=(\frac{3}{17}+\frac{-20}{17})+(\frac{2}{9}+\frac{-2}{9})+(\frac{5}{8}+\frac{3}{8})$

$=\frac{-17}{17}+\frac{0}{9}+\frac{8}{8}$

$=(-1)+0+1=0$

c.

$=\frac{-5}{12}+\frac{6}{11}+\frac{7}{17}+\frac{5}{11}+\frac{5}{12}$

$=(\frac{-5}{12}+\frac{5}{12})+(\frac{6}{11}+\frac{5}{11})+\frac{7}{17}$

$=\frac{0}{12}+\frac{11}{11}+\frac{7}{17}$

$=0+1+\frac{7}{17}=\frac{24}{17}$

d.

$=\frac{9}{16}+\frac{-8}{27}+1+\frac{7}{16}+\frac{-19}{27}$

$=(\frac{9}{16}+\frac{7}{16})+1+(\frac{-8}{27}+\frac{-19}{27})$

$=\frac{16}{16}+1+\frac{-27}{27}$

$=1+1+(-1)=1$