3a) 

\(\left(\dfrac{105}{31}-\dfrac{31}{202}+\dfrac{104}{91}\right)\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\\ =\left(\dfrac{105}{31}-\dfrac{31}{202}+\dfrac{104}{91}\right)\cdot\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)\\ =\left(\dfrac{105}{31}-\dfrac{31}{202}+\dfrac{104}{91}\right)\cdot0=0\)

\(b.\left(\dfrac{2022}{71}-\dfrac{371}{20}+\dfrac{10}{93}\right)\cdot\left(\dfrac{1}{4}-\dfrac{1}{5}-\dfrac{1}{20}\right)\\ =\left(\dfrac{2022}{71}-\dfrac{371}{20}+\dfrac{10}{93}\right)\cdot\left(\dfrac{5}{20}-\dfrac{4}{20}-\dfrac{1}{20}\right)\\ =\left(\dfrac{2022}{71}-\dfrac{371}{20}+\dfrac{10}{93}\right)\cdot0=0\)

Câu `3`

`a, (105/31 - 31/202 + 104/91)(1/2 - 1/3 - 1/6)`

`= (105/31 - 31/202 + 104/91)(3/6 - 2/6 - 1/6)`

`= (105/31 - 31/202 + 104/91) . 0`

`= 0`

`b, (2022/71 - 371/20 + 10/93)(1/4 - 1/5 - 1/20)`

`= (2022/71 - 371/20 + 10/93)(5/20- 4/20 - 1/20)`

`= (2022/71 - 371/20 + 10/93) . 0`

`=0`

bài 4

\(a.\dfrac{6}{7}\cdot\left(\dfrac{2}{5}-\dfrac{6}{7}\right) =\dfrac{6}{7}\cdot\left(-\dfrac{16}{35}\right)=-\dfrac{96}{245}\\ b.\dfrac{6}{7}+\dfrac{5}{7}\cdot\dfrac{5}{8}-\dfrac{8}{9}\\ =\dfrac{6}{7}+\dfrac{25}{56}-\dfrac{8}{9}=\dfrac{209}{504}\)

Câu 13:

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

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

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

\(=\dfrac{3}{4}\cdot\dfrac{2}{35}=\dfrac{3}{2\cdot35}=\dfrac{3}{70}\)

=>Chọn D

Câu 14:

\(\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right)\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\)

\(=\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right)\left(\dfrac{4}{12}-\dfrac{3}{12}-\dfrac{1}{12}\right)\)

\(=\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{5}{39}\right)\cdot0=0\)

=>Chọn C

Câu 15:

\(\left(\dfrac{4}{3}+\dfrac{8}{3}\right)\left(\dfrac{7}{4}-\dfrac{6}{4}\right):\left(\dfrac{7}{5}+\dfrac{12}{5}\right)\)

\(=\dfrac{12}{3}\cdot\dfrac{1}{4}:\dfrac{19}{5}\)

\(=\dfrac{12}{12}\cdot\dfrac{5}{19}=\dfrac{5}{19}\)

=>Chọn B

Câu 6:

\(\dfrac{19}{24}-\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{7}{24}\)

\(=\dfrac{12}{24}-\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}=-\dfrac{1}{3}\)

=>Chọn A

Câu 7:

\(\dfrac{2}{5}+\dfrac{-1}{6}-\dfrac{3}{4}-\dfrac{-2}{3}\)

\(=\dfrac{24}{60}+\dfrac{-10}{60}-\dfrac{45}{60}+\dfrac{40}{60}\)

\(=\dfrac{24+40-55}{60}=\dfrac{9}{60}=\dfrac{3}{20}\)

=>Chọn C

Câu 8:

\(\left(\dfrac{4}{3}-\dfrac{2}{3}\right)\left(\dfrac{7}{10}-\dfrac{3}{10}\right)-\dfrac{1}{5}\left(\dfrac{8}{6}-\dfrac{7}{6}\right)\)

\(=\dfrac{2}{3}\cdot\dfrac{4}{10}-\dfrac{1}{5}\cdot\dfrac{1}{6}\)

\(=\dfrac{2}{3}\cdot\dfrac{2}{5}-\dfrac{1}{30}=\dfrac{4}{15}-\dfrac{1}{30}=\dfrac{7}{30}\)

=>Chọn A

Câu 9:

\(\dfrac{3}{15}\cdot\dfrac{5}{9}:\dfrac{-18}{17}\cdot\dfrac{14}{17}\)

\(=\dfrac{1}{5}\cdot\dfrac{5}{9}\cdot\dfrac{-17}{18}\cdot\dfrac{14}{17}\)

\(=\dfrac{1}{9}\cdot\dfrac{-7}{9}=\dfrac{-7}{81}\)

=>Chọn D

Câu 10:

\(\left(\dfrac{13}{23}+\dfrac{1313}{2323}-\dfrac{131313}{232323}\right)\left(\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{10}{21}\right)\)

\(=\left(\dfrac{13}{23}+\dfrac{13}{23}-\dfrac{13}{23}\right)\left(\dfrac{7}{21}+\dfrac{3}{21}-\dfrac{10}{21}\right)\)

\(=\dfrac{13}{23}\cdot0=0\)

=>Chọn A

Câu 11: \(\left(\dfrac{4}{5}+\dfrac{1}{2}\right)\left(\dfrac{3}{15}-\dfrac{8}{13}\right)\)

\(=\left(\dfrac{8}{10}+\dfrac{5}{10}\right)\left(\dfrac{1}{5}-\dfrac{8}{13}\right)\)

\(=\dfrac{13}{10}\left(\dfrac{13}{65}-\dfrac{40}{65}\right)=\dfrac{13}{10}\cdot\dfrac{-27}{65}=\dfrac{-27}{50}\)

=>Chọn C

Câu 12:

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

\(=\left(-\dfrac{9}{12}+\dfrac{28}{12}\right):\left(\dfrac{4}{18}-\dfrac{45}{18}\right)\)

\(=\dfrac{19}{12}\cdot\dfrac{18}{-41}\)

\(=\dfrac{-19}{41}\cdot\dfrac{3}{2}=\dfrac{-57}{82}\)

=>Chọn B

Câu 1:

\(\left(-\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{-5}{2}\right)\cdot\dfrac{-30}{73}\)

\(=\left(-\dfrac{10}{30}+\dfrac{12}{30}-\dfrac{75}{30}\right)\cdot\dfrac{-30}{73}\)

\(=\dfrac{-73}{30}\cdot\dfrac{-30}{73}=1\)

=>Chọn C

Câu 2:

\(\left(\dfrac{1}{2}+\dfrac{-1}{3}+\dfrac{1}{4}+\dfrac{1}{6}\right):\dfrac{3}{4}\)

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

\(=\left(\dfrac{1}{3}+\dfrac{1}{4}\right)\cdot\dfrac{4}{3}=\dfrac{7}{12}\cdot\dfrac{4}{3}=\dfrac{7}{9}\)

=>Chọn B

Câu 3:

\(\dfrac{1}{4}-\dfrac{2}{3}:\dfrac{5}{6}-\dfrac{11}{18}\cdot\dfrac{9}{22}\)

\(=\dfrac{1}{4}-\dfrac{2}{3}\cdot\dfrac{6}{5}-\dfrac{11}{22}\cdot\dfrac{9}{18}\)

\(=\dfrac{1}{4}-\dfrac{12}{15}-\dfrac{1}{2}\cdot\dfrac{1}{2}=-\dfrac{12}{15}=-\dfrac{4}{5}\)

=>Chọn A
Câu 4:

\(\dfrac{3}{4}\cdot\dfrac{8}{2}-\dfrac{-1}{3}+\dfrac{-5}{18}:\dfrac{1}{9}\)

\(=\dfrac{3}{4}\cdot4+\dfrac{1}{3}+\dfrac{-5}{18}\cdot9\)

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

=>Không có câu nào đúng

Câu 5: 

\(\left(-\dfrac{36}{45}-\dfrac{25}{100}-\dfrac{22}{33}\right):\left(-\dfrac{309}{120}\right)\)

\(=\left(\dfrac{4}{5}+\dfrac{1}{4}+\dfrac{2}{3}\right):\dfrac{103}{40}\)

\(=\dfrac{4\cdot12+1\cdot15+2\cdot20}{60}\cdot\dfrac{40}{103}\)

\(=\dfrac{48+15+40}{60}\cdot\dfrac{40}{103}=\dfrac{103}{60}\cdot\dfrac{40}{103}=\dfrac{40}{60}=\dfrac{2}{3}\)

=>Chọn D

Số đường thẳng vẽ được là:

\(\dfrac{n\left(n-1\right)}{2}\left(đường\right)\)

Câu 13: Đổi thời gian sang giờ dưới dạng phân số tối giản 
a) 20 phút = 20/60 = 1/3 giờ
b) 45 phút = 45/60 = 3/4 giờ
c) 90 phút = 90/60 = 3/2 giờ

Câu 14: a) 40 phút = 40/60 = 2/3 giờ
b) 80 phút = 80/60 = 4/3 giờ
c) 150 phút = 150/60 = 5/2 giờ

15) 10/25, 12/30, 14/35, 16/40, 18/45, 20/50, 22/55, 24/60, 26/65, 28/70, 30/75, 32/80, 34/85, 36/90, 38/95
16) 21/17, 42/34, 63/51, 84/68
17) số phần bạn đã tiêu là: 20000/500000 = 1/25
18) tỉ số kẹo cho em là: 25/45 = 5/9

câu 19) tổng số tiền đã tiêu: 
100000 + 35000 + 75000 = 210000 (đồng)
phần số tiền đã tiêu là:  
210000/300000 = 7/10
câu 20) sau 15p lượng nước chảy vào bể chiếm là:
15/50 = 3/10

Câu 8:

a: \(\dfrac{-45}{-125}=\dfrac{45}{125}=\dfrac{45:5}{125:5}=\dfrac{9}{25}\)

b: \(\dfrac{-300}{200}=\dfrac{-300:100}{200:100}=\dfrac{-3}{2}\)

c: \(\dfrac{63}{-7}=\dfrac{-63}{7}=\dfrac{-63:7}{7:7}=\dfrac{-9}{1}=-9\)

Câu 9:

\(4=\dfrac{4\cdot8}{8}=\dfrac{32}{8}\)

\(-7=\dfrac{-7\cdot8}{8}=\dfrac{-56}{8}\)

\(13=\dfrac{13\cdot8}{8}=\dfrac{104}{8}\)

Câu 10:

\(3=\dfrac{3\cdot\left(-7\right)}{-7}=\dfrac{-21}{-7}\)

\(-5=\dfrac{\left(-5\right)\cdot\left(-7\right)}{-7}=\dfrac{35}{-7}\)

\(13=\dfrac{13\cdot\left(-7\right)}{-7}=\dfrac{-91}{-7}\)

Câu 11:

\(\dfrac{-9}{39}=\dfrac{-3}{13};\dfrac{12}{9}=\dfrac{4}{3};\dfrac{35}{10}=\dfrac{7}{2}\)

1: Số số hạng của dãy là:

\(\left(90-12\right):3+1=78:3+1=27\left(số\right)\)

Tổng của dãy số là \(\left(90+12\right)\times\dfrac{27}{2}=1377\)

2: Số số hạng của dãy là:

\(\dfrac{100-8}{4}+1=\dfrac{92}{4}+1=23+1=24\left(số\right)\)

Tổng của dãy số là: \(\left(100+8\right)\times\dfrac{24}{2}=108\times12=1296\)

3: 101-100+99-98+...+3-2+1

=(101-100)+(99-98)+...+(3-2)+1

=1+1+...+1

=51

1, Số số hạng:

 (90−12):3+1= 27

Tổng của dãy số: 

 100−84+1=924+1=23+1= 24

Tổng của dãy số: