a) 11/7 + (-5/21)

= 33/21 - 5/21

= 28/21

= 4/3

b) -5/8 + 12/7 + 13/8 + 2/7

= (-5/8 + 13/8) + (12/7 + 2/7)

= 1 + 2

= 3

c) -3/7 + 5/13 + (-4/7)

= 5/13 - (3/7 + 4/7)

= 5/13 - 1

= -8/13

d) -3/4 + (-1/4) + 2/7 + 5/7 + 3/5

= (-3/4 - 1/4) + (2/7 + 5/7) + 3/5

= -1 + 1 + 3/5

= 0 + 3/5

= 3/5

e) 14/13 + (-1/13 - 19/20)

= 14/13 - 1/13 - 19/20

= (14/13 - 1/13) - 19/20

= 1 - 19/20

= 1/20

này là phải tính cả quy đồng ra hả bạn

\(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{2021\cdot2023}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2021\cdot2023}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{2023}\right)=\dfrac{1}{2}\cdot\dfrac{2022}{2023}=\dfrac{1011}{2023}\)

=1/1.3+1/3.5+1/5.7+......+1/2021.2023

=1/1-1/3+1/3-1/5+....+1/2021-1/2023

=1/1-1/2023

=1-1/2023

=2023/2023-1/2023

=2022/2023

Đáp án là : 2022/2023

(không bít có đúng không nữa :_3)

\(\dfrac{-2}{5}\cdot\dfrac{4}{7}+\dfrac{-3}{5}\cdot\dfrac{2}{7}+\dfrac{-3}{5}\)

\(=\dfrac{-2}{5}\cdot\dfrac{4}{7}+\dfrac{-3}{5}\left(\dfrac{2}{7}+1\right)\)

\(=\dfrac{-2}{5}\cdot\dfrac{4}{7}+\dfrac{-3}{5}\cdot\dfrac{9}{7}\)

\(=\dfrac{-8-27}{35}=\dfrac{-35}{35}=-1\)

\(\dfrac{20}{1\cdot6}+\dfrac{20}{6\cdot11}+...+\dfrac{20}{101\cdot106}\)

\(=4\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{101\cdot106}\right)\)

\(=4\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)

\(=4\left(1-\dfrac{1}{106}\right)=4\cdot\dfrac{105}{106}=\dfrac{105\cdot2}{53}=\dfrac{210}{53}\)

Bạn thử tham khảo nhé!  

a: \(\dfrac{4}{13}+\dfrac{-12}{39}=\dfrac{4}{13}-\dfrac{4}{13}=0\)

b: \(\dfrac{27}{23}-\dfrac{-5}{21}-\dfrac{4}{23}+\dfrac{16}{21}+\dfrac{1}{2}\)

\(=\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)

\(=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)

c: \(\dfrac{-8}{9}+\dfrac{1}{9}\cdot\dfrac{2}{9}+\dfrac{1}{9}\cdot\dfrac{7}{9}\)

\(=\dfrac{-8}{9}+\dfrac{1}{9}\left(\dfrac{2}{9}+\dfrac{7}{9}\right)\)

\(=\dfrac{-8}{9}+\dfrac{1}{9}=\dfrac{-7}{9}\)

d: \(\dfrac{2}{\left(-3\right)^2}+\dfrac{5}{-12}-\dfrac{-3}{4}\)

\(=\dfrac{2}{9}-\dfrac{5}{12}+\dfrac{3}{4}\)

\(=\dfrac{8}{36}-\dfrac{15}{36}+\dfrac{27}{36}=\dfrac{19}{36}\)

- Với \(p=3\Rightarrow8p-1=8.3-1=23\) là số nguyên tố và \(8p+1=25\) là hợp số

- Với \(p\ne3\Rightarrow p\) không chia hết cho 3

\(\Rightarrow p=3k+1\) hoặc \(p=3k+2\)

Với \(p=3k+1\Rightarrow8p+1=8\left(3k+1\right)+1=24k+9=3\left(8k+3\right)\) chia hết cho 3 \(\Rightarrow\) là hợp số

Với \(p=3k+2\Rightarrow8p-1=8\left(3k+2\right)-1=24k+15=3\left(8k+5\right)\) chia hết cho 3 \(\Rightarrow\) là hợp số

Vậy số còn lại luôn là hợp số

\(\dfrac{-2}{7}\cdot\dfrac{7}{4}+\dfrac{-2}{7}\cdot\dfrac{-3}{4}-2\dfrac{1}{7}\)

\(=\dfrac{-2}{7}\left(\dfrac{7}{4}-\dfrac{3}{4}\right)-\dfrac{15}{7}\)

\(=\dfrac{-2}{7}-\dfrac{15}{7}=\dfrac{-17}{7}\)

Lời giải:

Gọi chiều dài và chiều rộng ban đầu là $a$ và $b$ (m) 

Theo bài ra ta có:

$(a+36)b.0,84=ab.1,05$

$\Rightarrow b[(a+36).0,84-1,05a]=0$

$\Rightarrow (a+36).0,84-1,05a=0$

$\Rightarrow 30,24=0,21a$

$\Rightarrow a=144$ (m) 

Vậy chiều dài mới là: $a+36=144+36=180$ (m)

Bài 2:

a: \(\dfrac{7}{8}+x=\dfrac{3}{5}\)

=>\(x=\dfrac{3}{5}-\dfrac{7}{8}=\dfrac{24-35}{40}=\dfrac{-11}{40}\)

b: \(\dfrac{17}{2}:x=5\)

=>\(x=\dfrac{17}{2}:5\)

=>\(x=\dfrac{17}{2\cdot5}=\dfrac{17}{10}\)

c: \(x-\dfrac{3}{8}=2+\dfrac{1}{4}\)

=>\(x-\dfrac{3}{8}=\dfrac{9}{4}\)

=>\(x=\dfrac{9}{4}+\dfrac{3}{8}=\dfrac{18}{8}+\dfrac{3}{8}=\dfrac{21}{8}\)

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

=>\(\dfrac{3}{5}\left(x-2\right)=\dfrac{1}{5}-\dfrac{1}{2}=\dfrac{-3}{10}\)

=>\(x-2=-\dfrac{1}{2}\)

=>\(x=2-\dfrac{1}{2}=\dfrac{3}{2}\)

Bài 1:

a: \(\dfrac{-3}{4}+\dfrac{1}{5}=\dfrac{-15}{20}+\dfrac{4}{20}=\dfrac{-15+4}{20}=\dfrac{-11}{20}\)

b: \(\dfrac{-2}{5}-\dfrac{1}{3}=\dfrac{-6}{15}-\dfrac{5}{15}=\dfrac{-6-5}{15}=\dfrac{-11}{15}\)

c: \(\dfrac{3}{7}\cdot\dfrac{2}{5}-\dfrac{2}{5}=\dfrac{2}{5}\left(\dfrac{3}{7}-1\right)=\dfrac{2}{5}\cdot\dfrac{-4}{7}=\dfrac{-8}{35}\)

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

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

\(=\dfrac{1}{4}+\dfrac{3}{4}\cdot\dfrac{1}{6}=\dfrac{1}{4}+\dfrac{1}{8}=\dfrac{3}{8}\)

e: \(\dfrac{7}{2}\cdot\dfrac{8}{13}+\dfrac{8}{13}\cdot\dfrac{-5}{12}+\dfrac{8}{13}\)

\(=\dfrac{8}{13}\left(\dfrac{7}{2}-\dfrac{5}{2}+1\right)\)

\(=\dfrac{8}{13}\cdot2=\dfrac{16}{13}\)

f: \(1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

\(=1+\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+\dfrac{1}{8\cdot10}+\dfrac{1}{10\cdot12}\)

\(=1+\dfrac{1}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{10\cdot12}\right)\)

\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{12}\right)\)

\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{12}\right)\)

\(=1+\dfrac{1}{2}\cdot\dfrac{5}{12}=1+\dfrac{5}{24}=\dfrac{29}{24}\)

-1/4 + 2/5 . x = 4/15

2/5 . x = 4/15 + 1/4

2/5 . x = 31/60

x = 31/60 : 2/5

x = 31/24

-1/4+2/5.x=4/15

        2/5.x=4/15-1/4

        2/5.x=1/60

              X=1/60:2/5

              X=1/60.5/2

             X= 1/24

-1/4+2/5.x=4/15