Ta có:

\(\dfrac{-2}{3}< \dfrac{-1}{3}< 0< \dfrac{1}{2}\)

Sắp xếp:
\(\dfrac{-2}{3};\dfrac{-1}{3};0;\dfrac{1}{2}\)

−23;−13;0;12

3

−2

​

;

3

−1

​

;0;

2

1

​

.

−23;−13;0;123−2​;3−1​;0;21​.

a) \(\dfrac{25}{6}:\dfrac{5}{3}-\left(\dfrac{-1}{4}\right)\)

\(=\dfrac{25}{6}\cdot\dfrac{3}{5}+\dfrac{1}{4}\)

\(=\dfrac{5}{2}+\dfrac{1}{4}\)

\(=\dfrac{10}{4}+\dfrac{1}{4}\)

\(=\dfrac{11}{4}\)

b) \(\dfrac{1}{8}\cdot\dfrac{3}{2}+\dfrac{1}{8}\cdot\dfrac{-1}{2}\)

\(=\dfrac{1}{8}\cdot\left(\dfrac{3}{2}-\dfrac{1}{2}\right)\)

\(=\dfrac{1}{8}\cdot\dfrac{2}{2}\)

\(=\dfrac{1}{8}\)

a) 256:53−(−14)625​:35​−(4−1​)

=256⋅35+14=625​⋅53​+41​

=52+14=25​+41​

=5.2+14=45.2+1​

=114=411​

b) 18⋅32+18⋅(−12)81​⋅23​+81​⋅(−21​)

=18⋅(32−12)=81​⋅(23​−21​)

=18⋅22=81​⋅22​

=18⋅1=18=81​⋅1=81​
 

= -1/2 + 3/5 - 1/9 + 1/27 - 7/18 + 4/35 + 2/7

= (-1/2 - 1/9 - 7/18) + (3/5 + 4/35 + 2/7)  + 1/27

= (-9/18 - 2/18 - 7/18) + (21/35 + 4/35 + 10/35) + 1/27

= -18/18 + 35/35 + 1/27

= -1 + 1 + 1/27

= 1/27

a) \(\dfrac{1-\dfrac{1}{3}-\dfrac{1}{6}}{\dfrac{1}{10}-\dfrac{1}{15}}\) 

\(=\dfrac{\dfrac{6}{6}-\dfrac{2}{6}-\dfrac{1}{6}}{\dfrac{3}{30}-\dfrac{2}{30}}\)

\(=\dfrac{3}{6}:\dfrac{1}{30}\)

\(=\dfrac{1}{2}:\dfrac{1}{30}\)

\(=15\)

b) \(\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{12}-\dfrac{1}{2}\)

\(=-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-\dfrac{1}{20}-\dfrac{1}{30}-\dfrac{1}{42}-\dfrac{1}{56}-\dfrac{1}{72}+\dfrac{8}{9}\)

\(=-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{72}\right)+\dfrac{8}{9}\)

\(=-\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}\right)+\dfrac{8}{9}\) 

\(=-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)+\dfrac{8}{9}\)

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

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

\(=0\)

Nhanh hộ mk

Mk đang vội

Bài 7:

Chiều dài của khu đất là:

\(3\times1,72=5,16\left(km\right)\)

Diện tích khu đất là:

\(1,72\times5,16=8,8752\left(km^2\right)\)

Chu vi của khu đất là:
\(\left(1,72+5,16\right)\times2=13,76\left(km\right)\)

ĐS: ... 

A = 2023 + 2023² + 2023³ + ... + 2023¹⁰⁰⁰⁰

⇒ 2023A = 2023² + 2023³ + 2023⁴ + ... + 2023¹⁰⁰⁰¹

⇒ 2022A = 2023A - A

= (2023² + 2023³ + 2023⁴ + ... + 2023¹⁰⁰⁰¹) - (2023 + 2023² + 2023³ + ... + 2023¹⁰⁰⁰⁰) 

= 2023¹⁰⁰⁰¹ - 2023

⇒ 2022A + 2023 = 2023¹⁰⁰⁰¹ - 2023 + 2023

= 2023¹⁰⁰⁰¹

= 2023².2023⁹⁹⁹⁹ ⋮ 2023²

Vậy (2022A + 2023) ⋮ 2023²

Ngày thứ nhất đọc được :

   90 x 4 / 9 = 40 (trang)

Ngày thứ hai đọc được :

  90 x 2/5 = 36 (trang)

Ngày thứ ba đọc được :

  90 - 36 - 40 = 14 (trang)

\(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+...+\dfrac{1}{45}\)

\(\dfrac{1}{2}A=\dfrac{1}{2}\cdot\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{45}\right)\)

\(\dfrac{1}{2}A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{90}\)

\(\dfrac{1}{2}A=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\)

\(\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{10}\)

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

\(A=\dfrac{2}{5}:\dfrac{1}{2}\)

\(A=\dfrac{4}{5}\)

D = 14 + 25 + 36 + ... + 100103 = (1 + 100)(4 + 103)/2 = 101107/2 = 5407

E = 13 + 24 + 35 + ... + 98100 = (1 + 98)(3 + 100)/2 = 99103/2 = 5094

mik cần giải bằng số k cho chữ nha (để viết ra sẽ dễ hiểu hơn)!!!\

\(-\dfrac{9}{16}.\dfrac{13}{3}-\left(-\dfrac{3}{4}\right)^2.\dfrac{19}{3}\\ =-\dfrac{9}{16}.\dfrac{13}{3}-\dfrac{9}{16}.\dfrac{19}{3}\\ =-\dfrac{9}{16}.\left(\dfrac{13}{3}+\dfrac{19}{3}\right)\\ =-\dfrac{9}{16}.\dfrac{32}{3}\\ =-\dfrac{3.3.16.2}{16.3}=-3.2\\ =-6\)