A=\(\frac{3}{5}\): \(\frac{4}{5}\) + \(\frac{3}{7}\):\(\frac{4}{7}\)+ \(\frac{3}{13}\): \(\frac{4}{13}\)+\(\frac{3}{295}\): \(\frac{4}{295}\)

A= \(\frac{3}{4}\)+ 3/4 + 3/4 + 3/4

A=3/4 . 4 = 3

Ta có: \(\frac{3}{5}+\frac{3}{7}+\frac{3}{13}+\frac{3}{295}=3.\left(1+\frac{1}{5}+\frac{1}{7}+\frac{1}{13}+\frac{1}{295}\right)\)

\(\frac{4}{5}+\frac{4}{7}+\frac{4}{13}+\frac{4}{295}=4.\left(1+\frac{1}{5}+\frac{1}{7}+\frac{1}{13}+\frac{1}{295}\right)\)

\(\Rightarrow\frac{\frac{3}{5}+\frac{3}{7}+\frac{3}{13}+\frac{3}{295}}{\frac{4}{5}+\frac{4}{7}+\frac{4}{13}+\frac{4}{295}}=\frac{3.\left(1+\frac{1}{5}+\frac{1}{7}+\frac{1}{13}+\frac{1}{295}\right)}{4.\left(1+\frac{1}{5}+\frac{1}{7}+\frac{1}{13}+\frac{1}{295}\right)}=\frac{3}{4}\)

\(A=\frac{\frac{3}{5}+\frac{3}{7}+\frac{3}{13}+\frac{3}{295}}{\frac{4}{5}+\frac{4}{7}+\frac{4}{13}+\frac{4}{295}}=\frac{3\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{13}+\frac{1}{295}\right)}{4\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{13}+\frac{1}{295}\right)}=\frac{3}{4}\)

Để chứng minh tổng \( A = 1 - 4 - 7 + 10 + 13 - 16 - 19 + 22 + \dots - 295 + 298 + 301 - 304 \) chia hết cho 3, chúng ta có thể nhóm các số có cùng dấu và tính tổng của từng nhóm.

Nhóm các số cùng dấu:

\( (1 - 4 - 7) + (10 + 13 - 16) + (19 + 22 + \dots + 298 + 301) - 304 \)

Từ mẫu số 19 đến 301, có \( \frac{301 - 19}{3} + 1 = 95 \) số chia hết cho 3. Vì vậy, tổng của chúng là \( 95 \times 3 = 285 \).

Suy ra, tổng \( A \) sẽ là tổng các số đó trừ đi 304:

\( 285 - 304 = -19 \)

Vì -19 không chia hết cho 3, nên ta không thể chứng minh rằng tổng \( A \) chia hết cho 3.

 A = 1 - 4 - 7 +10 +13 - 16 - 19 +22 + .... - 295 + 298 +301 - 304  

A = (1-4) + (-7+10) + (13-16) + (-19+22) + ... + (-295+298) + (301-304)

A = (-3) + 3 + (-3) + 3 + ... + 3 + (-3) \(⋮\) 3

Vậy A\(⋮\) 3

TICK NHA! CÁCH NÀY DỄ HIỂU NÈ BẠN

\(1,-\dfrac{4}{7}+\dfrac{2}{3}\times\dfrac{-9}{14}\)

\(=\dfrac{-4}{7}+\dfrac{-18}{42}\)

\(=\dfrac{-4\times6}{7\times6}+\dfrac{-18}{42}\)

\(=\dfrac{-20}{42}+\dfrac{-18}{42}\)

\(=-\dfrac{38}{42}\)

\(=-\dfrac{19}{21}\)

\(2,\dfrac{17}{13}-\left(\dfrac{4}{13}-11\right)\)

\(=\dfrac{17}{13}-\dfrac{4}{13}+11\)

\(=\dfrac{13}{13}+11\)

\(=1+11\)

\(=12\)

\(3,8\dfrac{2}{7}-\left(3\dfrac{4}{9}+4\dfrac{2}{7}\right)\)

\(=\dfrac{58}{7}-\left(\dfrac{31}{9}+\dfrac{30}{7}\right)\)

\(=\dfrac{58}{7}-\dfrac{31}{9}-\dfrac{30}{7}\)

\(=\dfrac{58}{7}-\dfrac{30}{7}-\dfrac{31}{9}\)

\(=\dfrac{28}{7}-\dfrac{31}{9}\)

\(=\dfrac{28\times9}{7\times9}-\dfrac{31\times7}{9\times7}\)

\(=\dfrac{252}{63}-\dfrac{217}{63}\)

\(=\dfrac{35}{63}\)

\(=\dfrac{5}{9}\)

\(5,\left(\dfrac{2}{3}-1\dfrac{1}{2}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

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

\(=\left(\dfrac{2\times2}{3\times2}-\dfrac{3\times3}{2\times3}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

\(=\left(\dfrac{4}{6}-\dfrac{9}{6}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

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

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

\(=\dfrac{-15}{24}+\dfrac{1}{2}\)

\(=\dfrac{-15}{24}+\dfrac{1\times12}{2\times12}\)

\(=\dfrac{-15}{24}+\dfrac{12}{24}\)

\(=\dfrac{-3}{24}\)

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

\(6,\dfrac{-5}{13}+\dfrac{2}{5}+\dfrac{-8}{13}+\dfrac{3}{5}-\dfrac{3}{7}\)

\(=\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)-\dfrac{3}{7}\)

\(=\dfrac{-13}{13}+\dfrac{5}{5}-\dfrac{3}{7}\)

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

\(=-\dfrac{3}{7}\)

\(7,\dfrac{6}{5}\times\dfrac{3}{7}+\dfrac{6}{5}:\dfrac{7}{10}+\dfrac{6}{5}\)

\(=\dfrac{6}{5}\times\dfrac{3}{7}+\dfrac{6}{5}\times\dfrac{10}{7}+\dfrac{6}{5}\)

\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+1\right)\)

\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+\dfrac{1\times7}{1\times7}\right)\)

\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+\dfrac{7}{7}\right)\)

\(=\dfrac{6}{5}\times\dfrac{20}{7}\)

\(=\dfrac{120}{35}\)

\(=\dfrac{24}{7}\)

a)-84:4+3^9:3^7+5^0

=-21+(3^9:3^7)+1

=-21+3^2+1

=-21+9+1

=-12+1

=-11

b)295-(31-2^5.5)^2

=295-(31-32.5)^2

=295-(-129)^2

=295+129^2

=295-16641

=-16346

tick cho mk nha bạn

a) -84 : 4 + 3^ 9 : 3 ^ 7 + 5 ^0

=-84:4+3^2+1

=-84:4+9+1

=-21+9+1

=-12+1

=-11

b) 295 - ( 31 - 2^ 5. 5) ^2

= 295 - ( 31 -32. 5)^2

= 295 - (-129)^2

=295-16641

=-16346

a)- 11

b) - 16346

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

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

\(=2-1\)

\(=1\)

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

\(=\left(\frac{7}{9}+\frac{2}{9}\right)-\left(\frac{5}{12}+\frac{7}{12}\right)\)

\(=1-1\)

\(=0\)

các câu sau tương tự

A=1

B=0

C=ÂM 8/15

D=0

E=2

F=3/2

H=2/3 

LẦN SAU CHO KHÓ SÍU NHA LỚP 5 CŨNG LÀM ĐC

Lời giải:

$-1+4-7+10-13+16-...-295+298-301$

$=(-1+4)+(-7+10)+(-13+16)+.....+(-295+298)-301$
$=3+3+3+....+3-301$

Số lần xuất hiện của 3 là: $[(298-1):3+1]:2=50$

$S=3.50-301=-151$