Để:

1111111*33333333 chia hết cho 7 thì:

⇒ 11111111*3333333 + (3 x 5) phải chia hết cho 7

⇒ 11111111+* x 100000000 + 33333333 + 15 chia hết cho 7 

⇒ 44444459 + * x 100000000 chia hết cho 7 

⇒ * = 2 

* = 2

Đặt \(x\) là số cần tìm ta được : \(A=\overline{11111111x33333333}\)

\(\)Ta làm phép tính sau :

\(1.3=3\rightarrow3+1=4.3=12\rightarrow12+1=13.4=52\rightarrow52+1=53.3=159\rightarrow159+1=160.3=480\rightarrow480+1=481.3=1443\rightarrow1443+1=1444.3=4332\rightarrow4332+1=4333.3=12999\)

\(\left(12999+x\right).3=3x+38997\)

\(3x+38997+3=3x+3900\rightarrow\left(3x+3900\right).3=9x+11700\)

\(9x+11700+3=9x+11703\rightarrow\left(9x+11703\right).3=27x+35109\)

\(27x+35109+3=27x+35112\rightarrow\left(27x+35112\right).3=81x+105336\rightarrow\left(81x+105336\right).3=243x+316017\)

\(243x+316017+3=243x+316020\rightarrow\left(243x+316020\right).3=729x+948060\)

\(729x+948060+3=729x+948063\rightarrow\left(729x+948063\right).3=2187x+\text{2844189}\)

\(2187x+2844192+3=2187x+2844192\rightarrow\left(2187x+2844192\right).3=6561x+8532576\)

\(6561x+8532576+3=6561x+8532579\rightarrow\left(6561x+8532579\right).3=19683x+25597737\)

\(19683x+25597737+3=19683x+25597740\)

Để \(A⋮7\Leftrightarrow19683x+25597740⋮7\)

 mà \(25597740=3656820.7⋮7\)

       \(19683\) \(⋮̸\) \(7\)

\(\Rightarrow x=7\)

Vậy \(x=7\) thỏa yêu cầu đề bài

414474220

Tk mik nha~

~shizadon~

bn chỉ cần cộng ở máy tính các chữ số là đc

k nhé cảm ơn

=414474220

TL

a, 100005175327

b, 148904438

c, 10746660

HT

Mình mất 5 phút để giải, bạn mất 1 giây để t.i.c.k, nhớ t.i.c.k mình nhá

\(P=-\frac{7}{4}.\left(\frac{33}{12}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)\)

\(P=-\frac{7}{4}.\left(\frac{33}{12}+\frac{33.101}{20.101}+\frac{33x10101}{30x10101}+\frac{33x1010101}{42x1010101}\right)\)

\(P=-\frac{7}{4}.\left(\frac{33}{12}+\frac{33}{20}+\frac{33}{30}+\frac{33}{42}\right)\)

\(P=-\frac{7}{4}.\left(\frac{11}{4}+\frac{33}{20}+\frac{11}{10}+\frac{11}{14}\right)\)

\(P=-\frac{77}{8}.\left(\frac{1}{6}+\frac{3}{10}+\frac{1}{15}+\frac{1}{21}\right)=-\frac{77}{8}.\frac{35+63+14+10}{210}=-\frac{11x122}{8x30}\)

\(P=-\frac{671}{120}\)

P = -7/4 x (33/12 + 3333/2020 + 333333/303030 + 33333333/42424242)
   = -7/4 x (33/12 + 33/20 + 33/30 + 33/42)
   = -7/4 x [33 x (1/12 + 1/20 + 1/30 + 1/42)]
   = -7/4 x [33 x (35/420 + 21/420 + 14/420 + 10/420)]
   = -7/4 x (33 x 80/420)
   = -7/4 x  33 x 4/21
   = -7/4 x 4/21 x 33 (= -7x4 / 4x21   x33)
   = -7/21 x 33 (= -7x33 / 21 = -1x7x3x11 / 3x7)
   = -11/1
   = -11
Đáp số P = -11

Các số gạch đi là do rút gọn phân số nhé!!!

\(B=\dfrac{7}{4}\left(\dfrac{33}{12}+\dfrac{33}{20}+\dfrac{33}{30}+\dfrac{33}{42}\right)\)

\(=\dfrac{7}{4}\left(\dfrac{11}{4}+\dfrac{33}{20}+\dfrac{11}{10}+\dfrac{11}{14}\right)\)

\(=\dfrac{7}{4}\cdot\dfrac{11\cdot35+33\cdot7+11\cdot14+11\cdot10}{140}\)

\(=\dfrac{880}{20\cdot4}=11\)

\(C=\dfrac{\left(\dfrac{53}{4}-\dfrac{59}{27}-\dfrac{65}{6}\right)\cdot\dfrac{5751}{25}+\dfrac{187}{4}}{\dfrac{100}{21}:\dfrac{-41}{21}}\)

\(=\dfrac{\dfrac{25}{108}\cdot\dfrac{5751}{25}+\dfrac{187}{4}}{\dfrac{-100}{41}}\)

\(=\dfrac{\dfrac{5751+187\cdot27}{108}}{\dfrac{-100}{41}}=100\cdot\dfrac{-41}{100}=-41\)

\(\frac{7}{4}\left(\frac{33}{12}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)\)

=\(\frac{7}{4}\left(\frac{33}{12}+\frac{33}{20}+\frac{33}{30}+\frac{33}{42}\right)\)

=\(\frac{7}{4}.33\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

=\(\frac{231}{4}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

=\(\frac{231}{4}\left(\frac{1}{3}-\frac{1}{7}\right)\)

=\(\frac{231}{4}.\frac{4}{21}\)

= 11