Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bài 1:
1/6 + -5/7 : x = - 7/18
5/7: x = 1/6 + 7/18
5/7: x = 3/18 + 7/18
5/7: x = 5/9
x = 5/7 : 5/9
x = 5/7 x 9/5
x = 9/7
Vậy x = 9/7
Bài 2:
Câu a:
(1/2 + 1).(1/3 + 1).(1/4 + 1)...(1/999 + 1)
= (1/2 + 2/2).(1/3 + 3/3)...(1/999 + 999/999)
= 3/2.4/3....1000/999
= 1000/2
= 500
Bài 1:
\(\Leftrightarrow-\dfrac{5}{7}:x=-\dfrac{7}{18}-\dfrac{1}{6}=\dfrac{-7}{18}-\dfrac{3}{18}=\dfrac{-10}{18}=\dfrac{-5}{9}\)
=>x=5/9:5/7=7/9
Bài 2:
a: \(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{1000}{999}=\dfrac{1000}{2}=500\)
b: \(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-999}{1000}\)
\(=-\dfrac{1}{1000}\)
Câu c:
C = 3/2^2.8/3^2.15/4^2...99/10^2
C = \(\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\ldots\times\) \(\frac{9.11}{10.10}\)
C = \(\frac{1.2.3\ldots9}{2.3\ldots10}\) x \(\frac{3.4.\ldots11}{2.3.\ldots10}\)
C = \(\frac{1}{10}\) x \(\frac{11}{2}\)
C = 11/20
\(1)A=\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(=\frac{2\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}\)
\(=\frac{2}{4}=\frac{1}{2}\)
\(2)B=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}\)
\(=\frac{1.1}{1.2}.\frac{2.2}{2.3}.\frac{3.3}{3.4}.\frac{4.4}{4.5}\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}\)
\(=\frac{1.2.3.4}{2.3.4.5}=\frac{1}{5}\)
\(3)C=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}\)
\(=\frac{2.2.3.3.4.4.5.5}{1.3.2.4.3.5.4.6}\)
\(=\frac{2.5}{1.6}=\frac{2.5}{1.3.2}=\frac{5}{3}\)
\(4)D=\left(\frac{150}{1111}+\frac{5}{75}-\frac{14}{77}\right)\left(\frac{1}{5}-\frac{1}{6}-\frac{1}{30}\right)\)
\(=\left(\frac{150}{1111}+\frac{5}{75}-\frac{14}{77}\right)\left(\frac{6}{30}-\frac{5}{30}-\frac{1}{30}\right)\)
\(=\left(\frac{150}{1111}+\frac{5}{75}-\frac{14}{77}\right).0=0\)
\(5)M=8\frac{2}{7}-\left(3\frac{4}{9}+3\frac{9}{7}\right)\) \(N=\left(10\frac{2}{9}+2\frac{3}{5}\right)-6\frac{2}{9}\)
\(=\frac{58}{7}-\left(\frac{31}{9}+\frac{30}{7}\right)\) \(=\left(\frac{92}{9}+\frac{13}{5}\right)-\frac{56}{9}\)
\(=\frac{58}{7}-\left(\frac{217}{63}+\frac{270}{63}\right)\) \(=\left(\frac{460}{45}+\frac{117}{45}\right)-\frac{280}{45}\)
\(=\frac{58}{7}-\frac{487}{63}\) \(=\frac{577}{45}-\frac{280}{45}\)
\(=\frac{522}{63}-\frac{487}{63}=\frac{5}{9}\) \(=\frac{33}{5}\)
\(P=M-N\)
\(\Rightarrow P=\frac{5}{9}-\frac{33}{5}\)
\(\Rightarrow P=\frac{25}{45}-\frac{297}{45}\)
\(\Rightarrow P=\frac{-272}{45}\)
Vậy P = \(\frac{-272}{45}\)
\(6)E=10101\left(\frac{5}{111111}+\frac{5}{222222}-\frac{4}{3.7.11.13.37}\right)\)
\(=\frac{5}{11}+\frac{5}{22}-\left(10101.\frac{4}{111111}\right)\)
\(=\frac{10}{22}+\frac{5}{22}-\frac{4}{11}\)
\(=\frac{15}{22}-\frac{8}{22}=\frac{7}{22}\)
\(7)F=\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}+\frac{2}{7}-\frac{2}{13}}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{256}+\frac{3}{64}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)
\(=\frac{1\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{13}\right)}{2\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{13}\right)}.\frac{3\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{256}+\frac{1}{64}\right)}{1\left(1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}\right)}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{16}{64}-\frac{4}{64}+\frac{1}{64}-\frac{1}{256}\right)}{1\left(\frac{64}{64}-\frac{16}{64}+\frac{4}{64}-\frac{1}{64}\right)}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{13}{64}-\frac{1}{256}\right)}{1.\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{52}{256}-\frac{1}{256}\right)}{\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{51}{256}\right)}{\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{\frac{153}{256}}{\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{153}{256}:\frac{51}{64}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3}{4}+\frac{5}{8}\)
\(=\frac{3}{8}+\frac{5}{8}=1\)
Xin lỗi tớ đã làm hết buổi tối mà chỉ có 7 bài mong bạn thông cảm cho mình nhé !
B= (2/3-1/4+5/11):(5/12+1-7/11)
B=(8/12-3/12+5/11):(5/12+1-7/11)
B=(5/12+5/11):(5/12+1-7/11)
B=115/132:(17/12-7/11)
B=115/132:103/132
B=115/103
Mik làm mẫu cho 1 con nè. các câu sau cxn tương tự từ trái wa phải.Nều bạn tính toán kém thì cứ làm như câu mẫu trên. Mik mà làm bài này thì mik làm theo cách nhanh hơn cơ. Chúc bạn học tốt và có 1 ngày tốt lành nghen. Có j cần giúp đỡ thì cứ bảo mik
1) =3/2 . 4/3 . 5/4 ...... 100/99 = 100/2 = 50
2) = -1/2 . -2/3 .-3/4 ..... . -98/99 = 1/99 (Tích này có 98 thừa số âm, 98 là số chẵn nên tích mang dấu dương)
3) =(1.3)/(2.2) . (2.4)/(3.3) . (3.5)/(4.4) ......... (29.31)/(30.30)
= (1.2.3.....31)/(2.3.4......30) . (3.4.5......29)/(2.3.4....30)
= 31 . 1/60
= 31/60
4) =1/3 - 1/7 + 1/7 - 1/11 + 1/11 - 1/15 + ... + 1/107 - 1/111
= 1/3 - 1/111
= 12/37
5) = 2/(3.5) + 2/(5.7) + 2/(7.9) +... + 2/(19.21)
= 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + .... + 1/19 - 1/21
= 1/3 - 1/21
= 2/7
6) Đặt biểu thức là A, lấy A chia cho 7 được
A/7 = 1/(10.11) + 1/(11.12) + 1/(12.13) + ... + 1/ (69.70)
= 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + ... + 1/69 - 1/70
= 1/10 - 1/70
= 3/35
Suy ra A = 3/35 . 7 = 3/5
7) Đặt biểu thức là B, lấy B chia cho 2 được
B/2 = 3/(15.18) + 3/(18.21) + 3/(21.24) +... + 3/(87.90)
= 1/15 - 1/18 + 1/18 - 1/21 + 1/21 - 1/24 + ... + 1/87 - 1/90
= 1/15 - 1/90
= 1/18
Suy ra B = 1/18 . 2 = 1/9
Chúc bạn học tốt!
\(G=\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}+1\right)......\left(\frac{1}{99}+1\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot......\cdot\frac{100}{99}\)
\(\frac{100}{2}=50\)
\(I=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{99}-1\right)\)
\(=\left(-\frac{1}{2}\right)\left(-\frac{2}{3}\right)\left(-\frac{3}{4}\right).....\left(-\frac{98}{99}\right)\)
Do số thừa số là số chẵn,nên:
\(I=\frac{1}{2}\cdot\frac{2}{3}\cdot.....\cdot\frac{98}{99}=\frac{1}{99}\)
\(A=\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}.....\cdot\frac{899}{30^2}\)
\(=\frac{3\cdot1}{2\cdot2}\cdot\frac{4\cdot2}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot.....\cdot\frac{29\cdot31}{30\cdot30}\)
\(=\frac{1\cdot31}{2\cdot30}=\frac{31}{60}\)
\(GIA=\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+.....+\frac{4}{107\cdot111}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+.....+\frac{1}{107}-\frac{1}{111}\)
\(=\frac{1}{3}-\frac{1}{111}=\frac{108}{333}\)