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Bài 1 câu a:
1/-8 + -5/8
= -1/8 - 5/8
= -6/8
= -3/4
Câu b:
-1/21 + -1/28
= -4/84 - 3/84
= - 7/854
Câu c:
-5/9 + 8/15 + -2/11 + 4/-9 + 7/15
= (8/15+ 7/15) - (5/9 + 4/9) - 2/11
= 1 - 1 - 2/11
= 0 - 2/11
= - 2/11
Câu d:
-25/-75 + 17/34 + 121/- 132
= 1/3 + 1/2 - 11/12
= 4/12 + 6/12 - 11/12
= 10/12 - 11/12
= - 1/12
Bài 2a:
51/23 = 5151/2323 = 515151/232323
\(\frac{5151}{2323}\) = \(\frac{5151:101}{2323:101}\) = \(\frac{51}{23}\) (1)
\(\frac{515151}{232323}\) = \(\frac{515151:10101}{232323:10101}\) = \(\frac{51}{23}\) (2)
Từ (1) và (2) ta có:
\(\frac{51}{23}=\frac{5151}{2323}=\frac{515151}{232323}\) (đpcm)
Câu a:
\(\frac{3939-101}{3.2929+505}\)
= \(\frac{101.\left(39-1\right)}{101.\left(3.29+5\right)}\)
= \(\frac{38}{87+5}\)
= \(\frac{38}{92}\)
= \(\frac{19}{46}\)
Câu c:
\(\frac{6.9-2.17}{63.3-119}\)
= \(\frac{2.\left(3.9-17\right)}{7.\left(9.3-17\right)}\)
= \(\frac27\)
Câu a:
(7\(^{2017}\) - 7\(^{2015}\)) ⋮ (7\(^{2014}\).7)
= 7\(^{2015}\).(7\(^2\) - 1) ⋮ 7\(^{2015}\)
= (7\(^{2015}\) : 7\(^{2015}\)).(49 - 1)
= 1.48
= 48
Câu b:
(2\(^{13}\) + 2\(^5\)) : (2\(^{10}\) + 2\(^2\))
= 2\(^5.\)(2\(^8\) + 1):[2\(^2\).(2\(^8\) + 1)]
= (2\(^5:2^2\)).[(\(2^8+1):\left(2^8+1\right)\)]
= 2\(^3\).1
= 8
\(\frac{2^5.7+2^5}{2^5.5^2-2^5.3}=\frac{2^5.\left(7+1\right)}{2^5.\left(5^2-3\right)}=\frac{8}{25-3}=\frac{8}{22}=\frac{4}{11}\)
\(\frac{3^4.5-3^6}{3^4.13+3^4}=\frac{3^4.\left(5-3^2\right)}{3^4.\left(13+1\right)}=\frac{5-9}{14}=\frac{-4}{14}=\frac{-2}{7}\)
\(\frac{-2}{7}=\frac{-22}{77}\)
\(\frac{4}{11}=\frac{28}{77}\)
cơ bản giống nhau nhé
Lời giải cho ý (D) các câu khác tương tự
\(D=13^1+13^3+13^5+...+13^{99}\)
\(13^2.D=13^3+13^5+13^7...+13^{99+2}\)
\(\left(13^2-1\right)D=13^3+13^5+13^7+...+13^{101}-\left(13^1+13^3+13^5+...+13^{99}\right)\)
\(D=\dfrac{13^{101}-13}{13^2-1}\)
a) 100 - 7.(x-5) = 68
7.(x - 5) = 100 - 68 = 32
x - 5 = \(\frac{32}{7}\)
x = \(\frac{32}{7}+5=\frac{67}{7}\)
b) 2(x-6)+2227:17=151
2( x -6) + 131 = 151
2 (x - 6) = 20
x - 6 = 20 : 2 = 10
x = 10 + 6 = 16
a/\(\frac{3939-101}{3.2929+505}=\frac{39.101-101}{8787+505}=\frac{101.\left(39-1\right)}{87.101+5.101}=\frac{101.38}{101.\left(87+5\right)}=\frac{38}{92}\)
\(=\frac{38}{92}\)
b/\(\frac{6.4+6.7}{6.5+12}=\frac{4+1.7}{1.5+2}=\frac{4+7}{5+2}=\frac{11}{7}\)
\(\frac{6.4+6.7}{6.5+12}\)\(=\frac{6.4+6.7}{6.5+6.2}\)\(=\frac{6.\left(4+7\right)}{6.\left(5+2\right)}\)\(=\frac{6.11}{6.7}\)\(=\frac{11}{7}\)
Câu c:
\(\frac{6.9+2.17}{63.3-119}\)
= \(\frac{2.3.9+2.17}{7.9.3-7.17}\)
= \(\frac{2.\left(27+17\right)}{7.\left(9.3-17\right)}\)
= \(\frac{2.44}{7.\left(27-17\right)}\)
= \(\frac{2.44}{7.10}\)
= \(\frac{44}{35}\)
Câu d:
\(\frac{25.9-25.17}{-8.80-8.10}\)
= \(\frac{25.\left(9-17\right)}{8.10\left(8+1\right)}\)
= \(\frac{5.5.\left(-8\right)}{-8.2.5.9}\)
= \(\frac{5}{18}\)
Câu e:
\(\frac{48.12-48.15}{-3.270-3.30}\)
= \(\frac{48.\left(12-15\right)}{-3.30.\left(9+1\right)}\)
= \(\frac{6.2.4.\left(-3\right)}{-3.6.5.2.5}\)
= \(\frac{4}{25}\)
Câu f:
\(\frac{2^5.7+2^5}{2^5.5^2-2^5.3}\)
= \(\frac{2^5.\left(7+1\right)}{2^5.\left(5^2-3\right)}\)
= \(\frac{8}{25-3}\)
= \(\frac{8}{22}\)
= \(\frac{4}{11}\)
Câu g:
\(\frac{3^4.5-3^6}{3^4.13+3^4}\)
= \(\frac{3^4.\left(5-3^2\right)}{3^4.\left(13+1\right)}\)
= \(\frac{5-9}{14}\)
= \(-\frac{4}{14}\)
= - \(\frac27\)