a) \(\dfrac{6}{11};\dfrac{6}{7};\dfrac{6}{6}\)
Chứng minh rằng:
\(\dfrac{a^{11}}{bc}+\dfrac{b^{11}}{ca}+\dfrac{c^{11}}{ab}\ge\dfrac{a^6+b^6+c^6+9}{2}\)
Tính nhanh:
\(a,A=\dfrac{\dfrac{5}{4}+\dfrac{5}{5}+\dfrac{5}{7}-\dfrac{5}{11}}{\dfrac{10}{4}+\dfrac{10}{5}+\dfrac{10}{7}-\dfrac{10}{11}}\)\(b,B=\dfrac{2+\dfrac{6}{5}-\dfrac{6}{7}-\dfrac{6}{11}}{\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{7}-\dfrac{2}{11}}\)
giúp mình với
\(a,A=\dfrac{\dfrac{5}{4}+\dfrac{5}{5}+\dfrac{5}{7}-\dfrac{5}{11}}{\dfrac{10}{4}+\dfrac{10}{5}+\dfrac{10}{7}-\dfrac{10}{11}}\\ =\dfrac{5.\left(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{11}\right)}{10.\left(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{11}\right)}\\ =\dfrac{5}{10}\\ =\dfrac{1}{2}\)
Vậy \(A=\dfrac{1}{2}\)
\(b,B=\dfrac{2+\dfrac{6}{5}-\dfrac{6}{7}-\dfrac{6}{11}}{\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{7}-\dfrac{2}{11}}\\ =\dfrac{3.\left(\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{7}-\dfrac{2}{11}\right)}{\dfrac{2}{3}+\dfrac{2}{5}-\dfrac{2}{7}-\dfrac{2}{11}}\\ =3\)
Vậy \(B=3\)
a,\(\dfrac{1}{7}\text{x}\dfrac{2}{7}+\dfrac{1}{7}\text{x}\dfrac{5}{7}+\dfrac{6}{7}\) b,\(\dfrac{6}{11}\text{x}\dfrac{4}{9}+\dfrac{6}{11}\text{x}\dfrac{7}{9}-\dfrac{6}{11}\text{x}\dfrac{2}{9}\)
c, \(\dfrac{4}{25}\text{x}\dfrac{5}{8}\text{x}\dfrac{25}{4}\text{x}24\)
`a)1/7xx2/7+1/7xx5/7+6/7`
`=1/7xx(2/7+5/7)+6/7`
`=1/7xx1+6/7`
`=1/7+6/7=1`
`b)6/11xx4/9+6/11xx7/9-6/11xx2/9`
`=6/11xx(4/9+7/9-2/9)`
`=6/11xx9/9`
`=6/11`
Sorry nãy ghi thiếu.
`c)4/25xx5/8xx25/4xx24`
`=(4xx5xx25xx24)/(25xx8xx4)`
`=(4xx5xx24)/(4xx8)`
`=(5xx24)/8`
`=5xx3=15`
a, \(\dfrac{1}{7}.\dfrac{2}{7}+\dfrac{1}{7}.\dfrac{5}{7}+\dfrac{6}{7}\)
\(=\dfrac{1}{7}.\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\dfrac{6}{7}\)
\(=\dfrac{1}{7}.1+\dfrac{6}{7}\)
\(=\dfrac{1}{7}+\dfrac{6}{7}=1\)
b, \(\dfrac{6}{11}.\dfrac{4}{9}+\dfrac{6}{11}.\dfrac{7}{9}-\dfrac{6}{11}.\dfrac{2}{9}\)
\(=\dfrac{6}{11}.\left(\dfrac{4}{9}+\dfrac{7}{9}-\dfrac{2}{9}\right)\)
\(=\dfrac{6}{11}.1=\dfrac{6}{11}\)
c, \(\dfrac{4}{25}.\dfrac{5}{8}.\dfrac{25}{4}.24\)
\(=\left(\dfrac{4}{25}.\dfrac{25}{4}\right).\left(\dfrac{5}{8}.24\right)\)
\(=1.15=15\)
\(a,\dfrac{-6}{11}:\left(\dfrac{3}{5}:\dfrac{4}{11}\right)\) b,\(\dfrac{7}{12}+\dfrac{5}{12}:6-\dfrac{11}{36}\)
\(c,\left(\dfrac{4}{5}+\dfrac{1}{2}\right):\left(\dfrac{3}{13}-\dfrac{8}{13}\right)\) \(d,\left(\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}\right):\left(\dfrac{5}{12}-1-\dfrac{7}{11}\right)\)
Giúp mik nha:>>
a: \(=\dfrac{-6}{11}:\dfrac{3\cdot11}{4\cdot5}=\dfrac{-6}{11}\cdot\dfrac{20}{33}=\dfrac{-2}{11}\cdot\dfrac{20}{11}=\dfrac{-40}{121}\)
b: \(=\dfrac{7}{12}+\dfrac{5}{72}-\dfrac{11}{36}=\dfrac{42}{72}+\dfrac{5}{72}-\dfrac{22}{72}=\dfrac{25}{72}\)
c: \(=\dfrac{13}{10}:\dfrac{-5}{13}=\dfrac{-169}{50}\)
Giải ô chữ dưới đây.
Biết rằng.
L. \(\dfrac{7}{6}+\dfrac{8}{6}\) T. \(\dfrac{1}{11}+\dfrac{7}{11}+\dfrac{9}{11}\)
Ạ. \(\dfrac{4}{11}+\dfrac{2}{11}\) Đ. \(\dfrac{3}{6}+\dfrac{1}{6}+\dfrac{7}{6}\) À. \(\dfrac{3}{11}+\dfrac{9}{11}\)
L: \(\dfrac{7}{6}\) +\(\dfrac{8}{6}\) = \(\dfrac{15}{6}\)
T: \(\dfrac{1}{11}\) + \(\dfrac{7}{11}\) + \(\dfrac{9}{11}\) = \(\dfrac{17}{11}\)
Ạ: \(\dfrac{4}{11}\) + \(\dfrac{2}{11}\) = \(\dfrac{6}{11}\)
Đ: \(\dfrac{3}{6}\) + \(\dfrac{1}{6}\) + \(\dfrac{7}{6}\) = \(\dfrac{11}{6}\)
À: \(\dfrac{3}{11}\) + \(\dfrac{9}{11}\) = \(\dfrac{12}{11}\)
a) \(\dfrac{ 3}{ 4 }\)+\(\dfrac{ -7 }{ 5 }\)+\(\dfrac{ 1 }{ 4 }\)+\(\dfrac{ -3 }{ 5 }\) b) \(\dfrac{ 4 }{ 9 }.\dfrac{7 }{ 11 }-\dfrac{4 }{ 11 }.\dfrac{ 2 }{9 } + \dfrac{ 6 }{ 11 }.\dfrac{ 4 }{ 9 }\)
a) 3/4 + (-7/5) + 1/4 + (-3/5)
= (3/4 + 1/4) + (-7/5 - 3/5)
= 1 - 2
= -1
b) 4/9 . 7/11 - 4/11 . 2/9 + 6/11 . 4/9
= 4/9 . (7/11 - 2/11 + 6/11)
= 4/9 . 1
= 4/9
a)
\(\dfrac{3}{4}+\dfrac{-7}{5}+\dfrac{1}{4}+\dfrac{-3}{5}\)
\(=\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{-7}{5}-\dfrac{3}{5}\right)\)
\(=1-2\)
\(=-1\)
b)
\(\dfrac{4}{9}.\dfrac{7}{11}-\dfrac{4}{11}.\dfrac{2}{9}+\dfrac{6}{11}.\dfrac{4}{9}\)
\(=\dfrac{28}{99}-\dfrac{8}{99}+\dfrac{24}{99}\)
\(=\dfrac{28-8+24}{99}\)
\(=\dfrac{44}{99}\)
\(=\dfrac{4}{9}\)
>, <, = ?
a) \(\dfrac{5}{8}\) kg \(\dfrac{6}{8}\) kg b) \(\dfrac{11}{12}l\) \(\dfrac{11}{14}l\) c) \(\dfrac{5}{6}\) m \(\dfrac{17}{18}\) m
\(\dfrac{13}{12}\) kg 1 kg \(\dfrac{5}{3}l\) \(\dfrac{15}{9}l\) \(\dfrac{16}{7}\) m 2 m
a)
\(\dfrac{5}{8}\left(kg\right)< \dfrac{6}{8}\left(kg\right)\)
Do 13 > 12 nên \(\dfrac{13}{12}>1\)
hay: \(\dfrac{13}{12}\left(kg\right)>1\left(kg\right)\)
b)
\(\dfrac{11}{12}\left(l\right)>\dfrac{11}{14}\left(l\right)\)
Có:
\(\dfrac{5}{3}=\dfrac{5\times3}{3\times3}=\dfrac{15}{9}\)
nên: \(\dfrac{5}{3}\left(l\right)=\dfrac{15}{9}\left(l\right)\)
c)
\(\dfrac{5}{6}=\dfrac{5\times3}{6\times3}=\dfrac{15}{18n}\)
nên \(\dfrac{5}{6}\left(m\right)< \dfrac{17}{8}\left(m\right)\)
Có: \(2=\dfrac{2\times7}{7}=\dfrac{14}{7}\)
nên: \(\dfrac{16}{7}\left(m\right)>2\left(m\right)\)
a) So sánh hai phân số:
\(\dfrac{6}{11}\) và \(\dfrac{8}{11}\) \(\dfrac{13}{8}\) và \(\dfrac{8}{8}\) \(\dfrac{7}{24}\) và \(\dfrac{1}{6}\) \(\dfrac{3}{2}\) và \(\dfrac{5}{4}\)
b) Viết các phân số sau theo thứ tự từ bé đến lớn:
\(\dfrac{1}{4},\dfrac{3}{4}\) và \(\dfrac{5}{8}\) \(\dfrac{2}{3},\dfrac{2}{9}\) và \(\dfrac{5}{9}\)
a)
b)
+) Quy đồng mẫu số ba phân số $\frac{1}{4};\frac{3}{4};\frac{5}{8}$
$\frac{1}{4} = \frac{{1 \times 2}}{{4 \times 2}} = \frac{2}{8}$
$\frac{3}{4} = \frac{{3 \times 2}}{{4 \times 2}} = \frac{6}{8}$ ; Giữ nguyên phân số $\frac{5}{8}$
Vì $\frac{2}{8} < \frac{5}{8} < \frac{6}{8}$ nên $\frac{1}{4} < \frac{5}{8} < \frac{3}{4}$
Vậy các phân số xếp theo thứ tự từ bé đến lớn là: $\frac{1}{4};\,\,\frac{5}{8};\,\,\frac{3}{4}$
+) Quy đồng mẫu số ba phân số $\frac{2}{3};\,\,\frac{2}{9};\,\,\frac{5}{9}$
$\frac{2}{3} = \frac{{2 \times 3}}{{3 \times 3}} = \frac{6}{9}$ ; Giữ nguyên phân số $\frac{2}{9}$; $\frac{5}{9}$
Vì $\frac{2}{9} < \frac{5}{9} < \frac{6}{9}$ nên $\frac{2}{9} < \frac{5}{9} < \frac{2}{3}$
Vậy các phân số xếp theo thứ tự từ bé đến lớn là $\frac{2}{9};\,\,\frac{5}{9};\,\,\frac{2}{3}$
\(A=\dfrac{-2}{3}:\dfrac{11}{5}+\dfrac{-2}{3}:\dfrac{11}{6}+4\dfrac{2}{3}\)
\(B=\left(\dfrac{11^2}{200}+0,415\right):0,01-\left(-2\right)^3\)