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1)
\(\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}\cdot\left(-2\right)^2\\ =\dfrac{6}{7}+\dfrac{5}{8}\cdot\dfrac{1}{5}-\dfrac{3}{16}\cdot4\\ =\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\\ =\dfrac{55}{16}-\dfrac{3}{4}\\ =\dfrac{13}{56}\)
2)
\(-\dfrac{1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{\left(-2\right)^2}{5}\\ =-\dfrac{1}{6}-\dfrac{1}{2}+\dfrac{4}{5}\\ =-\dfrac{2}{3}+\dfrac{4}{5}\\ =\dfrac{2}{15}\)
3)
\(2\dfrac{3}{4}\cdot\left(-0,4\right)+1\dfrac{3}{5}\cdot1,75+\left(-7,2\right):\dfrac{9}{11}\)
\(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{8}{5}\cdot\dfrac{7}{4}-\dfrac{36}{5}\cdot\dfrac{11}{9}\\ =-\dfrac{11}{10}+\dfrac{14}{5}-\dfrac{44}{5}\\ =-\dfrac{11}{10}-6\\ =-\dfrac{71}{10}\)
4)
\(\dfrac{1}{8}\cdot15\dfrac{2}{5}+1\dfrac{4}{5}\cdot\dfrac{7}{8}-17\dfrac{1}{5}\cdot\dfrac{1}{8}\)
\(=\dfrac{1}{8}\cdot\dfrac{77}{5}+\dfrac{9}{5}\cdot\dfrac{7}{8}-\dfrac{86}{5}\cdot\dfrac{1}{8}\)
\(=\dfrac{1}{8}\cdot\dfrac{77}{5}+\dfrac{63}{5}\cdot\dfrac{1}{8}-\dfrac{86}{5}\cdot\dfrac{1}{8}\)
\(=\dfrac{1}{8}\left(\dfrac{77}{5}+\dfrac{63}{5}-\dfrac{86}{5}\right)\\ =\dfrac{1}{8}\cdot\dfrac{54}{5}\\ =\dfrac{27}{20}\)
1: \(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{16}\cdot4=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\)
\(=\dfrac{48}{56}+\dfrac{7}{56}-\dfrac{42}{56}=\dfrac{13}{56}\)
2: \(=-\dfrac{1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{4}{5}\)
\(=\dfrac{19}{30}-\dfrac{1}{2}=\dfrac{19}{30}-\dfrac{15}{30}=\dfrac{4}{30}=\dfrac{2}{15}\)
3: \(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{8}{5}\cdot\dfrac{7}{4}+\dfrac{-36}{5}\cdot\dfrac{11}{9}\)
\(=\dfrac{-22+56}{20}+\dfrac{-44}{5}\)
\(=\dfrac{-71}{10}\)
1) \(\frac{5}{8}.\frac{7}{3}-\frac{5}{2}.\frac{1}{8}=\frac{5}{8}.\frac{7}{3}-\frac{5}{8}.\frac{1}{2}=\frac{5}{8}\left(\frac{7}{3}-\frac{1}{2}\right)=\frac{5}{8}.\frac{11}{6}=\frac{55}{48}\)
2) \(\frac{21}{10}.\frac{3}{4}-\frac{21}{10}.\frac{3}{4}=\frac{21}{10}\left(\frac{3}{4}-\frac{3}{4}\right)=\frac{21}{10}.0=0\)
3) \(\frac{-4}{11}:\frac{-6}{11}=\frac{-4}{11}.\frac{-11}{6}=\frac{-4.\left(-11\right)}{11.6}=\frac{-4.\left(-1\right)}{1.6}=\frac{4}{6}=\frac{2}{3}\)
4)\(\frac{2}{7}.\frac{14}{3}-1=\frac{2.14}{7.3}-1=\frac{2.2}{1.3}-1=\frac{4}{3}-1=\frac{1}{3}\)
5)\(\frac{4}{7}:\left(\frac{1}{5}.\frac{4}{7}\right)=\frac{4}{7}:\frac{4}{35}=\frac{4}{7}.\frac{35}{4}=\frac{4.35}{7.4}=\frac{1.5}{1.1}=5\)
6) \(\frac{12}{7}.\frac{7}{4}+\frac{35}{11}:\frac{245}{121}=\frac{12.7}{7.4}+\frac{35}{11}.\frac{121}{245}=\frac{3.1}{1.1}+\frac{35}{11}.\frac{121}{245}=3+\frac{35}{11}.\frac{121}{245}=3+\frac{35.121}{11.245}=\frac{1.11}{1.7}=\frac{11}{7}\)
a; \(\dfrac{3}{11}\) + \(\dfrac{5}{-9}\) + \(\dfrac{4}{11}\) - \(\dfrac{4}{9}\) + \(\dfrac{3}{17}\) + \(\dfrac{15}{11}\)
= (\(\dfrac{3}{11}\) + \(\dfrac{4}{11}\) + \(\dfrac{15}{11}\)) - (\(\dfrac{5}{9}\) + \(\dfrac{4}{9}\)) + \(\dfrac{3}{17}\)
= 2 - 1 + \(\dfrac{3}{17}\)
= 1 + \(\dfrac{3}{17}\)
= \(\dfrac{20}{17}\)
c; N = \(\dfrac{\dfrac{5}{7}-\dfrac{5}{9}-\dfrac{5}{11}}{\dfrac{15}{7}+\dfrac{15}{9}+\dfrac{15}{11}}\)
Phải là - \(\dfrac{5}{7}\) chỗ tử số mới đúng em nhé!
Câu a )
\(-\frac{3}{5}+\frac{9}{16}+-\frac{2}{5}+\frac{7}{16}=\left(-\frac{3}{5}+-\frac{2}{5}\right)+\left(\frac{9}{16}+\frac{7}{16}\right).\)
\(=\left(-1\right)+1=0\)
hk tốt !
\(\left(-\frac{1}{2}\right)^2\cdot2\cdot\frac{7}{4}\div\left(\frac{5}{8}-1\frac{3}{16}\right)\)
\(=\frac{1}{4}\cdot2\cdot\frac{7}{4}\div\left(\frac{10}{16}-\frac{19}{16}\right)\)
\(=\frac{7}{8}\div\left(-\frac{9}{10}\right)\)
\(=\frac{7}{8}\cdot\left(-\frac{10}{9}\right)\)
\(=-\frac{35}{36}\)
-1/2^2.7/4:(5/8-1 3/16)=1/4.7/4:(5/8-19/16)=1/4.7/4:(10/16-19/16)=1/4.7/4:-9/16=1/4.7/4.-16/9=1/4.-28/9=-7/9
Bài 2:
Ta thấy: 52 > 4.5
62 > 5.6
72 > 6.7
....
20172 > 2016.2017
\(\Rightarrow\)\(\frac{1}{5^2}< \frac{1}{4.5}\)
\(\frac{1}{6^2}< \frac{1}{5.6}\)
\(\frac{1}{7^2}< \frac{1}{6.7}\)
....
\(\frac{1}{2017^2}< \frac{1}{2016.2017}\)
Cộng vế với nhau, ta có:
\(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2017^2}\) < \(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{2016.2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{2016}-\frac{1}{2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}-\frac{1}{2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}\)( vì \(\frac{1}{2017}>0\))
k giúp mik ✅
a) 1/2 + 3/4 - (3/4 - 4 - 5)
= 1/2 + 3/4 - 3/4 + 4 + 5
= (3/4 - 3/4) + (4 + 5) + 1/2
= 0 + 9 + 1/2
= 19/2
b) [9/16 + 8/(-27)] - (19/27- 7/16 - 2)
= 9/16 - 8/27 - 19/27 + 7/16 + 2
= (9/16 + 7/16) + (-8/27 - 19/27) + 2
= 1 - 1 + 2
= 2
c) -5/8 . [4/9 + 7/(-12)]
= -5/8 . (-5/36)
= 25/288
d) 7/10 . (-3/5) + 7/10 . (-2/5) - (-3/10)
= 7/10 . (-3/5 - 2/5) + 3/10
= 7/10 . (-1) + 3/10
= -2/5
e) -3/7 . 5/9 + 4/9 . (-3/7) + 2 3/7
= -3/7 . (5/9 + 4/9) + 17/7
= -3/7 . 1 + 17/7
= 2
f) 8 2/7 - (3 4/9 + 4 2/7)
= 8 + 2/7 - 3 - 4/9 - 4 - 2/7
= (8 - 3 - 4) + (2/7 - 2/7) - 4/9
= 1 - 4/9
= 5/9
h) 3.(-1/2)² - (4/5 + 8/15) : 5/6
= 3.1/4 - 4/3 : 5/6
= 3/4 - 8/5
= -17/20