so sánh 2 phân số sau \(\frac{3}{-4}vs\frac{-1}{-4}\): \(\frac{15}{17}vs\frac{25}{27}\)
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a) \(\frac{3}{-4}=\frac{-3}{4};\frac{-1}{-4}=\frac{1}{4}\)
Vì - 3 < 1 nên \(\frac{-3}{4}< \frac{1}{4}\)
hay \(\frac{3}{-4}< \frac{-1}{-4}\)
Quy đồng mẫu ta được:
15/17=15.27/17.27=405/459
25/27=25.17/27.27=425/459
⇒405/459<425/459⇒15/17<25/27

Bài 1:
A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + (\(\frac45\) - \(\frac{3}{17}\) + \(\frac13\)) - \(\frac17\) + (- \(\frac{14}{30}\))
A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + \(\frac45\) - \(\frac{3}{17}\) + \(\frac13\) - \(\frac17\) - \(\frac{14}{30}\)
A = (\(\frac15\) + \(\frac45\)) + (\(\frac{3}{17}\) - \(\frac{3}{17}\)) - (\(\frac43-\frac13\)) - \(\frac{30}{210}\) - \(\frac{98}{210}\)
A = 1 + 0 - 1 - (\(\frac{30}{210}+\frac{98}{210}\))
A = 1 - 1 - \(\frac{228}{210}\)
A = 0 - \(\frac{128}{210}\)
A = - \(\frac{64}{105}\)
Bài 2:
B= (\(\frac58\) - \(\frac{4}{12}\) + \(\frac32\)) - (\(\frac58\) + \(\frac{9}{13}\)) - (\(\frac{-3}{2}\)) + \(\frac{7}{-15}\)
B = \(\frac58\) - \(\frac{4}{12}\) + \(\frac32\) - \(\frac58\) - \(\frac{9}{13}\) + \(\frac32\) - \(\frac{7}{15}\)
B = (\(\frac58\) - \(\frac58\)) + (\(\frac32\) + \(\frac32\)) - (\(\frac13\) + \(\frac{9}{13}\) + \(\frac{7}{15}\))
B = 0 + 3 - (\(\frac{65}{195}\) + \(\frac{135}{195}\) + \(\frac{91}{195}\))
B = 3 - (\(\frac{200}{195}\) + \(\frac{91}{195}\))
B = 3 - \(\frac{97}{65}\)
B = \(\frac{195}{65}\) - \(\frac{97}{65}\)
B = \(\frac{98}{65}\)

Vì \(2^{25}+1< 2^{27}+1\) nên \(\frac{2^{25}+1}{2^{27}+1}< 1\)
\(\Rightarrow\frac{2^{25}+1}{2^{27}+1}< \frac{2^{25}+1+3}{2^{27}+1+3}=\frac{2^{25}+4}{2^{27}+4}=\frac{2^2\left(2^{23}+1\right)}{2^2\left(2^{25}+1\right)}=\frac{2^{23}+1}{2^{25}+1}\)
Vậy \(\frac{2^{25}+1}{2^{27}+1}< \frac{2^{23}+1}{2^{25}+1}\)

\(\frac{\frac{4}{17}-\frac{4}{45}+\frac{4}{156}}{\frac{3}{17}-\frac{3}{45}+\frac{3}{156}}=\frac{4.\left(\frac{1}{17}-\frac{1}{45}+\frac{1}{156}\right)}{3.\left(\frac{1}{17}-\frac{1}{45}+\frac{1}{156}\right)}=\frac{4}{3}\)

Vì 15.27 < 17.25 nên \(\frac{15}{17}< \frac{25}{27}\)

d.
\(-\frac{31}{30}< -1\)
\(-1< -\frac{45}{47}\)
\(\Rightarrow-\frac{31}{30}< -\frac{45}{47}\)
Chúc bạn học tốt
Ta có : \(\frac{3}{-4}=\frac{-3}{4}< 0\)
\(\frac{-1}{-4}=\frac{1}{4}>0\)
\(\Rightarrow\frac{3}{-4}< \frac{-1}{-4}\) hay \(\frac{-3}{4}< \frac{1}{4}\)
Vậy : ....
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