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a) -90/189 + 45/84 - 78/126
= -10/21 + 15/28 - 13/21
= (-10/21 - 13/21) + 15/28
= -24/21 + 15/28
= -17/28
\(=\dfrac{1}{2}\cdot\dfrac{3}{4}+\dfrac{5}{8}=\dfrac{3}{8}+\dfrac{5}{8}=1\)
1. \(\Leftrightarrow\frac{59-x}{41}+1+\frac{57-x}{43}+1+\frac{55-x}{45}+1+\frac{51-x}{49}+1=-5+5\)
\(\Leftrightarrow\frac{100-x}{41}+\frac{100-x}{43}+\frac{100-x}{45}+\frac{100-x}{47}+\frac{100-x}{49}=0\)
\(\Leftrightarrow\left(100-x\right)\left(\frac{1}{41}+\frac{1}{43}+\frac{1}{45}+\frac{1}{47}+\frac{1}{49}\right)=0\)
\(\Leftrightarrow x-100=0\Leftrightarrow x=100\)
2. \(\Leftrightarrow\frac{x-5}{1990}+1+\frac{x-15}{1980}+1+\frac{x-25}{1970}=\frac{x-1990}{5}+1+\frac{x-1980}{15}+1+\frac{x-1970}{25}+1\)
\(\Leftrightarrow\frac{x-1995}{1990}+\frac{x-1995}{1980}+\frac{x-1995}{1970}=\frac{x-1995}{5}+\frac{x-1995}{15}+\frac{x-1995}{25}\)
\(\Leftrightarrow\frac{x-1995}{1990}+\frac{x-1995}{1980}+\frac{x-1995}{1970}-\frac{x-1995}{5}-\frac{x-1995}{15}-\frac{x-1995}{25}=0\)
\(\Leftrightarrow\left(x-1995\right)\left(\frac{1}{1990}+\frac{1}{1980}+\frac{1}{1970}-\frac{1}{5}-\frac{1}{15}-\frac{1}{25}\right)=0\)
\(\Leftrightarrow x-1995=0\Leftrightarrow x=1995\)
Câu 1;
\(\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}-\frac{2}{7}-\frac{2}{13}}\cdot\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{64}-\frac{3}{256}}{1-\frac{1}{4}-\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)
\(=\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{2\left(\frac{1}{3}-\frac{1}{7}-\frac{1}{13}\right)}\cdot\frac{3\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{64}-\frac{1}{256}\right)}{4\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{64}-\frac{1}{256}\right)}+\frac{5}{8}\)
\(=\frac{1}{2}\cdot\frac{3}{4}+\frac{5}{8}=\frac{3}{8}+\frac{5}{8}=1\)
Câu 2:
\(\frac{0,75-0,6+\frac{3}{7}+\frac{3}{13}}{2,75-2,2+\frac{11}{7}+\frac{11}{3}}=\frac{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}+\frac{3}{13}}{\frac{11}{4}-\frac{11}{5}+\frac{11}{7}+\frac{11}{3}}=\frac{3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}{11\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{13}\right)}=\frac{3}{11}\)
Câu 1;
13 −17 −113 23 −27 −213 ·34 −316 −364 −3256 1−14 −116 −164 +58
=13 −17 −113 2(13 −17 −113 ) ·3(14 −116 −164 −1256 )4(14 −116 −164 −1256 ) +58
=12 ·34 +58 =38 +58 =1
Câu 2:
\(\frac{74-x}{26}+\frac{75-x}{25}+\frac{76-x}{24}+\frac{77-x}{23}+\frac{78-x}{22}=-5\)
\(\frac{74-x}{26}+1+\frac{75-x}{25}+1+\frac{76-x}{24}+1+\frac{77-x}{23}+1+\frac{78-x}{22}=-5+5\)
\(\frac{74-x}{26}+\frac{26}{26}+\frac{75-x}{25}+\frac{25}{25}+\frac{76-x}{24}+\frac{24}{24}+\frac{77-x}{23}+\frac{23}{23}+\frac{78-x}{22}+\frac{22}{22}=0\)
\(\frac{100-x}{26}+\frac{100-x}{25}+\frac{100-x}{24}+\frac{100-x}{23}+\frac{100-x}{22}=0\)
\(\left(100-x\right)\left(\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{23}+\frac{1}{22}\right)=0\)
=>100-x=0 ( \(\left(\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{23}+\frac{1}{22}\right)\ne0\))
x=100
hahaha
a/ Ta có:
\(\frac{3}{124}=\frac{30}{1240}\) ; \(\frac{1}{41}=\frac{30}{1230}\) ; \(\frac{5}{207}=\frac{30}{1242}\) ; \(\frac{2}{83}=\frac{30}{1245}\)
Vì các phân số trên đều cùng tử nên ta so sánh mẫu : 1230<1240<1242<1242
=> \(\frac{30}{1230}>\frac{30}{1240}>\frac{30}{1242}>\frac{30}{1245}\)
Hay : \(\frac{1}{41}>\frac{3}{124}>\frac{5}{207}>\frac{2}{83}\)
b/ Ta có:
\(\frac{16}{9}=\frac{48}{27};\frac{24}{13}=\frac{48}{26}\)
Vì 27>26
=> \(\frac{16}{9}< \frac{24}{13}\)
3124=3012403124=301240 ; 141=301230141=301230 ; 5207=3012425207=301242 ; 283=301245283=301245
Vì các phân số trên đều cùng tử nên ta so sánh mẫu : 1230<1240<1242<1242
=> 301230>301240>301242>301245301230>301240>301242>301245
Hay : 141>3124>5207>283141>3124>5207>283
b/ Ta có:
169=4827;2413=4826169=4827;2413=4826
Vì 27>26
=> 169<2413169<2413