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\(a.\) \(25,4-\frac{1}{4}\div x+1250\%=37,5\)
\(25,4-0.25\div x+12,5=37,5\)
\(25,4-0,25\div x=37,5-12,5\)
\(25,4-0,25\div x=25\)
\(0,25\div x=25,4-25\)
\(0,25\div x=0,4\)
\(x=0,25\div0,4\)
\(x=0,625\)
\(b.\)\(3\frac{1}{8}\div\left(\frac{2}{5}-x\right)\times\frac{8}{25}=3\)
\(\frac{3\times8+1}{8}\div\left(\frac{2}{5}-x\right)=3\div\frac{8}{25}\)
\(\frac{25}{8}\div\left(\frac{2}{5}-x\right)=\frac{75}{8}\)
\(\frac{2}{5}-x=\frac{25}{8}\div\frac{75}{8}\)
\(\frac{2}{5}-x=\frac{25}{8}\times\frac{8}{75}\)
\(\frac{2}{5}-x=\frac{1}{3}\)
\(x=\frac{2}{5}-\frac{1}{3}=\frac{6}{15}-\frac{5}{15}\)
\(x=\frac{1}{15}\)
a)25,4-\(\frac{1}{4}\): x +1250%=37,5
25,4 - 0,25 : x + 12,5 = 37,5
25,4 - 0,25 : x =37,5 -12,5
25,4 - 0,25 : x = 25
0,25 : x = 25,4 -25
0,25 : x = 0,4
x = 0,25;0,4
x = 0,625
b) \(3\frac{1}{8}:\left(\frac{2}{5}-x\right)\times\frac{8}{25}=3\)
\(3,125:\left(0,4-x\right)\times0,32=3\)
\(3,125:\left(0,4-x\right)=3:0,32\)
\(3,125:\left(0,4-x\right)=9,375\)
\(0,4-x=3,125:9,375\)
\(0,4-x=\frac{1}{3}\)
\(x=0,4-\frac{1}{3}\)
\(x=\frac{1}{15}\)
\(x+x\times3:\frac{2}{9}+x:\frac{2}{7}=252\)
\(x+x\times\left(3:\frac{2}{9}\right)+x\times\frac{7}{2}=252\)
\(x+x\times\frac{27}{2}+x\times\frac{7}{2}=252\)
\(x\times\left(1+\frac{27}{2}+\frac{7}{2}\right)=252\)
\(x\times18=252\)
\(x=14\)
\(\left[12\cdot15-x\right]\cdot\frac{1}{4}=120\cdot\frac{1}{4}\)
\(\Leftrightarrow\left[180-x\right]\cdot\frac{1}{4}=30\)
\(\Leftrightarrow180-x=30:\frac{1}{4}\)
\(\Leftrightarrow180-x=120\)
\(\Leftrightarrow x=60\)
a, 7/5 : x + 3/2 = 16/3
7/5 : x = 16/3 - 3/2
7/5 : x = 23/6
x = 7/5 : 23/6
x = 42/115
b, x : 1/5 + 1/7 = 3/5 . 18/21
x : 1/5 + 1/7 = 18/35
x : 1/5 = 18/35 - 1/7
x : 1/5 = 13/35
x = 13/35 . 1/5
x = 13/175
c, x - 1 và 1/3 : 2 = 5/7
x - 4/3 : 2 = 5/7
x - 4/3 = 5/7 . 2
x - 4/3 = 10/7
x = 10/7 + 4/3
x = 58/21
d, x + 2 và 3/5 . 1/6 = 35/36
x + 13/5 . 1/6 = 35/36
x + 13/5 = 35/36 : 1/6
x + 13/5 = 35/6
x = 35/6 - 13/5
x = 97/30
e, ( x + 3/2 ) : 2 = 7/10 + 1/5
( x + 3/2 ) : 2 = 9/10
x + 3/2 = 9/10 . 2
x + 3/2 = 9/5
x = 9/5 - 3/2
x = 3/10
\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(\Rightarrow M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow M=1-\frac{1}{100}\)
\(\Rightarrow M=\frac{100}{100}-\frac{1}{100}=\frac{99}{100}\)
\(b,N=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\)
\(\Rightarrow N=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)\)
\(\Rightarrow N=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{97}-\frac{1}{99}\right)\)
\(\Rightarrow N=\frac{1}{2}.\left(1-\frac{1}{99}\right)=\frac{1}{2}.\frac{98}{99}\)
\(\Rightarrow N=\frac{1.98}{2.99}=\frac{49.2}{2.99}=\frac{49}{99}\)
\(a,M=1-\frac{1}{100}=\frac{99}{100}\)
\(b=2N=\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{97x99}\)
\(=1-\frac{1}{99}=\frac{98}{99}\)
=>\(N=\frac{98}{99}:2=\frac{49}{99}\)
\(\dfrac{3}{4}\times\dfrac{8}{5}:1\dfrac{1}{6}\)
=\(\dfrac{6}{5}:\) \(\dfrac{7}{6}\)
=\(\dfrac{6}{5}\times\dfrac{6}{7}=\dfrac{36}{35}\)
2\(\dfrac{1}{3}\) x 1\(\dfrac{1}{4}\) -\(\dfrac{7}{5}\)
\(\dfrac{7}{3}\times\dfrac{5}{4}-\) \(\dfrac{7}{5}\)
\(\dfrac{35}{12}-\dfrac{7}{5}\)
\(\dfrac{175}{60}-\dfrac{84}{60}=\dfrac{91}{60}\)
4\(\dfrac{2}{3}+1\dfrac{1}{4} +2\dfrac{1}{3}+2\dfrac{3}{7}\)
(4 +2) + \(\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\) +1\(\dfrac{1}{4}\) + \(2\dfrac{3}{7}\)
6 + 1 + \(\dfrac{5}{4}\) + \(\dfrac{17}{7}\)
7 + \(\dfrac{103}{28}\)
\(\dfrac{299}{28}\)
Theo đề bài ,ta có biểu thức sau :
x * 2 + x * 1/5 = 1 và 3/5
x * 2 + x * 1/5 = 8/5
x * ( 2+1/5 ) = 8/5
x * 11/5 = 8/5
x = 8/5 : 11/5
x = 8/11