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1. 75% .x - 1/1/5 = 0,6x
=> 3/4x - 6/5 = 3/5x
=> 6/5 = 3/4x - 3/5x
=> 6/5 = 3/20x
=> x = 6/5 : 3/20 = 8
2.4/x=-y/6=0,5
=> 4/x=1/2
=> 4/x = 4/8
=> x = 8
-y/6 = 1/2
=> y = -3
ta có 4/8 = -(-3)/6 = 1/2
3. 2/5 + 2/7 - 2/9 = 146/315
6/5+6/7-6/9=146/105
mà 146/105 > 146/315
=> 2/5+2/7-2/9 > 6/5+6/7-6/9
Ta có :
\(S=\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^9}\)
\(\Leftrightarrow\)\(3S=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\)
\(\Leftrightarrow\)\(3S-S=\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)-\left(\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^9}\right)\)
\(\Leftrightarrow\)\(2S=\frac{1}{3}-\frac{1}{3^9}\)
\(\Leftrightarrow\)\(2S=\frac{3^8-1}{3^9}\)
\(\Leftrightarrow\)\(S=\frac{3^8-1}{2.3^9}\)
Ở đây mk chỉ ghi \(...\) cho nhanh nếu bạn làm vào vở thì ghi đầy đủ ra nhé
Bài 1:
a) Ta có: \(\frac{3}{5}+\frac{4}{15}\)
\(=\frac{9}{15}+\frac{4}{15}\)
\(=\frac{13}{15}\)
b) Ta có: \(\frac{-3}{5}+\frac{5}{7}\)
\(=\frac{-21}{35}+\frac{25}{35}=\frac{4}{35}\)
c) Ta có: \(\frac{5}{6}:\frac{-7}{12}\)
\(=\frac{5}{6}\cdot\frac{-12}{7}=\frac{-60}{42}=\frac{-10}{7}\)
d) Ta có: \(\frac{-21}{24}:\frac{-14}{8}\)
\(=\frac{-7}{8}:\frac{-7}{4}\)
\(=\frac{-7}{8}\cdot\frac{4}{-7}=\frac{4}{8}=\frac{1}{2}\)
e) Ta có: \(\frac{-3}{5}\cdot\frac{5}{7}+\frac{-3}{5}\cdot\frac{3}{7}+\frac{-3}{5}\cdot\frac{6}{7}\)
\(=\frac{-3}{5}\left(\frac{5}{7}+\frac{3}{7}+\frac{6}{7}\right)\)
\(=-\frac{3}{5}\cdot2=\frac{-6}{5}\)
f) Ta có: \(\frac{1}{3}\cdot\frac{4}{5}+\frac{1}{3}\cdot\frac{6}{5}-\frac{4}{3}\)
\(=\frac{1}{3}\cdot\frac{4}{5}+\frac{1}{3}\cdot\frac{6}{5}-\frac{1}{3}\cdot4\)
\(=\frac{1}{3}\left(\frac{4}{5}+\frac{6}{5}-4\right)\)
\(=\frac{1}{3}\cdot\left(-2\right)=\frac{-2}{3}\)
g) Ta có: \(\frac{4}{19}\cdot\frac{-3}{7}+\frac{-3}{7}\cdot\frac{5}{19}+\frac{5}{7}\)
\(=\frac{4}{19}\cdot\frac{-3}{7}+\frac{5}{19}\cdot\frac{-3}{7}+\frac{-3}{7}\cdot\frac{5}{-3}\)
\(=-\frac{3}{7}\left(\frac{4}{19}+\frac{5}{19}+\frac{-5}{3}\right)\)
\(=\frac{-3}{7}\cdot\left(\frac{27}{57}+\frac{-95}{57}\right)\)
\(=\frac{-3}{7}\cdot\frac{-68}{57}=\frac{68}{133}\)
h) Ta có: \(\frac{5}{9}\cdot\frac{7}{13}+\frac{5}{9}\cdot\frac{9}{13}-\frac{5}{9}\cdot\frac{3}{13}\)
\(=\frac{5}{9}\left(\frac{7}{13}+\frac{9}{13}-\frac{5}{13}\right)\)
\(=\frac{5}{9}\)
Bài 2:
b: x+25%x=-1,25
=>1,25x=-1,25
hay x=-1
c: x-75%x=1/4
=>1/4x=1/4
hay x=1
Bài 2:
a: =3/2-11/4=6/4-11/4=-5/4
b: =-49/6-17/2=-49/6-51/6=-100/6=-50/3
e. \(\frac{-3}{5}\cdot\frac{5}{7}+\frac{-3}{5}\cdot\frac{3}{7}+\frac{-3}{5}\cdot\frac{6}{7}=-\frac{3}{5}\left(\frac{5}{7}+\frac{3}{7}+\frac{6}{7}\right)=-\frac{3}{5}\cdot2=-\frac{6}{5}\)
f. \(\frac{1}{3}\cdot\frac{4}{5}+\frac{1}{3}\cdot\frac{6}{5}-\frac{4}{5}=\frac{1}{3}\left(\frac{4}{5}+\frac{6}{5}\right)-\frac{4}{5}=\frac{1}{3}\cdot2-\frac{4}{5}=\frac{2}{3}-\frac{4}{5}=-\frac{2}{15}\)
g. \(\frac{4}{19}\cdot\frac{-3}{7}+\frac{-3}{7}\cdot\frac{15}{19}+\frac{5}{7}=-\frac{3}{7}\left(\frac{4}{19}+\frac{15}{19}\right)+\frac{5}{7}=-\frac{3}{7}\cdot1+\frac{5}{7}=-\frac{3}{7}+\frac{5}{7}=\frac{2}{7}\)
h. \(\frac{5}{9}\cdot\frac{7}{13}+\frac{5}{9}\cdot\frac{9}{13}-\frac{5}{9}\cdot\frac{3}{13}=\frac{5}{9}\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)=\frac{5}{9}\cdot1=\frac{5}{9}\)
1. \(MSC=BCNN(5,9)=45\)
Quy đồng :
\(\frac{4}{5}=\frac{4\cdot9}{5\cdot9}=\frac{36}{45}\)
\(\frac{6}{9}=\frac{6\cdot5}{9\cdot5}=\frac{30}{45}\)
Mà \(36>30\Rightarrow\frac{36}{45}>\frac{30}{45}\). Vậy : \(\frac{4}{5}>\frac{6}{9}\)
2. \(\frac{9}{7}+\frac{6}{7}=\frac{15}{7}\)
\(\frac{7}{9}+\frac{7}{6}=\frac{42}{54}+\frac{63}{54}=\frac{105}{54}=\frac{35}{18}\)
Tự so sánh :v