tính nhanh 9/7 * 7/9 * 4/5 * 5/4
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có \(\frac{\frac{4}{5}-\frac{4}{11}+\frac{4}{13}}{\frac{9}{5}-\frac{9}{11}+\frac{9}{13}}+\frac{\frac{5}{7}+\frac{5}{11}-\frac{5}{13}}{\frac{9}{7}+\frac{9}{11}-\frac{9}{13}}\)
\(=\frac{4\left(\frac{1}{5}-\frac{1}{11}+\frac{1}{13}\right)}{9\left(\frac{1}{5}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{5\left(\frac{1}{7}+\frac{1}{11}-\frac{1}{13}\right)}{9\left(\frac{1}{7}+\frac{1}{11}-\frac{1}{13}\right)}\)
\(=\frac{4}{9}+\frac{5}{9}=\frac{9}{9}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
4/9 x ( 5/7 + 2/5 + -2/7 + 7/5)
Rồi sau đó bạn tự tính phần trong ngoặc ra(có thể sử dụng các tính chất của phân số để tính cho nhanh) rồi nhân với 4/9 là xong
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=\frac{\frac{4}{3}+\frac{4}{5}-\frac{4}{9}}{\frac{7}{3}+\frac{7}{5}-\frac{7}{9}}\)
\(=\frac{4.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)}{7.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)}\)
\(=\frac{4}{7}\)
B= \(\frac{\frac{4}{3}+\frac{4}{5}-\frac{4}{9}}{\frac{7}{3}+\frac{7}{5}-\frac{7}{9}}\)=\(\frac{4.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)}{7.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)}\)= \(\frac{4}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
= 51/20
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= 3/14
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= 4/7 - 2/7
= 2/7
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= 17/45
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= 2/3
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= 2 x 1/4
= 1/2
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=\(\frac{5}{7}\)x\(\frac{5}{11}\)-\(\frac{5}{7}\)x\(\frac{2}{11}\)-\(\frac{5}{7}\)x\(\frac{14}{4}\)
A= \(\frac{5}{7}\)x(\(\frac{5}{11}\)-\(\frac{2}{11}\)-\(\frac{14}{4}\))
A=\(\frac{5}{7}\)x(\(\frac{3}{11}\)-\(\frac{14}{4}\))
A=\(\frac{5}{7}\)x\(\frac{-71}{22}\)
A=\(\frac{-355}{154}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(=\dfrac{4}{5}\cdot\dfrac{7}{3}\cdot\dfrac{3}{7}\cdot\dfrac{5}{4}+2011=2011+1=2012\)
b: \(=\dfrac{1}{3}\cdot\dfrac{9}{7}\cdot\dfrac{7}{9}=\dfrac{1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`!`
\(a,\dfrac{8}{9}\times\dfrac{7}{5}-\dfrac{7}{9}\times\dfrac{2}{5}+\dfrac{2}{9}\\ =\dfrac{8}{9}\times\left(\dfrac{7}{5}-\dfrac{2}{5}\right)+\dfrac{2}{9}\\ =\dfrac{8}{9}\times\dfrac{5}{5}+\dfrac{2}{9}\\ =\dfrac{8}{9}+\dfrac{2}{9}\\ =\dfrac{10}{9}\)
\(b,\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{3}{12}\\ =\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{1}{4}\\ =\dfrac{1}{4}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)\\ =\dfrac{1}{4}\times\dfrac{9}{9}\\ =\dfrac{1}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(=\left(\dfrac{4}{9}+\dfrac{5}{9}\right)+\left(\dfrac{1}{8}+\dfrac{7}{8}\right)=1+1=2\)
b: \(=\left(\dfrac{1}{6}+\dfrac{4}{6}+\dfrac{7}{6}\right)+\left(\dfrac{5}{12}+\dfrac{7}{12}\right)=2+1=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Leftrightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
\(A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+\frac{4}{7.9.11}+\frac{4}{9.11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
Đáp án là 1 nha
\(\frac{9}{7}x\frac{7}{9}x\frac{4}{5}x\frac{5}{4}=1x1=1\)