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\(\frac{33\cdot10^3}{2^3\cdot5\cdot10^3+7000}=\frac{33\cdot10^3}{40\cdot10^3+7\cdot10^3}=\frac{33\cdot10^3}{\left(40+7\right)\cdot10^3}=\frac{33}{47}\)
\(\frac{3774}{5217}=\frac{2\cdot3\cdot17\cdot37}{3\cdot37\cdot47}=\frac{2\cdot17}{47}=\frac{34}{47}\)
Vì 33 < 34 => \(\frac{33}{47}< \frac{34}{47}\)hay \(\frac{33\cdot10^3}{2^3\cdot5\cdot10^3+7000}< \frac{3774}{5217}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{33.10^3}{2^3.5.10^3+7000}=\frac{33.10^3}{2^3.5.10^3+7.10^3}=\frac{33.10^3}{10^3\left(2^3.5+7\right)}=\frac{33}{8.5+7}=\frac{33}{47}\)
\(\frac{3774}{5217}=\frac{3774:111}{5217:111}=\frac{34}{47}\)
Vì \(\frac{33}{47}< \frac{34}{47}\Rightarrow\frac{33.10^3}{2^3.5.10^3+7000}< \frac{3774}{5217}\)
\(\frac{33.10^3}{2^3.5.10^3+7000}=\frac{33.10^3}{8.5.10^3+7.10^3}\)
=\(\frac{33.10^3}{10^3\left(40+7\right)}=\frac{33}{47}\)
\(\frac{3774}{5217}=\frac{111.34}{111.47}=\frac{34}{47}\)
Vậy: \(\frac{3774}{5217}>\frac{33.10^3}{2^3.5.10^3+7000}\)
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Áp dụng tính chất cơ bản của phân số để rút gọn:
\(\frac{33.10^3}{2^3.5.10^3+7000}=\frac{33.10^3}{2^3.5.10^3+7.10^3}=\frac{33.10^3}{10^3\left(40+7\right)}=\frac{33}{47}\) (1)
\(\frac{3774}{5217}=\frac{3774\div111}{5217\div111}=\frac{34}{47}\) (2)
Từ (1) và (2) ta có: \(\frac{3774}{5217}>\frac{33.10^3}{2^3.5.10^3+7000}\)
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\(A=\frac{33\cdot10^3}{2^3\cdot5\cdot10^3+7000}=\frac{33\cdot10^3}{2^3\cdot5\cdot10^3+7\cdot10^3}=\frac{33\cdot10^3}{10^3(2^3\cdot5+7)}=\frac{33\cdot10^3}{10^3\cdot47}=\frac{33}{47}\)
\(B=\frac{3774}{5217}=\frac{34\cdot111}{47\cdot111}=\frac{34}{47}\)
\(=>\frac{33}{47}< \frac{34}{47}\)nên \(A< B\)
\(\frac{33.10^3}{2^3.5.10^3+7000}\)= \(\frac{33.10^3}{2^3.5.10^3+7.10^3}\)
=\(\frac{33.10^3}{10^3.\left(2^3.5+7\right)}\)
=\(\frac{33.10^3}{10^3.47}\)
=\(\frac{33}{47}\)