Đề bài

Rút gọn các phân số sau để được phân số tối giản (có sử dụng ước chung lớn nhất): a) \(\frac{{24}}{{146}};\) b) \(\frac{{64}}{{92}};\) c) \(\frac{{27}}{{63}};\) d) \(\frac{{55}}{{185}}\); e)\(\frac{{51}}{{150}}\) ; g) \(\frac{{64}}{{156}}\).

Lời giải chi tiết

a) Ta có: \(24 = {2^3}.3;\quad 146 = 2.73\)\(\begin{array}{l} \Rightarrow UCLN(24,146) = 2\\ \Rightarrow \frac{{24}}{{146}} = \frac{{2.12}}{{2.73}} = \frac{{12}}{{73}}.\end{array}\)b) Ta có: \(64 = {2^6};\quad 92 = {2^2}.23\)\(\begin{array}{l} \Rightarrow UCLN(64,92) = {2^2} = 4\\ \Rightarrow \frac{{64}}{{92}} = \frac{{4.16}}{{4.23}} = \frac{{16}}{{23}}.\end{array}\)c) Ta có: \(27 = {3^3};\quad 63 = {3^2}.7\)\(\begin{array}{l} \Rightarrow UCLN(27,63) = {3^2} = 9\\ \Rightarrow \frac{{27}}{{63}} = \frac{{9.3}}{{9.7}} = \frac{3}{7}.\end{array}\)d) Ta có: \(55 = 5.11;\quad 185 = 5.37\)\(\begin{array}{l} \Rightarrow UCLN(55,185) = 5\\ \Rightarrow \frac{{55}}{{185}} = \frac{{5.11}}{{5.37}} = \frac{{11}}{{37}}.\end{array}\)e) Ta có: \(51 = 3.17;\quad 150 = {2.3.5^2}\)\(\begin{array}{l} \Rightarrow UCLN(51,150) = 3\\ \Rightarrow \frac{{51}}{{150}} = \frac{{3.17}}{{3.50}} = \frac{{17}}{{50}}.\end{array}\)g) Ta có: \(64 = {2^6};\quad 156 = {2^2}.3.13\)\(\begin{array}{l} \Rightarrow UCLN(64,156) = {2^2} = 4\\ \Rightarrow \frac{{64}}{{156}} = \frac{{4.16}}{{4.39}} = \frac{{16}}{{39}}.\end{array}\)