Question

15．大于$\frac{2}{7}$而小于$\frac{4}{7}$的分?jǐn)?shù)只有$\frac{3}{7}$．×．（判斷對(duì)錯(cuò)）

Answer 1

分析 根據(jù)分?jǐn)?shù)的基本性質(zhì)可知，$\frac{2}{7}$=$\frac{4}{14}$=$\frac{6}{21}$=…，$\frac{4}{7}$=$\frac{8}{14}$=$\frac{12}{21}$=…，則大于$\frac{2}{7}$而小于$\frac{4}{7}$的分?jǐn)?shù)有$\frac{3}{7}$，$\frac{5}{14}$、$\frac{6}{14}$、$\frac{7}{14}$，$\frac{7}{21}$、$\frac{8}{21}$、$\frac{9}{21}$、$\frac{10}{21}$、$\frac{11}{21}$，…．即大于$\frac{2}{7}$而小于$\frac{4}{7}$的分?jǐn)?shù)有無(wú)數(shù)個(gè)．

解答 解：由于$\frac{2}{7}$=$\frac{4}{14}$=$\frac{6}{21}$=…，$\frac{4}{7}$=$\frac{8}{14}$=$\frac{12}{21}$=…，
則大于$\frac{2}{7}$而小于$\frac{4}{7}$的分?jǐn)?shù)有$\frac{3}{7}$，$\frac{5}{14}$、$\frac{6}{14}$、$\frac{7}{14}$，$\frac{7}{21}$、$\frac{8}{21}$、$\frac{9}{21}$、$\frac{10}{21}$、$\frac{11}{21}$，…．
即大于$\frac{2}{7}$而小于$\frac{4}{7}$的分?jǐn)?shù)有無(wú)數(shù)個(gè)．
故答案為：×．

點(diǎn)評(píng) 分?jǐn)?shù)的基本性質(zhì)：分?jǐn)?shù)的分子與分母同時(shí)乘或除以同一個(gè)數(shù)（0除外），分?jǐn)?shù)的大小不變．