化简 (2 1/3-1/2)/(3/4+3 2/3)

解答

化简

\frac{2 \frac{1}{3} - \frac{1}{2}}{\frac{3}{4} + 3 \frac{2}{3}}

\frac{22}{53}

十进制

0.41509 \dots

求解步骤

\frac{2 \frac{1}{3} - \frac{1}{2}}{\frac{3}{4} + 3 \frac{2}{3}}

将带分数转换为假分式:

2 \frac{1}{3} = \frac{7}{3}

= \frac{\frac{7}{3} - \frac{1}{2}}{\frac{3}{4} + 3 \frac{2}{3}}

将带分数转换为假分式:

3 \frac{2}{3} = \frac{11}{3}

= \frac{\frac{7}{3} - \frac{1}{2}}{\frac{3}{4} + \frac{11}{3}}

\frac{7}{3} - \frac{1}{2} = \frac{11}{6}

= \frac{\frac{11}{6}}{\frac{3}{4} + \frac{11}{3}}

\frac{3}{4} + \frac{11}{3} = \frac{53}{12}

= \frac{\frac{11}{6}}{\frac{53}{12}}

使用分式法则:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{11 \cdot 12}{6 \cdot 53}

消掉

\frac{11 \cdot 12}{6 \cdot 53} : \frac{22}{53}

= \frac{22}{53}

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