2 脱式计算。注意运算顺序，能简算的要简算。(2)/(9)+(1)/(2) div (4)/(7) (35)/(24) times (4)/(25) div (14)/(15) ((7)/(12)-(5)/(36))div (1)/(6)(7)/(9) div ((7)/(9)times (2)/(3)) (2)/(9)times (1)/(5)+(7)/(9) div 5 (5)/(6) times [(1)/(2) div ((3)/(4)-(1)/(3))]
题目解答
答案
- $\frac{2}{9} + \frac{1}{2} \div \frac{4}{7} = \frac{2}{9} + \frac{7}{8} = \frac{79}{72}$
- $\frac{35}{24} \times \frac{4}{25} \div \frac{14}{15} = \frac{7}{30} \times \frac{15}{14} = \frac{1}{4}$
- $(\frac{7}{12} - \frac{5}{36}) \div \frac{1}{6} = \frac{4}{9} \times 6 = \frac{8}{3}$
- $\frac{7}{9} \div (\frac{7}{9} \times \frac{2}{3}) = \frac{7}{9} \times \frac{27}{14} = \frac{3}{2}$
- $\frac{2}{9} \times \frac{1}{5} + \frac{7}{9} \div 5 = \frac{2}{45} + \frac{7}{45} = \frac{1}{5}$
- $\frac{5}{6} \times [\frac{1}{2} \div (\frac{3}{4} - \frac{1}{3})] = \frac{5}{6} \times \frac{6}{5} = 1$
答案：
$\boxed{\begin{array}{cccccc}\frac{79}{72} & \frac{1}{4} & \frac{8}{3} & \frac{3}{2} & \frac{1}{5} & 1 \\\end{array}}$
解析
考查要点：本题主要考查分数的四则混合运算能力，包括运算顺序、分数除法的转化、约分技巧、简便运算方法（如乘法分配律、除法性质等）。
解题核心思路：
- 运算顺序：先处理括号内运算，再按乘除优先、加减后的顺序计算；
- 分数除法转乘法：除以一个分数等于乘以它的倒数；
- 约分简化：在乘除运算中优先约分，减少计算量；
- 简便运算：观察算式结构，灵活运用除法性质（如$a \div (a \times b) = \frac{1}{b}$）或乘法分配律。
第1题 $\frac{2}{9}+\frac{1}{2} \div \frac{4}{7}$
处理除法
$\frac{1}{2} \div \frac{4}{7} = \frac{1}{2} \times \frac{7}{4} = \frac{7}{8}$
加法运算
$\frac{2}{9} + \frac{7}{8} = \frac{16}{72} + \frac{63}{72} = \frac{79}{72}$
第2题 $\frac{35}{24} \times \frac{4}{25} \div \frac{14}{15}$
乘除法连续运算
$\frac{35}{24} \times \frac{4}{25} = \frac{35 \times 4}{24 \times 25} = \frac{7}{30}$
$\frac{7}{30} \div \frac{14}{15} = \frac{7}{30} \times \frac{15}{14} = \frac{1}{4}$
第3题 $(\frac{7}{12}-\frac{5}{36}) \div \frac{1}{6}$
括号内减法
$\frac{7}{12} - \frac{5}{36} = \frac{21}{36} - \frac{5}{36} = \frac{16}{36} = \frac{4}{9}$
除法转乘法
$\frac{4}{9} \div \frac{1}{6} = \frac{4}{9} \times 6 = \frac{24}{9} = \frac{8}{3}$
第4题 $\frac{7}{9} \div (\frac{7}{9} \times \frac{2}{3})$
利用除法性质简化
$\frac{7}{9} \div \left(\frac{7}{9} \times \frac{2}{3}\right) = \frac{7}{9} \div \frac{14}{27} = \frac{7}{9} \times \frac{27}{14} = \frac{3}{2}$
第5题 $\frac{2}{9}\times \frac{1}{5}+\frac{7}{9} \div 5$
统一为乘法
$\frac{2}{9} \times \frac{1}{5} + \frac{7}{9} \times \frac{1}{5} = \left(\frac{2}{9} + \frac{7}{9}\right) \times \frac{1}{5} = 1 \times \frac{1}{5} = \frac{1}{5}$
第6题 $\frac{5}{6} \times \left[\frac{1}{2} \div \left(\frac{3}{4}-\frac{1}{3}\right)\right]$
括号内减法
$\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12}$
处理除法
$\frac{1}{2} \div \frac{5}{12} = \frac{1}{2} \times \frac{12}{5} = \frac{6}{5}$
最终乘法
$\frac{5}{6} \times \frac{6}{5} = 1$