题目内容

5.脱式计算下列各题,能简算的要简算.
(1)$\frac{4}{9}×\frac{1}{5}÷\frac{4}{5}$       
(2)$24×(\frac{1}{8}+\frac{1}{6})$
(3)$\frac{3}{5}×\frac{3}{4}+\frac{2}{5}×\frac{3}{4}$
(4)$\frac{2}{3}×\frac{2}{5}$÷$\frac{1}{3}$-$\frac{2}{5}$
(5)$\frac{1}{8}÷[{\frac{3}{4}×(\frac{3}{5}-\frac{2}{15})}]$.

分析 (1)按照从左到右的顺序计算;
(2)(3)根据乘法分配律简算;
(4)先算乘法,再算除法,最后算减法;
(5)先算小括号里面的减法,再算中括号里面的乘法,最后算括号外的除法.

解答 解:(1)$\frac{4}{9}×\frac{1}{5}÷\frac{4}{5}$      
=$\frac{4}{45}$×$\frac{5}{4}$
=$\frac{1}{9}$;

(2)$24×(\frac{1}{8}+\frac{1}{6})$
=24×$\frac{1}{8}$+24×$\frac{1}{6}$
=3+4
=7;

(3)$\frac{3}{5}×\frac{3}{4}+\frac{2}{5}×\frac{3}{4}$
=($\frac{3}{5}$+$\frac{2}{5}$)×$\frac{3}{4}$
=1×$\frac{3}{4}$
=$\frac{3}{4}$;

(4)$\frac{2}{3}×\frac{2}{5}$÷$\frac{1}{3}$-$\frac{2}{5}$
=$\frac{4}{15}$×3-$\frac{2}{5}$
=$\frac{4}{5}$-$\frac{2}{5}$
=$\frac{2}{5}$;

(5)$\frac{1}{8}÷[{\frac{3}{4}×(\frac{3}{5}-\frac{2}{15})}]$
=$\frac{3}{8}$÷[$\frac{3}{4}$×$\frac{7}{15}$]
=$\frac{3}{8}$×$\frac{20}{7}$
=$\frac{15}{14}$.

点评 本题考查了四则混合运算,注意运算顺序和运算法则,灵活运用所学的运算定律进行简便计算.

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