题目内容

18.下列各题怎样算简便就怎样算.
$\frac{1}{4}$+$\frac{3}{4}$×$\frac{8}{15}$  2-$\frac{3}{4}$÷$\frac{9}{10}$  $\frac{5}{12}$÷9+$\frac{1}{9}$×$\frac{7}{12}$ 
($\frac{5}{6}$-$\frac{3}{5}$)÷$\frac{1}{30}$  10-($\frac{2}{5}$+$\frac{3}{5}$×2)$\frac{3}{5}$×[(2-0.6)÷$\frac{7}{15}$].

分析 (1)先算乘法,再算加法;
(2)先算除法,再算减法;
(3)、(4)根据乘法分配律进行简算;
(5)先算乘法,再算加法,最后算减法;
(6)先算减法,再算除法,最后算乘法.

解答 解:(1)$\frac{1}{4}$+$\frac{3}{4}$×$\frac{8}{15}$
=$\frac{1}{4}$+$\frac{2}{5}$
=$\frac{13}{20}$;

(2)2-$\frac{3}{4}$÷$\frac{9}{10}$
=2-$\frac{5}{6}$
=1$\frac{1}{6}$;

(3)$\frac{5}{12}$÷9+$\frac{1}{9}$×$\frac{7}{12}$
=$\frac{5}{12}$×$\frac{1}{9}$+$\frac{1}{9}$×$\frac{7}{12}$
=($\frac{5}{12}$+$\frac{7}{12}$)×$\frac{1}{9}$
=1×$\frac{1}{9}$
=$\frac{1}{9}$;

(4)($\frac{5}{6}$-$\frac{3}{5}$)÷$\frac{1}{30}$
=($\frac{5}{6}$-$\frac{3}{5}$)×30
=$\frac{5}{6}$×30-$\frac{3}{5}$×30
=25-18
=7;

(5)10-($\frac{2}{5}$+$\frac{3}{5}$×2)
=10-($\frac{2}{5}$+$\frac{6}{5}$)
=10-$\frac{8}{5}$
=8$\frac{2}{5}$;

(6)$\frac{3}{5}$×[(2-0.6)÷$\frac{7}{15}$]
=$\frac{3}{5}$×[1.4÷$\frac{7}{15}$]
=$\frac{3}{5}$×3
=$\frac{9}{5}$.

点评 考查了运算定律与简便运算,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简便计算.

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