Question

2．计算下面各题，能简算要简算

$\frac{6}{7}$×16.31-2.31×$\frac{6}{7}$	3-$\frac{12}{19}$÷$\frac{28}{57}$-$\frac{2}{3}$	（0.75-$\frac{3}{16}$）×（$\frac{2}{9}$+$\frac{1}{3}$）
$\frac{13}{15}$×3.75×$\frac{3}{52}$	$\frac{5}{27}$×$\frac{3}{8}$+0.375×$\frac{7}{27}$+$\frac{4}{27}$×37.5%	$\frac{3}{4}$+$\frac{1}{4}$÷$\frac{3}{5}$

Answer 1

分析 ①用乘法分配律计算．a×c+b×c=（a+b）×c．
②把除法变成乘法，再从左往右计算．
③先算加减法，再算乘法．
④把小数变成分数，再约分计算．
⑤用乘法分配律计算．
⑥先算除法，再算加法．

解答 解：①$\frac{6}{7}$×16.31-2.31×$\frac{6}{7}$
=（16.31-2.31）×$\frac{6}{7}$
=14×$\frac{6}{7}$
=12

②3-$\frac{12}{19}$÷$\frac{28}{57}$-$\frac{2}{3}$
=3-$\frac{12}{19}$×$\frac{57}{28}$-$\frac{2}{3}$
=3-$\frac{9}{7}$-$\frac{2}{3}$
=$\frac{12}{7}-\frac{2}{3}$
=$\frac{22}{21}$

③（0.75-$\frac{3}{16}$）×（$\frac{2}{9}$+$\frac{1}{3}$）
=$\frac{9}{16}×\frac{5}{9}$
=$\frac{5}{16}$

④$\frac{13}{15}$×3.75×$\frac{3}{52}$
=$\frac{13}{15}$×$\frac{15}{4}$×$\frac{3}{52}$
=$\frac{13}{4}×\frac{3}{52}$
=$\frac{3}{16}$

⑤$\frac{5}{27}$×$\frac{3}{8}$+0.375×$\frac{7}{27}$+$\frac{4}{27}$×37.5%
=（$\frac{5}{27}$+$\frac{7}{27}$+$\frac{4}{27}$）×37.5%
=$\frac{16}{27}×\frac{3}{8}$
=$\frac{2}{9}$

⑥$\frac{3}{4}$+$\frac{1}{4}$÷$\frac{3}{5}$
=$\frac{3}{4}$+$\frac{1}{4}$×$\frac{5}{3}$
=$\frac{9}{12}+\frac{5}{12}$
=$\frac{13}{12}$

点评 本题利用具体的算式考查了学生对于乘法运算定律的理解和运用．