Question

2．能簡(jiǎn)便計(jì)算要簡(jiǎn)便計(jì)算．

（$\frac{2}{3}$+$\frac{1}{6}$）×24	$\frac{9}{32}$÷[$\frac{4}{3}$×（$\frac{7}{16}$-$\frac{1}{4}$）]	$\frac{7}{10}$×$\frac{1}{6}$+$\frac{3}{10}$÷6	$\frac{2}{9}$+$\frac{1}{2}$÷$\frac{4}{5}$+$\frac{3}{8}$
56×$\frac{17}{57}$	$\frac{5}{6}$×$\frac{7}{8}$+$\frac{5}{6}$×$\frac{1}{8}$	$\frac{3}{85}$×86．

Answer 1

分析 ①用乘法分配律計(jì)算．乘法分配律：兩個(gè)數(shù)的和，乘以一個(gè)數(shù)，可以拆開來(lái)算，積不變．如a×（b+c）=ab+ac．
②先算小括號(hào)里面的減法，再算中括號(hào)里面的乘法，最后算除法．
③把除法變成乘法，再用乘法分配律計(jì)算．
④先算除法算式，再算同分母的分?jǐn)?shù)相加．
⑤把56變成57-1，再用乘法分配律計(jì)算．
⑥用乘法分配律計(jì)算．
⑦把86變成85+1，用乘法分配律計(jì)算．

解答 解：①（$\frac{2}{3}$+$\frac{1}{6}$）×24
=24×$\frac{2}{3}$+$\frac{1}{6}$×24
=16+4
=20

②$\frac{9}{32}$÷[$\frac{4}{3}$×（$\frac{7}{16}$-$\frac{1}{4}$）]
=$\frac{9}{32}$÷[$\frac{4}{3}$×$\frac{3}{16}$]
=$\frac{9}{32}×\frac{4}{1}$
=$\frac{9}{8}$

③$\frac{7}{10}$×$\frac{1}{6}$+$\frac{3}{10}$÷6
=$\frac{7}{10}$×$\frac{1}{6}$+$\frac{3}{10}$×$\frac{1}{6}$
=$\frac{1}{6}×（\frac{7}{10}+\frac{3}{10}）$
=$\frac{1}{6}×1$
=$\frac{1}{6}$

④$\frac{2}{9}$+$\frac{1}{2}$÷$\frac{4}{5}$+$\frac{3}{8}$
=$\frac{2}{9}+\frac{1}{2}×\frac{5}{4}+\frac{3}{8}$
=$\frac{2}{9}+（\frac{5}{8}+\frac{3}{8}）$
=$\frac{2}{9}+1$
=$1\frac{2}{9}$

⑤56×$\frac{17}{57}$
=（57-1）×$\frac{17}{57}$
=57×$\frac{17}{57}-1×\frac{17}{57}$
=$17-\frac{17}{57}$
=$16\frac{40}{57}$

⑥$\frac{5}{6}×\frac{7}{8}+\frac{5}{6}×\frac{1}{8}$
=$\frac{5}{6}×（\frac{7}{8}+\frac{1}{8}）$
=$\frac{5}{6}$

⑦$\frac{3}{85}×86$
=$\frac{3}{85}×（85+1）$
=$\frac{3}{85}×85+\frac{3}{85}$
=$3+\frac{3}{85}$
=$3\frac{3}{85}$

點(diǎn)評(píng) 本題利用具體的算式考查了學(xué)生對(duì)于乘法分配律和加法結(jié)合律的應(yīng)用．