Question

16．脫式計(jì)算，能簡(jiǎn)算的要簡(jiǎn)便計(jì)算

$\frac{11}{12}$×$\frac{5}{7}$×84	（$\frac{4}{5}$-$\frac{4}{15}$）×$\frac{5}{12}$	$\frac{7}{13}$×$\frac{3}{10}$+$\frac{7}{13}$
$\frac{19}{24}$-$\frac{9}{16}$×$\frac{4}{27}$	$\frac{2}{9}$×$\frac{6}{7}$+$\frac{2}{9}$×$\frac{1}{7}$	144÷$\frac{1}{12}$÷12

Answer 1

分析 ①$\frac{11}{12}×$$\frac{5}{7}$×84，運(yùn)用乘法結(jié)合律簡(jiǎn)算；
②（$\frac{4}{5}$-$\frac{4}{15}$）×$\frac{5}{12}$，運(yùn)用乘法分配律簡(jiǎn)算；  
③$\frac{7}{13}$×$\frac{3}{10}$+$\frac{7}{13}$，運(yùn)用乘法分配律簡(jiǎn)算；
④$\frac{19}{24}$-$\frac{9}{16}$×$\frac{4}{27}$，先算乘法，再算減法；
⑤$\frac{2}{9}$×$\frac{6}{7}$+$\frac{2}{9}$×$\frac{1}{7}$，運(yùn)用乘法分配律簡(jiǎn)算；  
⑥144÷$\frac{1}{12}$÷12，把除數(shù)轉(zhuǎn)化為乘它的倒數(shù)，再按照分?jǐn)?shù)乘法的計(jì)算法則計(jì)算．

解答 解：①$\frac{11}{12}×$$\frac{5}{7}$×84
=$\frac{11}{12}×（\frac{5}{7}×84）$
=$\frac{11}{12}×60$
=55；

②（$\frac{4}{5}$-$\frac{4}{15}$）×$\frac{5}{12}$   
=$\frac{4}{5}×\frac{5}{12}-\frac{4}{15}×\frac{5}{12}$
=$\frac{1}{3}-$$\frac{1}{9}$
=$\frac{2}{9}$；

③$\frac{7}{13}$×$\frac{3}{10}$+$\frac{7}{13}$
=$\frac{7}{13}×（\frac{3}{10}+1）$
=$\frac{7}{13}×\frac{13}{10}$
=$\frac{7}{10}$；

④$\frac{19}{24}$-$\frac{9}{16}$×$\frac{4}{27}$ 
=$\frac{19}{24}-\frac{1}{12}$
=$\frac{17}{24}$；

⑤$\frac{2}{9}$×$\frac{6}{7}$+$\frac{2}{9}$×$\frac{1}{7}$  
=$\frac{2}{9}×（\frac{6}{7}+\frac{1}{7}）$
=$\frac{2}{9}×1$
=$\frac{2}{9}$；

⑥144÷$\frac{1}{12}$÷12
=$144×12×\frac{1}{12}$
=144．

點(diǎn)評(píng) 此題考查的目的是理解掌握分?jǐn)?shù)四則混合運(yùn)算的順序以及它們的計(jì)算法則，并且能夠靈活選擇簡(jiǎn)便方法進(jìn)行計(jì)算．