Question

11．能簡(jiǎn)算的要簡(jiǎn)算
$\frac{1}{5}$+$\frac{2}{9}$×$\frac{3}{10}$                $\frac{23}{98}$×99                   $\frac{15}{16}$×17-$\frac{15}{16}$
$\frac{5}{13}$×$\frac{7}{9}$+$\frac{5}{9}$×$\frac{2}{13}$            $\frac{4}{7}$×$\frac{6}{13}$+$\frac{3}{7}$×$\frac{6}{13}$            （$\frac{24}{9}$+$\frac{8}{3}$）×$\frac{1}{24}$．

Answer 1

分析 ①$\frac{1}{5}$+$\frac{2}{9}$×$\frac{3}{10}$，先算乘法，再算加法；
②$\frac{23}{98}$×99，轉(zhuǎn)化為：$\frac{23}{98}×（98+1）$，運(yùn)用乘法分配律簡(jiǎn)算；                  
③$\frac{15}{16}$×17-$\frac{15}{16}$，運(yùn)用乘法分配律簡(jiǎn)算；
④$\frac{5}{13}$×$\frac{7}{9}$+$\frac{5}{9}$×$\frac{2}{13}$，轉(zhuǎn)化為：$\frac{5}{13}$×$\frac{7}{9}$+$\frac{2}{9}$×$\frac{5}{13}$，運(yùn)用乘法分配律簡(jiǎn)算；
⑤$\frac{4}{7}$×$\frac{6}{13}$+$\frac{3}{7}$×$\frac{6}{13}$，運(yùn)用乘法分配律簡(jiǎn)算；
⑥（$\frac{24}{9}$+$\frac{8}{3}$）×$\frac{1}{24}$，運(yùn)用乘法分配律簡(jiǎn)算．

解答 解：①$\frac{1}{5}$+$\frac{2}{9}$×$\frac{3}{10}$ 
=$\frac{1}{5}+\frac{1}{15}$
=$\frac{3}{15}+\frac{1}{15}$
=$\frac{4}{15}$；

②$\frac{23}{98}$×99  
=$\frac{23}{98}×（98+1）$
=$\frac{23}{98}×98+\frac{23}{98}×1$
=$23+\frac{23}{98}$
=$23\frac{23}{98}$；
               
③$\frac{15}{16}$×17-$\frac{15}{16}$
=$\frac{15}{16}×（17-1）$
=$\frac{15}{16}×16$
=15；

④$\frac{5}{13}$×$\frac{7}{9}$+$\frac{5}{9}$×$\frac{2}{13}$
=$\frac{5}{13}$×$\frac{7}{9}$+$\frac{2}{9}$×$\frac{5}{13}$
=$\frac{5}{13}×（\frac{7}{9}+\frac{2}{9}）$
=$\frac{5}{13}×1$
=$\frac{5}{13}$；

⑤$\frac{4}{7}$×$\frac{6}{13}$+$\frac{3}{7}$×$\frac{6}{13}$
=$（\frac{4}{7}+\frac{3}{7}）×\frac{6}{13}$
=$1×\frac{6}{13}$
=$\frac{6}{13}$；

⑥（$\frac{24}{9}$+$\frac{8}{3}$）×$\frac{1}{24}$
=$\frac{24}{9}×\frac{1}{24}+\frac{8}{3}×\frac{1}{24}$
=$\frac{1}{9}+\frac{1}{9}$
=$\frac{2}{9}$．

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．