Question

17．脫試計算（能簡便的要簡便算）
$\frac{4}{9}$÷$\frac{5}{17}$+$\frac{5}{9}$×$\frac{17}{5}$                        
（$\frac{2}{13}$+$\frac{5}{11}$）×13×11
0.575×19+1.9×4.25
$\frac{26}{27}$×28．

Answer 1

分析 ①$\frac{4}{9}÷$$\frac{5}{17}$+$\frac{5}{9}$×$\frac{17}{5}$  把除轉(zhuǎn)化為乘它的倒數(shù)，再運用乘法分配律簡算；                      
②（$\frac{2}{13}$+$\frac{5}{11}$）×13×11，運用乘法分配律簡算；
③0.575×19+1.9×4.25，將原式轉(zhuǎn)化為：5.75×1.9+1.9×4.25，再運用乘法分配律簡算；
④$\frac{26}{27}$×28，轉(zhuǎn)化為：$\frac{26}{27}×（27+1）$，運用乘法分配律簡算．

解答 解：①$\frac{4}{9}÷$$\frac{5}{17}$+$\frac{5}{9}$×$\frac{17}{5}$  
=$\frac{4}{9}×\frac{17}{5}+\frac{5}{9}×\frac{17}{5}$
=$（\frac{4}{9}+\frac{5}{9}）×\frac{17}{5}$
=$1×\frac{17}{5}$
=$\frac{17}{5}$；
                      
②（$\frac{2}{13}$+$\frac{5}{11}$）×13×11
=$\frac{2}{13}×13×11+\frac{5}{11}×11×13$
=22+65
=87；

③0.575×19+1.9×4.25
=5.75×1.9+1.9×4.25
=（5.75+4.25）×1.9
=10×1.9
=19；

④$\frac{26}{27}$×28
=$\frac{26}{27}×（27+1）$
=$\frac{26}{27}×27+\frac{26}{27}×1$
=26+$\frac{26}{27}$
=$26\frac{26}{27}$．

點評 此題考查的目的是理解掌握小數(shù)、分數(shù)四則混合運算的順序體積它們的計算法則，并且能夠靈活選擇簡便方法進行計算．