第2讲 乘除法的关系和乘法运算律(乘除法中的巧算)-四年级奥数下册同步精讲精练（西师大版）

293 第二讲 乘除法的关系和乘法运算律(乘除法中的巧算) 例1 (1) 25×17×4 =(25×4)×17 =100×17 =1700 (2) 125×25×8×4 =(125×8)×(25×4) =1000×100 =100000 (3) 25×32×125 =(25×4)×(8×125) =100×1000 =100000 (4) 25×25×16 =(25×4)×(25×4) =100×100 =10000 [同步精练] 1. 125×64×8 =125×8×64 =1000×64 =64000 72×25×4 =72×(25×4) =72×100 =7200 2. 125×(9×8) =125×8×9 =1000×9 =9000 25×64×125 =(25×8)×(8×125) =200×1000 =200000 3. 125×16 =125×8×2 =1000×2 =2000 50×13×2 =50×2×13 =100×13 =1300 294 例2 (1) 25×(10+4) =25×10+25×4 =250+100 =350 (2) 125×(80-8) =125×80-125×8 =10000-1000 =9000 (3) 25×38 =25×(40-2) =25×40-25×2 =1000-50 =950 (4) 125×888 =125×8×111 =1000×111 =111000 [同步精练] 1. 32×25 =8×(4×25) =8×100 =800 72×125×3 =(9×3)×(8×125) =27×1000 =27000 2. 401×267 =(400+1)×267 =400×267+1×267 =106800+267 =107067 128×101 =128×(100+1) =128×100+128×1 =12800+128 =12928 3. 307×199 =307×(200-1) =307×200-307×1 =61400-307 =61093 564×99 =564×(100-1) =564×100-564×1 =56400-564 =55836 295 例3 (1) 2600÷25 =(2600×4)÷(25×4) =10400÷100 =104 (2) 38700÷900 =(38700÷100)÷(900÷100) =387÷9 =43 (3) 34000÷125 =(34000×8)÷(125×8) =272000÷1000 =272 (4) (450+35)÷5 =450÷5+35÷5 =90+7 =97 (5) 325÷13÷5 =325÷5÷13 =65÷13 =5 [同步精练] 1. 1800÷25 =(1800×4)÷(25×4) =7200÷100 =72 3200÷25 =(3200×4)÷(25×4) =12800÷100 =128 296 2. 31800÷300 =(31800÷100)÷(300÷100) =318÷3 =106 27000÷125 =(27000×8)÷(125×8) =216000÷1000 =216 3. (280+15)÷5 =280÷5+15÷5 =56+3 =59 315÷9÷5 =315÷5÷9 =63÷9 =7 例4 (1) 306000÷8÷125 =306000÷(8×125) =306000÷1000 =306 (2) 5670÷(7×9) =5670÷7÷9 =810÷9 =90 (3) 636÷15×5 =636÷(15÷5) =636÷3 =212 (4) 25×(4×7) =25×4×7 =100×7 =700 [同步精练] 1. 6800÷25÷4 =6800÷(25×4) =6800÷100 =68 2550÷17÷25 =2550÷25÷17 =102÷17 =6 2. 23÷4+77÷4 =(23+77)÷4 =100÷4 =25 8÷7+9÷7+11÷7 =(8+9+11)÷7 =28÷7 =4 297 3. 78000÷125 =(78000×8)÷(125×8) =624000÷1000 =624 5600÷25 =(5600×4)÷(25×4) =22400÷100 =224 练 习 卷 1. 5×13×20 =5×20×13 =100×13 =1300 2. 27×25×4 =27×(25×4) =27×100 =2