第7讲 分数混合运算(分数计算中的技巧)-六年级奥数上册同步精讲精练（西师大版）

279 练 习 卷 1.A 2.B 3.D 4.2 不 同 20 排10号 (15,13) 5. 6.(1)正北 90 (2)教学楼、厕所 (3)(6,11) (5,2) 运动场 7.略(观测点不一样,答案不一样) 第七讲 分数混合运算 (分数计算中的技巧) 例1 (1) 32 33 ×17 =(1- 1 33 )×17 =1×17- 1 33 ×17 =17- 17 33 =16 16 33 (2) 28× 13 27 =(27+1)× 13 27 =27× 13 27 +1× 13 27 =13+ 13 27 =13 13 27 [同步精练] 1. 23 24 ×19 =(1- 1 24 )×19 =1×19- 1 24 ×19 =19- 19 24 =18 5 24 2. 36× 11 35 =(35+1)× 11 35 =35× 11 35 +1× 11 35 =11+ 11 35 =11 11 35 3. 8× 14 15 =8×(1- 1 15 ) 280 =8×1-8× 1 15 =8- 8 15 =7 7 15 4. 3 25 ×126 = 3 25 ×(125+1) = 3 25 ×125+ 3 25 ×1 =15+ 3 25 =15 3 25 例2 1998÷1998 1998 1999 =1998÷ 1998×1999+1998 1999 =1998÷ 1998×(1999+1) 1999 =1998÷ 1998×2000 1999 =1998× 1999 1998×2000 = 1999 2000 [同步精练] 1. 238÷238 238 239 =238÷ 238×239+238 239 =238÷ 238×(239+1) 239 =238÷ 238×240 239 =238× 239 238×240 = 239 240 2. 1999÷1999 1999 2000 =1999÷ 1999×2000+1999 2000 =1999÷ 1999×(2000+1) 2000 =1999÷ 1999×2001 2000 =1999× 2000 1999×2001 = 2000 2001 例3 1999+2000×1998 1999×2000-1 = 1999+2000×(1999-1) 1999×2000-1 = 1999+2000×1999-2000 1999×2000-1 = 2000×1999-1 1999×2000-1 =1 [同步精练] 1. 362+548×361 362×548-186 = 362+548×(362-1) 362×548-186 281 = 362+548×362-548 362×548-186 = 548×362-186 362×548-186 =1 2. 1988+1989×1987 1988×1989-1 = 1988+1989×(1988-1) 1988×1989-1 = 1988+1989×1988-1989 1988×1989-1 = 1989×1988-1 1988×1989-1 =1 例4 1 1×2 + 1 2×3 + 1 3×4 + 1 4×5 + 1 5×6 =1- 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + 1 4 - 1 5 + 1 5 - 1 6 =1- 1 6 = 5 6 [同步精练] 1. 1 1×2 + 1 2×3 + 1 3×4 +…+ 1 99×100 =1- 1 2 + 1 2 - 1 3 + 1 3 - 1 4 +…+ 1 99 - 1 100 =1- 1 100 = 99 100 2. 1 2 + 1 6 + 1 12 + 1 20 + 1 30 = 1 1×2 + 1 2×3 + 1 3×4 + 1 4×5 + 1 5×6 =1- 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + 1 4 - 1 5 + 1 5 - 1 6 =1- 1 6 = 5 6 3. 1+ 1 2 + 1 6 + 1 12 + 1 20 + 1 30 + 1 42 + 1 56 + 1 72 + 1 90 =1+ 1 1×2 + 1 2×3 + 1 3×4 + 1 4×5 + 1 5×6 + 1 6×7 + 1 7×8 + 1 8×9 + 1 9×10 =1+1- 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + 1 4 - 1 5 + 1 5 - 1 6 + 1 6 - 1 7 282 + 1 7 - 1 8 + 1 8 - 1 9 + 1 9 - 1 10 =1+1- 1 10 =2- 1 10 =1 9 10 练