1 [2026 四川绵阳期中,中]计算:$-16-(-21)+(-12)-35-(-3).$

1.【解】$-16-(-21)+(-12)-35-(-3) = -16+21-12-35+3 = -(16+12+35)+(21+3) = -39.$

2[2026山东东营质检,中]计算：$(-\dfrac{3}{2})+(-\dfrac{5}{12})+\dfrac{5}{2}+(-\dfrac{7}{12})$

2.【解】原式$= [ (-\dfrac{3}{2})+\dfrac{5}{2} ] + [ (-\dfrac{5}{12}) + (-\dfrac{7}{12}) ] =1+(-1)=0.$

3[2026浙江杭州期末,中]计算:$(-\frac{1}{2})-(-0.25)+(-\frac{1}{8})-\frac{7}{8}-(+\frac{3}{4})$

3.【解】原式$= (-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{3}{4}) + (-\dfrac{1}{8}-\dfrac{7}{8}) = -1 -1 = -2.$

4[2026山东临沂期中,中]计算:$(-1.25)×\frac{5}{7}×(-4)×(-\frac{7}{5})$

4.【解】原式$=[(-1.25)×(-4)]×[ \dfrac{5}{7}×(-\dfrac{7}{5}) ] =5×(-1)=-5.$
关键点拨
将除法转化为乘法后,把能约分的结合在一起,使计算更简便.

5[2026山东菏泽质检,中]计算:$45×(-25)×\frac{7}{8}×(-\frac{11}{15})÷\frac{1}{4}×(-1\frac{1}{7})$

5.【解】原式$=-( 45×\dfrac{11}{15})×(25×4)×( \dfrac{7}{8}×\dfrac{8}{7}) =-33×100×1=-3\ 300.$

6 [2026河北张家口期中,中]计算:$4×(-3\dfrac{6}{7})-3×(-3\dfrac{6}{7})-6×3\dfrac{6}{7}$

6.【解】原式$=-\dfrac{27}{7}×(4-3+6) =-\dfrac{27}{7}×7=-27.$

7 [2026河南郑州质检,中]计算:$1 - 3×2 + 5 + 7 - 9×2 + 11 + 13 - 15×2 + 17 + \dots + 2011 - 2013×2 + 2015 + 2017$.
8 [2026山西太原期末,较难]计算:$(-\dfrac{1}{2}×\dfrac{3}{2})×(-\dfrac{2}{3}×\dfrac{4}{3})×(-\dfrac{3}{4}×\dfrac{5}{4})×···×(-\dfrac{2021}{2022}×\dfrac{2023}{2022})$.

7.【解】原式$=(1-3×2+5)+(7-9×2+11)+(13-15×2+17) + \dots + (2\ 011 - 2\ 013×2 + 2\ 015) + 2\ 017 = 2\ 017.$
关键点拨
负数的个数为2 021,根据偶正奇负,可确定结果为负数.
8.【解】原式$= - \dfrac{1}{2} × ( \dfrac{3}{2} × \dfrac{2}{3} ) × ( \dfrac{4}{3} × \dfrac{3}{4} ) × ( \dfrac{5}{4} × \dfrac{4}{5} ) × \dots × ( \dfrac{2\ 022}{2\ 021} × \dfrac{2\ 021}{2\ 022} ) × \dfrac{2\ 023}{2\ 022} = -\dfrac{1}{2}×1×1×1×\dots×1×\dfrac{2\ 023}{2\ 022} = -\dfrac{2\ 023}{4\ 044}.$