《2025年一本暑假衔接五年级数学人教版》

4. 如果一个正方体的高减少3cm,那么它的表面积就减少$96cm^{2}$,原来正方体的体积是多少立方厘米？

答案： $96÷4÷3=8(cm)$
$8×8×8=512(cm^{3})$
答：原来正方体的体积是$512cm^{3}$。

5. 如果$A= \frac {111110}{222222}$、$B= \frac {333330}{666662}$,那么A、B两个数中,哪个数比较大？B

答案： $\frac {1}{2}-\frac {111110}{222222}=\frac {1}{222222}$
$\frac {1}{2}-\frac {333330}{666662}=\frac {1}{666662}$
因为$\frac {1}{222222}＞\frac {1}{666662}$，所以$\frac {111110}{222222}＜\frac {333330}{666662}$。
答：A、B 两个数中，B 比较大。

6. 计算：$1\frac {1}{20}+2\frac {1}{30}+3\frac {1}{42}+4\frac {1}{56}+5\frac {1}{72}+6\frac {1}{90}$

答案： $1\frac {1}{20}+2\frac {1}{30}+3\frac {1}{42}+4\frac {1}{56}+5\frac {1}{72}+6\frac {1}{90}$
$=(1+2+3+4+5+6)+(\frac {1}{4×5}+\frac {1}{5×6}+\frac {1}{6×7}+\frac {1}{7×8}+\frac {1}{8×9}+\frac {1}{9×10})$
$=21+(\frac {1}{4}-\frac {1}{5}+\frac {1}{5}-\frac {1}{6}+\frac {1}{6}-\frac {1}{7}+\frac {1}{7}-\frac {1}{8}+\frac {1}{8}-\frac {1}{9}+\frac {1}{9}-\frac {1}{10})$
$=21+(\frac {1}{4}-\frac {1}{10})$
$=21\frac {3}{20}$

7. 计算：$\frac {1}{3}+\frac {2}{5}+\frac {3}{7}+\frac {7}{12}+\frac {9}{20}+\frac {11}{28}+\frac {17}{30}+\frac {25}{42}$

答案： $\frac {1}{3}+\frac {2}{5}+\frac {3}{7}+\frac {7}{12}+\frac {9}{20}+\frac {11}{28}+\frac {17}{30}+\frac {25}{42}$
$=\frac {1}{3}+\frac {2}{5}+\frac {3}{7}+\frac {1}{3}+\frac {1}{4}+\frac {1}{4}+\frac {1}{5}+\frac {1}{4}+\frac {1}{7}+\frac {2}{5}+\frac {1}{6}+\frac {1}{6}+\frac {3}{7}$
$=(\frac {1}{3}+\frac {1}{3}+\frac {1}{6}+\frac {1}{6})+(\frac {2}{5}+\frac {1}{5}+\frac {2}{5})+(\frac {3}{7}+\frac {1}{7}+\frac {3}{7})+(\frac {1}{4}+\frac {1}{4}+\frac {1}{4})$
$=1+1+1+\frac {3}{4}$
$=3\frac {3}{4}$