《2025年同步练习册配套检测卷六年级数学上册鲁教版五四制》

20. (10分)(1)先化简,再求值：$\frac{1}{2}m - 2(m - \frac{1}{3}n^{2}) - (\frac{3}{2}m - \frac{1}{3}n^{2})$,其中$m = -2$,$n = \frac{2}{3}$.
(2)先化简,再求值：$3x^{2}y - [2xy^{2} - 2(-x^{2}y + 4xy^{2})] - 5xy^{2}$,其中$x = -2$,$y = \frac{1}{2}$.

答案：
(1)
首先化简式子：
$\begin{aligned}\frac{1}{2}m - 2(m - \frac{1}{3}n^{2}) - (\frac{3}{2}m - \frac{1}{3}n^{2}) \\= \frac{1}{2}m - 2m + \frac{2}{3}n^{2} - \frac{3}{2}m + \frac{1}{3}n^{2} \\= (\frac{1}{2} - 2 - \frac{3}{2})m + (\frac{2}{3} + \frac{1}{3})n^{2} \\= -3m + n^{2}\end{aligned}$
当 $m = -2$，$n = \frac{2}{3}$ 时，代入得：
$\begin{aligned}-3×(-2)+(\frac{2}{3})^2\\=6 + \frac{4}{9} \\= 6\frac{4}{9}\end{aligned}$
(2)
首先化简式子：
$\begin{aligned}3x^{2}y - [2xy^{2} - 2(-x^{2}y + 4xy^{2})] - 5xy^{2} \\= 3x^{2}y - (2xy^{2} + 2x^{2}y - 8xy^{2}) - 5xy^{2} \\= 3x^{2}y - 2xy^{2} - 2x^{2}y + 8xy^{2} - 5xy^{2} \\= (3x^{2}y - 2x^{2}y) + (-2xy^{2} + 8xy^{2} - 5xy^{2}) \\= x^{2}y + xy^{2}\end{aligned}$
当 $x = -2$，$y = \frac{1}{2}$ 时，代入得：
$\begin{aligned}(-2)^2×\frac{1}{2}+(-2)×(\frac{1}{2})^2 \\= 4 × \frac{1}{2} - 2 × \frac{1}{4} \\= 2 - \frac{1}{2} \\= \frac{3}{2} （或 1.5)\end{aligned}$