1. 用合理的方法计算下面各题。
$6.13-\frac{2}{3}-\frac{1}{3}+0.87$ $\frac{9}{5}×56+33÷\frac{5}{9}+\frac{9}{5}$
$(0.48×0.49×1.5)÷(0.05×0.24×0.7)$ $124×\frac{31}{123}$

1. $6.13 - \frac{2}{3} - \frac{1}{3} + 0.87$
$\begin{aligned}&=(6.13 + 0.87) - (\frac{2}{3} + \frac{1}{3})\\&=7 - 1\\&=6\end{aligned}$
2. $\frac{9}{5}×56 + 33÷\frac{5}{9} + \frac{9}{5}$
$\begin{aligned}&=\frac{9}{5}×56 + 33×\frac{9}{5} + \frac{9}{5}×1\\&=\frac{9}{5}×(56 + 33 + 1)\\&=\frac{9}{5}×90\\&=162\end{aligned}$
3. $(0.48×0.49×1.5)÷(0.05×0.24×0.7)$
$\begin{aligned}&=(0.48÷0.24)×(0.49÷0.7)×(1.5÷0.05)\\&=2×0.7×30\\&=1.4×30\\&=42\end{aligned}$
4. $124×\frac{31}{123}$
$\begin{aligned}&=(123 + 1)×\frac{31}{123}\\&=123×\frac{31}{123} + 1×\frac{31}{123}\\&=31 + \frac{31}{123}\\&=31\frac{31}{123}\end{aligned}$

2. 解方程。
$3x + 0.75x = 3.75$ $\frac{7}{2}×\frac{2}{7}-4x=\frac{1}{2}$ $8×(x - 3)=32$

1. 解：$3x + 0.75x = 3.75$
合并同类项：$3.75x = 3.75$
系数化为$1$：$x = 3.75 ÷ 3.75 = 1$

2. 解：$\frac{7}{2} × \frac{2}{7} - 4x = \frac{1}{2}$
计算乘法：$1 - 4x = \frac{1}{2}$
移项：$-4x = \frac{1}{2} - 1 = -\frac{1}{2}$
系数化为$1$：$x = ( -\frac{1}{2} ) ÷ ( -4 ) = \frac{1}{8}$

3. 解：$8 × ( x - 3 ) = 32$
两边除以$8$：$x - 3 = 32 ÷ 8 = 4$
移项：$x = 4 + 3 = 7$

1. 如果一袋 500g 的桂圆干有 112 粒，那么 3kg 这样的桂圆干大约有多少粒？

3kg=3000g
3000÷500=6
112×6=672(粒)
答：3kg这样的桂圆干大约有672粒。