5. 化简下列各比。
$48:72$
$1.2:\dfrac{4}{7}$
$1.6\ \mathrm{dm}^2:0.25\ \mathrm{m}^2$
$1\ \mathrm{吨}:750\ \mathrm{千克}$

$48:72$
$=(48÷24):(72÷24)$
$=2:3$
$1.2:\dfrac{4}{7}$
$=\dfrac{6}{5}:\dfrac{4}{7}$
$=(\dfrac{6}{5}×35):(\dfrac{4}{7}×35)$
$=42:20$
$=21:10$
$1.6\ \mathrm{dm}^2:0.25\ \mathrm{m}^2$
$=1.6\ \mathrm{dm}^2:25\ \mathrm{dm}^2$
$=1.6:25$
$=(1.6×10):(25×10)$
$=16:250$
$=8:125$
$1\ \mathrm{吨}:750\ \mathrm{千克}$
$=1000\ \mathrm{千克}:750\ \mathrm{千克}$
$=1000:750$
$=(1000÷250):(750÷250)$
$=4:3$

6. 计算下列各题,能简算的要简算。
$\frac{6}{7} × \frac{3}{5} + \frac{1}{7} ÷ \frac{5}{3}$
$( \frac{4}{5} - \frac{2}{3} + \frac{1}{5} ) × \frac{15}{8}$
$\frac{4}{5} × \frac{5}{9} + \frac{5}{9}$
$( \frac{5}{6} + \frac{2}{7} + \frac{1}{3} ) × 42$
$( \frac{7}{8} + \frac{3}{16} ) × ( \frac{5}{9} + \frac{1}{3} )$
$( \frac{3}{4} - \frac{5}{8} ) ÷ ( \frac{1}{2} - \frac{1}{3} )$

$\begin{aligned}&\frac{6}{7} × \frac{3}{5} + \frac{1}{7} ÷ \frac{5}{3}\\=&\frac{6}{7}×\frac{3}{5}+\frac{1}{7}×\frac{3}{5}\\=&(\frac{6}{7}+\frac{1}{7})×\frac{3}{5}\\=&1×\frac{3}{5}\\=&\frac{3}{5}\end{aligned}$
---
$\begin{aligned}&( \frac{4}{5} - \frac{2}{3} + \frac{1}{5} ) × \frac{15}{8}\\=&( \frac{4}{5}+\frac{1}{5}-\frac{2}{3} ) × \frac{15}{8}\\=&( 1-\frac{2}{3} ) × \frac{15}{8}\\=&\frac{1}{3}×\frac{15}{8}\\=&\frac{5}{8}\end{aligned}$
---
$\begin{aligned}&\frac{4}{5} × \frac{5}{9} + \frac{5}{9}\\=&( \frac{4}{5}+1 ) × \frac{5}{9}\\=&\frac{9}{5}×\frac{5}{9}\\=&1\end{aligned}$
---
$\begin{aligned}&( \frac{5}{6} + \frac{2}{7} + \frac{1}{3} ) × 42\\=&\frac{5}{6}×42 + \frac{2}{7}×42 + \frac{1}{3}×42\\=&35+12+14\\=&61\end{aligned}$
---
$\begin{aligned}&( \frac{7}{8} + \frac{3}{16} ) × ( \frac{5}{9} + \frac{1}{3} )\\=&\frac{17}{16} × \frac{8}{9}\\=&\frac{17}{18}\end{aligned}$
---
$\begin{aligned}&( \frac{3}{4} - \frac{5}{8} ) ÷ ( \frac{1}{2} - \frac{1}{3} )\\=&\frac{1}{8} ÷ \frac{1}{6}\\=&\frac{1}{8}×6\\=&\frac{3}{4}\end{aligned}$

7. 看图列式计算。
(1) 爸爸月收入：？元
妈妈月收入：5500元 比爸爸少$\frac{2}{7}$
(2) 乒乓球：108个
羽毛球：
排球：？个
(3) $\frac{1}{3}$ ？千克 $\frac{1}{2}$ 600千克
(4) 剩$\frac{4}{7}$ 用去60 kg 共购买？kg

(1)
$\begin{aligned}5500÷(1-\frac{2}{7})&=5500÷\frac{5}{7}\\&=7700（元）\end{aligned}$
答：爸爸月收入7700元。
(2)
$\begin{aligned}108×\frac{4}{9}×\frac{1}{2}&=48×\frac{1}{2}\\&=24（个）\end{aligned}$
答：排球有24个。
(3)
$\begin{aligned}600×(1-\frac{1}{3}-\frac{1}{2})&=600×\frac{1}{6}\\&=100（千克）\end{aligned}$
答：所求部分是100千克。
(4)
$\begin{aligned}60÷(1-\frac{4}{7})&=60÷\frac{3}{7}\\&=140（\mathrm{kg}）\end{aligned}$
答：共购买140kg。