6. 有两根绳子,一根长为$160m$,比另一根短$\frac{1}{9}$,另一根长为()m。
A.$160÷(1-\frac{1}{9})$
B.$160÷(1+\frac{1}{9})$
C.$160×(1-\frac{1}{9})$
D.$160×(1+\frac{1}{9})$

A

设另一根绳子长为$x$米。
已知一根绳子长$160m$，比另一根短$\frac{1}{9}$，则可列出方程：
$x - \frac{1}{9}x = 160$
$\frac{8}{9}x = 160$
$x = 160 ÷ \frac{8}{9}$
$x = 160 × \frac{9}{8}$
$x = 160 ÷ (1 - \frac{1}{9})$
结论：A

1. 直接写得数。
$4÷\frac{4}{17}=$ $\frac{5}{16}×\frac{4}{5}=$ $0.25×4=$ $18×\frac{1}{6}=$
$4×\frac{5}{12}=$ $\frac{6}{11}÷3=$ $\frac{13}{42}×\frac{2}{26}=$ $1-\frac{1}{3}×\frac{1}{2}=$

17 $\frac{1}{4}$ 1 3 $\frac{5}{3}$ $\frac{2}{11}$ $\frac{1}{42}$ $\frac{5}{6}$

2. 能简算的要简算。
$\frac{4}{7}÷\frac{1}{3}+\frac{4}{7}×\frac{3}{2}$ $(\frac{5}{6}+20)÷\frac{5}{4}$ $3\frac{4}{5}×[(1-\frac{9}{10})÷0.01]$
$2.8×\frac{3}{5}÷(0.52+\frac{3}{5})$ $(\frac{5}{6}+\frac{7}{8}+\frac{11}{12})÷\frac{1}{24}$ $\frac{13}{17}×\frac{11}{14}+\frac{3}{14}×\frac{13}{17}$

$\frac{18}{7}$ $16\frac{2}{3}$ 38 1.5 63 $\frac{13}{17}$

$\frac{4}{7}÷\frac{1}{3}+\frac{4}{7}×\frac{3}{2}$
$=\frac{4}{7}×3+\frac{4}{7}×\frac{3}{2}$
$=\frac{4}{7}×(3+\frac{3}{2})$
$=\frac{4}{7}×\frac{9}{2}$
$=\frac{18}{7}$
$(\frac{5}{6}+20)÷\frac{5}{4}$
$=(\frac{5}{6}+20)×\frac{4}{5}$
$=\frac{5}{6}×\frac{4}{5}+20×\frac{4}{5}$
$=\frac{2}{3}+16$
$=16\frac{2}{3}$
$3\frac{4}{5}×[(1-\frac{9}{10})÷0.01]$
$=\frac{19}{5}×[\frac{1}{10}÷0.01]$
$=\frac{19}{5}×10$
$=38$
$2.8×\frac{3}{5}÷(0.52+\frac{3}{5})$
$=2.8×0.6÷(0.52+0.6)$
$=1.68÷1.12$
$=1.5$
$(\frac{5}{6}+\frac{7}{8}+\frac{11}{12})÷\frac{1}{24}$
$=(\frac{5}{6}+\frac{7}{8}+\frac{11}{12})×24$
$=\frac{5}{6}×24+\frac{7}{8}×24+\frac{11}{12}×24$
$=20+21+22$
$=63$
$\frac{13}{17}×\frac{11}{14}+\frac{3}{14}×\frac{13}{17}$
$=\frac{13}{17}×(\frac{11}{14}+\frac{3}{14})$
$=\frac{13}{17}×1$
$=\frac{13}{17}$

1. 一块长方形菜地,周围篱笆长为$140m$,长方形的长与宽的比是$4:3$,这块菜地的面积是多少？

$140÷ 2× \frac{4}{4+3}=40(m)$ $140÷ 2× \frac{3}{4+3}=30(m)$ $40× 30=1200(m^2)$

$140÷2×\frac{4}{4+3}=40(m)$
$140÷2×\frac{3}{4+3}=30(m)$
$40×30=1200(m^2)$