(1)$4×5\frac {3}{4}+5×6\frac {4}{5}+6×7\frac {5}{6}+7×8\frac {6}{7}$
$=4×(5+\frac {3}{4})+5×(6+\frac {4}{5})+6×(7+\frac {5}{6})+7×(8+\frac {6}{7})$
$=(4×5+4×\frac {3}{4})+(5×6+5×\frac {4}{5})+(6×7+6×\frac {5}{6})+(7×8+7×\frac {6}{7})$
$=(20+3)+(30+4)+(42+5)+(56+6)$
$=23+34+47+62$
$=166$
(2)$51\frac {2}{3}÷\frac {5}{3}+71\frac {3}{4}÷\frac {7}{4}+91\frac {4}{5}÷\frac {9}{5}$
$=(50+1\frac {2}{3})÷\frac {5}{3}+(70+1\frac {3}{4})÷\frac {7}{4}+(90+1\frac {4}{5})÷\frac {9}{5}$
$=50÷\frac {5}{3}+\frac {5}{3}÷\frac {5}{3}+70÷\frac {7}{4}+\frac {7}{4}÷\frac {7}{4}+90÷\frac {9}{5}+\frac {9}{5}÷\frac {9}{5}$
$=50×\frac {3}{5}+1+70×\frac {4}{7}+1+90×\frac {5}{9}+1$
$=30+1+40+1+50+1$
$=30+40+50+1+1+1$
$=123$
$=4×(5+\frac {3}{4})+5×(6+\frac {4}{5})+6×(7+\frac {5}{6})+7×(8+\frac {6}{7})$
$=(4×5+4×\frac {3}{4})+(5×6+5×\frac {4}{5})+(6×7+6×\frac {5}{6})+(7×8+7×\frac {6}{7})$
$=(20+3)+(30+4)+(42+5)+(56+6)$
$=23+34+47+62$
$=166$
(2)$51\frac {2}{3}÷\frac {5}{3}+71\frac {3}{4}÷\frac {7}{4}+91\frac {4}{5}÷\frac {9}{5}$
$=(50+1\frac {2}{3})÷\frac {5}{3}+(70+1\frac {3}{4})÷\frac {7}{4}+(90+1\frac {4}{5})÷\frac {9}{5}$
$=50÷\frac {5}{3}+\frac {5}{3}÷\frac {5}{3}+70÷\frac {7}{4}+\frac {7}{4}÷\frac {7}{4}+90÷\frac {9}{5}+\frac {9}{5}÷\frac {9}{5}$
$=50×\frac {3}{5}+1+70×\frac {4}{7}+1+90×\frac {5}{9}+1$
$=30+1+40+1+50+1$
$=30+40+50+1+1+1$
$=123$
答案：(1)$4×5\frac {3}{4}+5×6\frac {4}{5}+6×7\frac {5}{6}+7×8\frac {6}{7}$
$=4×(5+\frac {3}{4})+5×(6+\frac {4}{5})+6×(7+\frac {5}{6})+7×(8+\frac {6}{7})$
$=(4×5+4×\frac {3}{4})+(5×6+5×\frac {4}{5})+(6×7+6×\frac {5}{6})+(7×8+7×\frac {6}{7})$
$=(20+3)+(30+4)+(42+5)+(56+6)$
$=23+34+47+62$
$=166$
(2)$51\frac {2}{3}÷\frac {5}{3}+71\frac {3}{4}÷\frac {7}{4}+91\frac {4}{5}÷\frac {9}{5}$
$=(50+1\frac {2}{3})÷\frac {5}{3}+(70+1\frac {3}{4})÷\frac {7}{4}+(90+1\frac {4}{5})÷\frac {9}{5}$
$=50÷\frac {5}{3}+\frac {5}{3}÷\frac {5}{3}+70÷\frac {7}{4}+\frac {7}{4}÷\frac {7}{4}+90÷\frac {9}{5}+\frac {9}{5}÷\frac {9}{5}$
$=50×\frac {3}{5}+1+70×\frac {4}{7}+1+90×\frac {5}{9}+1$
$=30+1+40+1+50+1$
$=30+40+50+1+1+1$
$=123$
$=4×(5+\frac {3}{4})+5×(6+\frac {4}{5})+6×(7+\frac {5}{6})+7×(8+\frac {6}{7})$
$=(4×5+4×\frac {3}{4})+(5×6+5×\frac {4}{5})+(6×7+6×\frac {5}{6})+(7×8+7×\frac {6}{7})$
$=(20+3)+(30+4)+(42+5)+(56+6)$
$=23+34+47+62$
$=166$
(2)$51\frac {2}{3}÷\frac {5}{3}+71\frac {3}{4}÷\frac {7}{4}+91\frac {4}{5}÷\frac {9}{5}$
$=(50+1\frac {2}{3})÷\frac {5}{3}+(70+1\frac {3}{4})÷\frac {7}{4}+(90+1\frac {4}{5})÷\frac {9}{5}$
$=50÷\frac {5}{3}+\frac {5}{3}÷\frac {5}{3}+70÷\frac {7}{4}+\frac {7}{4}÷\frac {7}{4}+90÷\frac {9}{5}+\frac {9}{5}÷\frac {9}{5}$
$=50×\frac {3}{5}+1+70×\frac {4}{7}+1+90×\frac {5}{9}+1$
$=30+1+40+1+50+1$
$=30+40+50+1+1+1$
$=123$
1. 巧算:$139×\frac {137}{138}+137×1\frac {1}{138}$
答案：1. 139×$\frac{137}{138}$+137×1$\frac{1}{138}$
=(138+1)×$\frac{137}{138}$+137×$(1+\frac{1}{138})$
=137+$\frac{137}{138}$+137+$\frac{137}{138}$
=137×2+2×$(1-\frac{1}{138})$
=276-2×$\frac{1}{138}$
=275$\frac{68}{69}$
=(138+1)×$\frac{137}{138}$+137×$(1+\frac{1}{138})$
=137+$\frac{137}{138}$+137+$\frac{137}{138}$
=137×2+2×$(1-\frac{1}{138})$
=276-2×$\frac{1}{138}$
=275$\frac{68}{69}$
2. 巧算:$31\frac {1}{2}÷\frac {3}{2}+41\frac {1}{3}÷\frac {4}{3}+51\frac {1}{4}÷\frac {5}{4}$
答案：2. 31$\frac{1}{2}$÷$\frac{3}{2}$+41$\frac{1}{3}$÷$\frac{4}{3}$+51$\frac{1}{4}$÷$\frac{5}{4}$
=$(30+1\frac{1}{2})$÷$\frac{3}{2}$+$(40+1\frac{1}{3})$÷$\frac{4}{3}$+$(50+1\frac{1}{4})$÷$\frac{5}{4}$
=30÷$\frac{3}{2}$+1+40÷$\frac{4}{3}$+1+50÷$\frac{5}{4}$+1
=20+30+40+3
=93
=$(30+1\frac{1}{2})$÷$\frac{3}{2}$+$(40+1\frac{1}{3})$÷$\frac{4}{3}$+$(50+1\frac{1}{4})$÷$\frac{5}{4}$
=30÷$\frac{3}{2}$+1+40÷$\frac{4}{3}$+1+50÷$\frac{5}{4}$+1
=20+30+40+3
=93
3. 巧算:$76×(\frac {1}{23}-\frac {1}{53})+23×(\frac {1}{53}+\frac {1}{76})-53×(\frac {1}{23}-\frac {1}{76})$
答案：3. 76×$(\frac{1}{23}-\frac{1}{53})$+23×$(\frac{1}{53}+\frac{1}{76})$-53×$(\frac{1}{23}-\frac{1}{76})$
=76×$\frac{1}{23}$-76×$\frac{1}{53}$+23×$\frac{1}{53}$+23×$\frac{1}{76}$-53×$\frac{1}{23}$+53×$\frac{1}{76}$
=$\frac{1}{23}$×(76-53)-$\frac{1}{53}$×(76-23)+$\frac{1}{76}$×(23+53)
=$\frac{1}{23}$×23-$\frac{1}{53}$×53+$\frac{1}{76}$×76
=1-1+1
=1
【提示】分子都是1,分母有重复,可以先利用乘法分配律拆开计算,再寻找共同因数进行提取。
=76×$\frac{1}{23}$-76×$\frac{1}{53}$+23×$\frac{1}{53}$+23×$\frac{1}{76}$-53×$\frac{1}{23}$+53×$\frac{1}{76}$
=$\frac{1}{23}$×(76-53)-$\frac{1}{53}$×(76-23)+$\frac{1}{76}$×(23+53)
=$\frac{1}{23}$×23-$\frac{1}{53}$×53+$\frac{1}{76}$×76
=1-1+1
=1
【提示】分子都是1,分母有重复,可以先利用乘法分配律拆开计算,再寻找共同因数进行提取。