解:(1)
×
-
÷
+
×1
,
=(
+1
)×
-
×
,
=3×
-
,
=2-
,
=1
;
(2)49
÷7+1.5÷(0.5-
),
=(49+
)÷7+1.5÷(
-
),
=49÷7+
÷7+1.5÷
,
=7+
+1.5×6,
=7+
+9,
=16
;
(3)
×5
+4
×0.75,
=0.75×5
+4
×0.75,
=(5
+4
)×0.75,
=10×0.75,
=7.5;
(4)(6
×5.43+4.57÷
)-(
+
)×1.44,
=(
×5.43+4.57×
)-(
×1.44+
×1.44),
=(5.43+4.57)×
-(2.1+1.2),
=10×
-3.3,
=62.5-3.3,
=59.2.
分析:(1)把除法改为乘法,运用加法交换律与结合律简算;
(2)把49
拆成整数与分数相加的形式,运用除法的性质简算,1.5÷(0.5-
)按运算顺序计算;
(3)把
改为小数,运用乘法分配律的逆运算简算;
(4)第一个括号把除法改为乘法,运用乘法分配律的逆运算简算,(
+
)×1.44,运用乘法分配律简算.
点评:分数四则混合运算的解题方法不是一成不变的,要根据题目的具体情况,如数的特征、运算符号等决定做题方法.