这道题该怎么做？

选化除为乘，然后交换4.75X16/11+4.75X6/11在一起相加，15又1/4X6/11+15又1/4X16/11在一起相加，分别利用乘法分配律，得到4.75X2+15.25X2,再一次利用分配律，得到20X2=40.

4.75÷11/16+15又1/4×6/11+4.75×6/11+15又1/4÷11/16
=4.75×16/11+15.25×6/11+4.75×6/11+15.25×16/11
=4.75×（16/11+6/11）+15.25×（6/11+16/11）
=4.75×2+15.25×2
=（4.75+15.25）×2
=20×2
=40

如图

结果为40。

需要用到乘法的分配律。详细过程如图:

4.75÷11/16+（15+1/4）x6/11+4.75x6/11+（15+1/4）÷11/16
=4.75÷11/16+61/4x6/11+4.75x6/11+61/4÷11/16
=4.75x16/11+61/4x6/11+4.75x6/11+61/4x16/11
=4.75x16/11+4.75x6/11+61/4x6/11+61/4x16/11
=(4.75x16/11+4.75x6/11)+(61/4x6/11+61/4x16/11)
=4.75(16/11+6/11)+61/4(6/11+16/11)
=4.75x22/11+61/4x22/11
=4.75x2+61/4x2
=9.5+61/2
=19/2+61/2
=80/2
=40

观察原式发现两项有4.75，两项有15¼，可以提取公因式再计算