解:①19.98×37-199.8×1.9+1998×0.82,
=19.98×37-19.98×19+19.98×82,
=19.98×(37-19+82),
=19.98×100,
=1998;
②9999×7+1111×37,
=1111×63+1111×37,
=1111×(63+37),
=1111×100,
=111100;
③231÷231

,
=231÷(231+

),
=231÷

,
=231÷

,
=231÷

,
=231÷231÷233×232,
=

;
④(70+

)×

,
=(69

)×

,
=69×


,
=1

,
=

.
分析:①19.98×37-199.8×1.9+1998×0.82,根據(jù)積的變化規(guī)律,一個(gè)因數(shù)擴(kuò)大10、100倍,另一個(gè)因數(shù)縮小10、100倍,積不變.轉(zhuǎn)化為:19.98×37-19.98×19+19.98×82,再利用乘法分配律簡算;
②9999×7+1111×37,根據(jù)積的變化規(guī)律,將其轉(zhuǎn)化為:1111×63+1111×37,再利用乘法分配律簡算;
③231÷231

,先把帶分?jǐn)?shù)化成假分?jǐn)?shù),分子部分用乘法分配律簡算,再把除數(shù)轉(zhuǎn)化為乘這個(gè)數(shù)的倒數(shù)進(jìn)行計(jì)算;
④(70+

)×

.把括號里面轉(zhuǎn)化為(69+

)×

,再利用乘法分配律進(jìn)行簡算;
點(diǎn)評:此題主要考查根據(jù)整數(shù)的運(yùn)算定律、運(yùn)算性質(zhì),對小數(shù)、分?jǐn)?shù)四則混合運(yùn)算進(jìn)行簡算.