问题1.在不进行实际加法和除法运算的情况下，将69和96之和除以
(i)11(ii)15
解决方案：
(i)11
According to the rule when ab + ba is divided by 11 then the quotient is (a + b) if a and b are digits of the numbers.
Therefore, the sum of 69 and 96 is when divided by 11 then we will get
a + b = 6 + 9 = 15
Hence, our quotient is 15.
(ii)15
According to the rule when ab + ba is divided by (a + b) then the quotient is 11 if a and b are digits of the numbers.
Therefore, the sum of 69 and 96 is when divided by 15 then we will get 11 as quotient.
Hence, our quotient is 15.
问题2。在不执行实际计算的情况下，将94-49除以
(i)9(ii)5
解决方案：
(i)9
According to the rule when ab – ba is divided by 9 then the quotient is (a – b) if a and b are digits of the numbers and are having reverse digits.
Therefore, the computation of 94 -49 is when divided by 9 then we will get
a – b = 9 – 4 = 5
Hence, our quotient is 5.
(ii)5
According to the rule when ab – ba is divided by (a – b) then the quotient is 9 if a and b are digits of the numbers and are having reverse digits.
Therefore, the computation of 94 -49 is when divided by 5 then we will get 9 as our quotient.
问题3.将985的数字和通过循环排列985的数字获得的另外两个数字的和分别除以111、22和37。查找每种情况下的商。
解决方案：
When the sum of a 3 digit cyclic number is divided by 111 then the quotient is the value of the sum of its digits.
i.e.
9 + 8 + 5 = 22.
Hence our quotient is 22.
According to the rule, the sum of a 3 digit cyclic number is when divided by the sum of its digits, then the quotient obtained is 111.
When, 3 × 37 = 111
Quotient = 3 × (Sum of the digits) = 3 × 22 = 66
问题4.将985和958的差除以9得到的商。
解决方案：
According to the rule, when unit’s and ten’s digits are interchanged, then the difference of the numbers when divided by 9, gives a quotient as the difference between the unit’s and the ten’s digit.
Quotient is 8 – 5 = 3