问题1：零是有理数吗?您能以p / q的形式写吗，其中p和q是整数，q≠0?
解决方案：
Yes, zero is a rational number.
It can be written in p/q form provided that q ≠ 0.
For Example: 0/5, 0/6, 0/7 etc.
问题2：找到1到2之间的五个有理数。
解决方案：
We know how to find a rational number between two numbers x and y = (x + y)/2
Now let’s find 5 rational numbers between 1 and 2.
Step 1: Rational number between 1 and 2
= (1 + 2)/2
= 3/2
Step 2: Rational number between 1 and 3/2
= (1 + 3/2)/2
= 5/4
Step 3: Rational number between 1 and 5/4
= (1 + 5/4)/2
= 9/8
Step 4: Rational number between 3/2 and 2
= 1/2 [(3/2) + 2)]
= 7/4
Step 5: Rational number between 7/4 and 2
= 1/2 [7/4 + 2]
= 15/8
Therefore, 5 rational numbers between 1 and 2 are 9/8, 5/4, 3/2, 7/4, 15/8
问题3：找出3到4之间的六个有理数。
解决方案：
To find n rational numbers between any two rational numbers we have to Multiply and divide both the numbers by n+1.
n = 6
So, n + 1 = 7
Multiplying and dividing 3 and 4 by 7,
3 × 7/7 = 21/7
4 × 7/7 = 28/7
Now we have to choose 6 rational numbers between 21/7 and 28/7
Therefore, 6 rational numbers between 3 and 4 are 22/7, 23/7, 24/7, 25/7, 26/7, 27/7
问题4：找出3/5和4/5之间的五个有理数。
解决方案：
To find n rational numbers between any two rational numbers we have to Multiply and divide both the numbers by n+1.
n = 5
So, n + 1 = 6
Multiplying and dividing 3/5 and 4/5 by 6,
3/5 × 6/6 = 18/30
4/5 × 6/6 = 24/30
Now we have to choose 5 rational numbers between 18/30 and 24/30
Therefore, 5 rational numbers between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22,30, 23/30
问题5：以下陈述是对还是错?给出答案的理由。
(i)每个整数都是自然数。
(ii)每个整数都是有理数。
(iii)每个有理数都是整数。
(iv)每个自然数都是整数，
(v)每个整数都是整数。
(vi)每个有理数都是整数。
解决方案：
(i) False.
Reason: because 0 is a whole number but not a natural number.
(ii) True
Reason: because every integer can be represented in the form of a fraction n/1.
(iii) False.
Reason: numbers such as 4/3, 2/9, 7/5 are rational numbers but not integers.
(iv) True.
Reason: every natural number is a whole number because whole numbers are positive integers including 0 and natural number are positive integers.
(v) False.
Reason: Negative numbers are not whole numbers.
(vi) False.
Reason: numbers such as 4/3, 2/9, 7/5 are rational numbers but not whole numbers.