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：
A number is a rational number if it can be written in the form of p/q, where p and q are integers and q ≠ 0
- Therefore, we can write 0 in the form of 0/1, 0/2, 0/3, 0/4.
- As well as, q can be a negative integer also, 0/-1, 0/-2, 0/-3, 0/-4.
So we can see 0 can be written in p/q, form hence 0 is a rational number.
问题2：找出3到4之间的六个有理数。
解决方案：
We can find infinite rational numbers between 3 and 4.
Now we have to find 6 rational numbers between 3 and 4 we will multiply and divide both the numbers 3 and 4 by (6 + 1) 7.
- 3 = 3 × 7/7 = 21/7
- 4 = 4 × 7/7 = 28/7
Hence the 6 rational numbers are 23/7, 24/7, 25/7, 26/7, 27/7, and 28/7.
问题3：找出3/5和4/5之间的五个有理数。
解决方案：
We need to find 5 rational numbers between 3/5 and 4/5.
Multiply both numerator and denominator by (5 + 1) 6.
- 3/5 = 3/5 × 6/6 = 18/30
- 4/5 = 4/5 × 6/6 = 24/30
Hence, the 5 rational number between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22/30 and 23/30.
问题4：说明以下陈述是对还是错。给出答案的理由。
(i)每个自然数都是整数。
(ii)每个整数都是整数。
(iii)每个有理数都是整数。
解决方案：
(i) Every natural number is a whole number.
True
Explanation: The natural numbers starts from 1, 2, 3, 4 …..
The whole number starts from 0, 1, 2, 3 , 4 …..
Here it is clearly seen that whole number contains all the natural numbers and 0 also
Therefore, every natural number is a whole number but not every whole number is not a natural number as 0 is a whole number but not a natural number.
(ii) Every integer is a whole number.
False
Explanation: Integers are the numbers that have both positive and negative numbers including 0,
Example: …..-4, -3, -2, -1, 0, 1, 2, 3, 4 ……
Whereas whole numbers begin from 0 to infinite
Example: 0, 1, 2, 3, 4…..
Here we can see every whole number is an integer but not all the integers are the whole number.
(iii) Every rational number is a whole number.
False
Explanation: Rational numbers are the numbers that can be written in the form of p/q where q ≠ 0.
Example: 0, 2/5, 4/17, 7/15 …..
Whole numbers are that starts from 0 to infinity
As we know whole numbers can be written in the form of 0/1, 1/1, 2/1, …
Thus, every whole number is a rational number but every rational number is not a whole number.
