问题1.找到-3到1之间的有理数。
解决方案：
Between two rational numbers x and y
Rational number = (x + y) / 2
= (-3 + 1) / 2
= -2/2
= -1
So, the rational number between -3 and 1 is -1
问题2。找出小于2的五个有理数。
解决方案：
Five rational numbers less than 2 can be 0, 1, -2/5, 3/2, -4/5
问题3.在-2/9和5/9之间找到两个有理数
解决方案：
The rational number between -2/9 and 5/9 is
= (-2/9 + 5/9)/2
= (3/9) / 2
3 is the common factor
= 1/3/2
= 1/3 * 1/2
= 1/6
Now the rational number between -2/9 and 1/6 is
= (-2/9 + 1/6) / 2
LCM is 18
= ((-2 × 2 + 1 × 3) /18) / 2
= (-4 + 3) / 36
= -1/36
Rational numbers between -2/9 and 5/9 are -1/36, 1/6
问题4.找到两个介于1/5和1/2之间的有理数
解决方案：
The rational number between 1/5 and 1/2 is
= (1/5 + 1/2)/2
LCM is 10
= ((1 × 2 + 1 × 5) / 10) / 2
= (2 + 5) / 20 = 7/20
Now the rational number between 1/5 and 7/20 is
= (1/5 + 7/20) / 2
LCM is 20
= ((1 × 4 + 7 × 1) / 20) / 2
= (4 + 7) / 40
= 11/40
Rational number between 1/5 and 1/2 are 7/20, 11/40
问题5.找到1/4至1/2之间的十个有理数。
解决方案：
Other than average method, rational numbers can be found by converting the given rational numbers into equivalent rational numbers with same denominators.
The LCM for 4 and 2 is 4.
1/4 = 1/4
1/2 = (1 × 2) / 2 * 2= 2/4
1/4 = (1 × 20 / 4 × 20) = 20/80
2/4 = (2 × 20 / 4 × 20) = 40/80
So, we now know that 21, 22, 23,…39 are integers between numerators 20 and 40.
Rational numbers between 1/4 and 1/2 are 21/80, 22/80, 23/80, …., 39/80
问题6.在-2/5和1/2之间找到十个有理数。
解决方案：
Other than average method, rational numbers can be found by converting the given rational numbers into equivalent rational numbers with same denominators.
The LCM for 5 and 2 is 10.
-2/5 = (-2 × 2) / 10 = -4/10
1/2 = (1 × 5) / 10 = 5/10
-4/10 = (-4 × 2 / 10 × 2) = -8/20
5/10 = (5 × 2 / 10 × 2) = 10/20
So, we now know that -7, -6, -5,…10 are integers between numerators -8 and 10.
Rational numbers between -2/5 and 1/2 are -7/20, -6/20, -5/20, …., 9/20
问题7.找到3/5和3/4之间的十个有理数。
解决方案：
Other than average method, rational numbers can be found by converting the given rational numbers into equivalent rational numbers with same denominators.
The LCM for 5 and 4 is 20.
3/5 = 3 × 4/5 × 4 = 12/20
3/4 = 3 × 5/4 × 5 = 15/20
Making the denominator 100
12/20 = 12 × 5/20 × 5 = 60/100
15/20 = 15 × 5/20 × 5 = 75/100
Rational numbers between 3/5 and 3/4 are 61/100, 62/100, 63/100, …., 74/100