有理数的密度性质是什么？
数制是表示数轴数字的系统方式。这些数字使用一组符号和规则来描述。这些数字位于属于 0-9 的区间内。这些数字也称为数字，可以使用各种数学运算进行操作。所有的计算，如计数、输入和操作，都可以使用数轴的计算来执行。
有理数
有理数是以分数形式表示的数，p/q，其中 p 和 q 是整数，并且 q 不等于 0。数字系统中的整个有理数集由字母表示问：换句话说，如果一个数可以表示为分数，其中分子和分母都是整数值，则该数称为有理数。这些有理数还可以进一步简化以获得纯整数或十进制值。
密度属性
如果 a/b < c/d，那么假设存在一个有理数 g/h 使得它遵循性质，a/b < g/h < c/d
密度属性表明在两个指定的有理数之间，存在另一个有理数。例如，对于给定的两个有理数，0 和 1/2，在这两个有理数之间存在一个有理数 1/4。在按递增顺序排列这些有理数时，
0、1/4、1/2
给定有理数 0 和 1/4 之间的有理数是 1/8，而 1/4 和 1/2 之间的有理数相当于 3/8。
给定有理数集之间的有理数可以通过计算两个有理数的平均值来计算。
例如，为了计算 0 和 1/4 之间的有理数，我们只需将有理数 0 和 1/4 相加，然后将和除以整数值 2。
将两个整数值相加，
0 + 1/4 = 1/4
现在将 1/4 除以 2
1/4 ÷ 2 = 1/4 ÷ 2/1
1/4 ÷ 2 = 1/4 × 1/2
1/4 ÷ 2 = (1 × 1)/(4 × 2)
1/4 ÷ 2 = 1/8
为了计算 1/4 和 1/2 之间的有理数，只需将 1/4 和 1/2 相加，然后将和除以 2，我们得到，
1/4 + 1/2 = 1/4 + (1 × 2)/(2 × 2)
1/4 + 1/2 = 1/4 + 2/4
1/4 + 1/2 = (1 + 2)/4
1/4 + 1/2 = 3/4
现在将 3/4 除以 2，
3/4 ÷ 2 = 3/4 ÷ 2/1
3/4 ÷ 2 = 3/4 × 1/2
3/4 ÷ 2 = (3 × 1)/(4 × 2)
3/4 ÷ 2 = 3/8
示例问题
问题 1. 找到 1/2 和 2/3 之间的有理数？
解决方案：
Here we have to find a rational number between 1/2 and 2/3
First take the average of both the rational numbers
= (1/2 + 2/3)/2
Taking LCM of 2 and 3
LCM of 2 and 3 = 6
= ((1×3)+(2×2)/6 )/2
= 3+4/6/2
= 7/6 × 1/2
= 7/12
Therefore,
Rational number between 1/2 and 2/3 is 7/12.
问题 2. 找到 3/4 和 5/8 之间的两个有理数？
解决方案：
Here we have to find a rational number between 3/4 and 5/8
First take the average of both the rational numbers
= (3/4 + 5/8)/2
Taking LCM of 4 and 8
LCM of 4 and 8 = 8
= ((3×2)+(5×1)/8 )/2
= 6+5/8/2
= 11/8 × 1/2
= 11/16
Now finding the other rational number between 3/4 and 11/16
First take the average of both the rational numbers
= (3/4 + 11/16)/2
Taking LCM of 4 and 16
LCM of 4 and 16 = 16
= ((3×4)+(11×1)/16 )/2
= 12+11/16/2
= 23/16 × 1/2
= 23/32
Therefore,
Rational number between 3/4 and 5/8 are 11/16 and 23/32.
问题 3. 找出 4/3 和 5/4 之间的三个有理数？
解决方案：
Here we have to find a rational number between 4/3 and 5/4
First take the average of both the rational numbers
= (4/3 + 5/4)/2
Taking LCM of 3 and 4
LCM of 3 and 4 = 12
= ((4×4)+(5×3)/12 )/2
= 16+15/12/2
= 31/12 × 1/2
= 31/24
Now finding the second rational number between 4/3 and 31/24
First take the average of both the rational numbers
= (4/3 + 31/24)/2
Taking LCM of 3 and 24
LCM of 3 and 24 = 24
= ((4×6)+(31×1)/24 )/2
= 24+31/24/2
= 55/24 × 1/2
= 55/48
Further for finding third rational number between 31/24 and 5/4
First take the average of both the rational numbers
= (31/24 + 5/4)/2
Taking LCM of 24 and 4
LCM of 24 and 4 = 24
= ((31×1)+(5×6)/24 )/2
= 31+30/24/2
= 61/24 × 1/2
= 61/48
Therefore,
Ration numbers between 4/3 and 5/4 are 55/48, 31/24, and 61/48.