找出 3 到 4 之间的四个有理数

在数学中，有理数是一种形式为p/q的实数，其中 q 不等于 0。如果分母和分子都是整数且分母不为零，我们可以将任何分数归类为有理数.拆分有理数的结果是一个十进制数，它可以是终止小数或循环小数。

有理数的例子

17 和 -34 是有理数。值得注意的是，同一个有理数可以用几种方式写成整数的比率。 7和21/3是同一个有理数。 0 也是一个有理数，因为它可以以分数形式表示为 0/1、0/2、0/2 等。

如何找到两个有理数之间的有理数？

在两个有理数之间，存在“n”个有理数。可以使用两种替代方法来找到两个有理数之间的有理数。让我们看一下这两种不同的方法。

方法一：

计算给定有理数的等效分数并计算它们之间的有理数。这些数字应该是必要的合理数字。

方法二：

计算提供的两个有理数的平均值。必要的有理数应该是平均值。用旧的和新得到的有理数重复这个方法，找到更多的有理数。

找出 3 到 4 之间的四个有理数

解决方案：

Approach 1:

Let us follow the first approach to find out the rational numbers between 3 and 4.

The equivalent fraction for 3⁄1 can be 6⁄2 and for 4⁄1 can be 16⁄4.

Now, the numbers are 6⁄2 and 16⁄4, so the required rational number can be in between these numbers.

The ratio of numerator and denominator of the required number should be between the given number.

Hence, the four rational numbers between 3 and 4 are 10⁄3, 11⁄3, 7⁄2 and 15⁄4.

Approach 2:

Let us follow the second approach to find out the rational numbers between 3 and 4.

The formula to calculate the mean is given as:

m = sum of the terms/number of the terms

Here, the given terms are 3 and 4, so the mean is:

m = (3 + 4) / 2 = 7/2 = 3.5

Now, the mean of 3 and 3.5 is:

m = (3 + 3.5) / 2 = 6.5 / 2 = 3.25

Now, the mean of 3.5 and 4 is:

m = (3.5 + 4) / 2 = 7.5 / 2 = 3.75

Now, the mean of 3.25 and 3.5 is:

m = (3.25 + 3.5) / 2 = 6.75 / 2 = 3.375

Hence, the four rational numbers between 3 and 4 are 3.25, 3.375, 3.5 and 3.75.

类似问题

问题 1：7 到 9 之间的三个有理数是多少？

解决方案：

Here, the given terms are 7 and 9, so the mean is:

m = (7 + 9) / 2 = 16 / 2 = 8

Now, the mean of 7 and 8 is:

m = (7 + 8) / 2 = 15 / 2 = 7.5

Now, the mean of 8 and 9 is:

m = (8 + 9) / 2 = 17 / 2 = 8.5

Hence, the three rational numbers between 7 and 9 are 7.5, 8 and 8.5.

问题 2：1 和 4 之间的两个有理数是多少？

解决方案：

Here, the given terms are 1 and 4, so the mean is:

m = (1 + 4) / 2 = 5 / 2 = 2.5

Now, the mean of 1 and 2.5 is:

m = (1 + 2.5) / 2 = 3.5 / 2 = 1.75

Hence, the two rational numbers between 1 and 4 are 1.75 and 2.5.