写出介于 -2⁄5 和 ½ 之间的任意 5 个有理数

有理数是一种形式为p/q的实数，其中 q 在数学中不等于 0。如果分母和分子都是整数并且分母不为零，则任何分数都可以归类为有理数。十进制数可以是终止小数，也可以是循环小数，是有理数相除的结果。

有理数的例子

3、4、5 等是有理数的一些示例，因为它们可以用分数形式表示为 3/1、4/1 和 5/1。数字“0”也是有理数，因为它可以用多种方式表示，包括0/1、0/2、0/3等。然而，1/0、2/0、3/0 等等都是非理性的，因为它们给了我们无限的价值。

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。

写出介于 -2⁄5 和 ½ 之间的任意 5 个有理数

解决方案：

Approach 1:

Let us follow the first approach to find out the rational numbers between -2⁄5 and 1⁄2.

The equivalent fraction for −2⁄5 can be −4⁄10 and for 1⁄2 can be 5⁄10.

Now, the numbers are −4⁄10 and 5⁄10, 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 five rational numbers between −2⁄5 and 1⁄2 are −3⁄10, −1⁄10, 0, 2⁄10 and 4⁄10. In decimal form, these numbers can be expressed as −0.3, −0.1, 0, 0.2 and 0.4.

Approach 2:

Let us follow the second approach to find out the rational numbers between −2⁄5 and 1⁄2.

The formula to calculate the mean is given as:

m = sum of the terms/number of the terms

Here, the given terms are −2⁄5 and 1⁄2, so the mean is:

m = (−2 ⁄ 5 + 1 ⁄ 2) / 2 = 1/20 = 0.05

Now, the mean of −2⁄5 and 1⁄20 is:

m = (−2 ⁄ 5 + 1 ⁄ 20) / 2 = (−0.4 + 0.05) / 2 = −0.175

Now, the mean of −2⁄5 and −0.175 is:

m = (−0.4 −0.175) / 2 = −0.575/2 = −0.2875

Now, the mean of 1⁄2 and 1⁄20 is:

m = (0.5 + 0.05) / 2 = 0.55 / 2 = 0.275

Now, the mean of 1 ⁄ 2 and 0.275 is:

m = (0.5 + 0.275) / 2 = 0.775 / 2 = 0.3875

Hence, the five rational numbers between −2⁄5 and 1⁄2 are −0.2875, −0.175, 0.05, 0.275 and 0.3875.

类似问题

问题 1：4 到 7 之间的三个有理数是多少？

解决方案：

Here, the given terms are 4 and 7, so the mean is:

m = (7 + 4) / 2 = 11 / 2 = 5.5

Now, the mean of 7 and 5.5 is:

m = (7 + 5.5) / 2 = 12.5 / 2 = 6.25

Now, the mean of 5.5 and 4 is:

m = (5.5 + 4) / 2 = 9.5 / 2 = 4.75

Hence, the three rational numbers between 4 and 7 are 4.75, 5.5, and 6.25.

问题 2：1 和 2 之间的两个有理数是多少？

解决方案：

Here, the given terms are 1 and 2, so the mean is:

m = (1 + 2) / 2 = 3 / 2 = 1.5

Now, the mean of 1 and 1.5 is:

m = (1 + 1.5) / 2 = 2.5 / 2 = 1.25

Hence, the two rational numbers between 1 and 2 are 1.25 and 1.5.