两个整数的商总是有理数吗？

数系涉及质数、奇数、偶数、有理数、整数等不同种类的数。这些数可以用事实的形式表示，也可以用适当的表达式表示。例如，数字形式的20、25等整数也可以写成20和25。数字系统或数字系统被定义为表示数字和数字的简单/容易的系统。它是以数学和算术形式显示数字的特殊方式。

数字

数字用于各种算术值，适合传达各种算术工作，如加法、减法、乘法等，这些在日常生活中适用于计算的原因。一个数字的价值取决于数字、它在数字中的位置值以及数字系统的立场。数字通常也称为数字，是用于计数、测量、指定和计算基本量的数值。数字是用于测量或计算数字的原因的数字。它由数字组成，如 4、5、78 等。

数字类型

有不同类型的数字。数字根据它们共享的关系和它们所反映的特征在数字系统中的不同集合之间进行区分。例如，整数从 0 生成并终止于无穷大。让我们更详细地了解这些类型，

• 自然数：自然数也称为从 1 到无穷大的正数。自然数组由“N”表示。它是我们通常用于计数的整数。自然数组可以表示为 N = 1, 2, 3, 4, 5, 6, 7,…
• 整数：整数也称为正数，它与自然数相似，但也包括零，包括从 0 到无穷大。整数不包含分数或小数。整数组由“W”表示。该组可以显示为 W = 0, 1, 2, 3, 4, 5,…
• 整数：整数是包含所有正数的字符组，零以及从负无穷到正无穷的所有负数加起来。该组不涉及分数和小数。整数组由“Z”表示。整数组可以表示为 Z = ...,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,...
• 十进制数：任何包含小数点的整数值都是十进制数。它可以表示为 2.5、0.567 等。
• 实数：实数是一组不涉及任何虚数的整数。它涉及所有的正整数、负整数、分数和十进制值。一般用“R”表示。
• 复数：复数是一组涉及虚数的数字。它可以表示为 x + y，其中“x”和“y”是实数。它由“C”表示。
• 有理数：有理数是可以表示为两位数之比的数字。它涉及所有的数字，可以用分数或小数表示。它由'Q'表示。它可以写成小数，小数点后有无穷无尽的不重复数字。它由“P”表示。

两个整数的商总是有理数吗？

回答：

First, let’s learn about Rational numbers and Integers,

• Rational number: Rational numbers are the divisor of two numbers in the form p/q, where p and q are numbers and q ≠ 0. Because of the basic formation of integers, p/q formation, most people find it hard to distinguish between fractions and rational numbers. When a rational number is divided, the output is in decimal form, which can be alternatively ending or repeating. 2,6,8, and so on are some examples of rational numbers as they can be shown in fraction form as 2/1, 6/1, and 8/1
• Integers: Integers are the group of numerals involving all the positive add up numerals, zero as well as all negative add up numerals which include from negative infinity to positive infinity. The group doesn’t involve fractions and decimals. The group of numerals is shown by ‘Z’. The group of integers can be shown as Z = …,-8, -7, -6, -5, -1, 0, 1, 2, 3, 4, 5,… The integer with no decimal or fractional part from the group of negative and positive integers, including zero.

1. Positive Integers: The integer numeral is positive if it is greater than zero. Example: 1, 2, 3, 4,…
2. Negative Integers: The integer numeral is negative if it is less than zero. Example: -1, -2, -3, -4,… and here Zero is a whole number it is neither negative nor positive integer. It is a whole number. Z = {… -5, -4, -3, -2, -1, 0, …}

As per both the definition of Integer and Rational number, 

It is rightly said that the quotient of two number is always a rational number.

Step-by-step explanation:

• If A and B are numbers it means that they are rational number and when quotient is caused by division of earlier two then the quotient must be rational as well.
• With A is any number B is not being zero, then  A/B will always be rational number.
• So, It is true that the quotient of two numbers is always a rational number.

类似问题

问题 1：将以下每一项识别为非理性或理性：1/2、80/1244、11和 √3。

解决方案：

Since a rational number is the one that can be indicated as a ratio. This represent that it can be shown as a fraction wherein both denominator and numerator are whole numbers.

1. 1/2 is a rational number as it can be shown as a fraction. 1/2 = 0.5
2. Fraction 80/1244 is rational.
3. 11, also be written as 11/1. Again a rational number.
4. Value of √3 = 1.732050…. It is a infinite value and hence cannot be written as a fraction. It is an irrational number.

问题2：识别带分数，1 ¹ / ₂是否是有理数。

解决方案：

The Simplest form of 1¹/₂ is 3/2

Top one = 3, which is an number

Bottom one = 2, is an number and not equal to zero.

So, yes, 3/2 is a rational number.

问题 3：确定给定的数字是有理数还是无理数。

1. 1.75
2. 0.01
3. 0.5
4. 0.09
5. √3

解决方案：

The given numbers are in decimal forms. To find whether the given integer is decimal or not, we have to convert it into the fraction form (i.e., p/q)

If the divisor of the fraction is not equal to zero, then the integer is rational, or else, it is irrational.

Decimal Number	Fraction	Rational Number
1.75	7/4	YES
0.01	1/100	YES
0.5	1/2	YES
0.09	1/11	YES
√3	?	NO

问题4：0是有理数吗？

解决方案：

Yes, 0 is a rational number because it is an numeral, that can be written in any formation                                                       Such as 0/4, 0/5, where b i.e., (4, 5) is a non-zero numeral. 

It can be written in the formation: p/q = 0/1. Hence, we gather that 0 is a rational number.

问题 5：识别 4 到 5 之间的有理数。

解决方案：

Rational number between 4 and 5 = (4 + 5)/2

= 9/2