What are rational number.

 Rational number

What are rational numbers?

Rational numbers are a type of number that can be expressed as the ratio of two integers. In other words, they can be written as a fraction where the numerator and denominator are both integers. Rational numbers can be positive, negative, or zero, and they can be expressed as either terminating or repeating decimals.

To understand rational numbers, it is first important to understand the concepts of integers and fractions. Integers are whole numbers, both positive and negative, that do not have any decimal or fractional parts. Fractions, on the other hand, are numbers that represent a part of a whole. They consist of a numerator, which represents the part being considered, and a denominator, which represents the whole. For example, the fraction 3/4 represents three parts out of a whole that is divided into four equal parts.

Rational numbers are similar to fractions in that they can be expressed as a ratio of two integers. However, rational numbers can also be expressed as decimals. Terminating decimals are those that end after a finite number of digits, while repeating decimals are those that repeat a pattern of digits infinitely.

To see why rational numbers are important, consider the following example. Suppose you need to divide a pizza evenly among 5 people. You can represent this situation as the fraction 1/5, where the numerator represents the portion of the pizza each person will receive, and the denominator represents the total number of people the pizza will be divided among. This fraction is a rational number, as it can be expressed as the ratio of two integers.

In general, rational numbers are important in mathematics because they form a fundamental part of the number system. They allow us to express quantities and measurements precisely, and they are used in a variety of mathematical applications, including geometry, algebra, and calculus.

Some important properties of rational numbers include closure under addition, subtraction, multiplication, and division. In other words, if you add, subtract, multiply, or divide two rational numbers, the result will also be a rational number. Additionally, rational numbers can be compared using the less than, greater than, and equal to operators, just like integers.

To further illustrate these properties, consider the following examples. Suppose you have the rational numbers 2/3 and 5/6. To add these two numbers, you need to find a common denominator. In this case, the least common multiple of 3 and 6 is 6, so you can rewrite both fractions with a denominator of 6:

2/3 + 5/6 = 4/6 + 5/6 = 9/6

This result is also a rational number, as it can be expressed as the ratio of two integers.

To subtract these two numbers, you can follow a similar process:

2/3 - 5/6 = 4/6 - 5/6 = -1/6

Again, this result is a rational number.

To multiply these two numbers, you simply multiply the numerators and denominators separately:

2/3 * 5/6 = (2*5)/(3*6) = 10/18

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:

10/18 = 5/9

This result is also a rational number.

To divide these two numbers, you can follow a similar process:

2/3 / 5/6 = 2/3 * 6/5 = 12/15

Again, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3:

12/15 = 4/5

This result is also a rational number.

Rational numbers can also be compared using the less than, greater than, and