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May 13, 2024We use basic math frequently in daily life, whether when figuring out your age, determining the temperature, or simply adding the bills. While doing so, we use different types of numbers that we already understand, such as natural numbers, whole numbers, integers, etc. Now, as you move to higher classes, you’ll learn more about numbers, and one crucial topic you’ll learn is Rational numbers. So, what is a rational number, and what are their properties? Read on to find out.
In mathematics, any number can be written as p/q, where q ≠ 0 is considered a rational number. Additionally, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers. The outcome of dividing a rational number, or fraction, will be a decimal number, either a terminating decimal or a repeating decimal. It is hard to tell fractions from rational numbers when the numbers are expressed in the p/q form. Unlike the numerator and denominator of rational numbers, which are made up of integers, fractions are composed of whole numbers. Examine the following conditions to determine whether a number is rational or not.
As mentioned above, a number is rational if it can be written as a fraction with both integers in the numerator and denominator. Some examples of rational numbers include:
There are two types of rational numbers:
Examples: 2/9 , 7/9, 5/7, -3/-5.
The top and bottom can both be multiplied by -1 even if the numerator and denominator of the rational numbers are negative. Since the sum of two negative signs equals a positive sign, the numerator and denominator are once more both positive integers.
Examples: –2/7, –0.5 are some examples of negative rational numbers. Here, 10.5 can also be written as -1/2.
If the denominator includes a negative integer, the numerator and denominator can both be multiplied by -1 to bring the minus sign to the top.
Here’s a table that could sum up the characteristics of positive and negative rational numbers.
Positive Rational Numbers | Negative Rational Numbers |
Both the numerator and denominators are of the same sign. | Numerators and denominators are of different sign. |
All the numbers will be greater than 0. | The numbers will be less than 0. |
Eg: 3/7 , 2/3, -1/-3 | Examples of negative rational numbers: -2/17, 9/-11 and -1/5. |
The subset of real numbers that adheres to all of the real number system’s features is known as a rational number. The following are a few of the crucial properties of rational numbers:
Since you are already proficient in adding, subtracting, multiplying, and dividing both numbers and fractions, let’s examine these fundamental operations on rational numbers right now.
Between any two rational numbers, there are an endless number of rational numbers. There are two simple ways for finding the rational numbers that lie between two rational numbers. Let’s now examine the two distinct approaches.
Approach 1
Find the rational numbers between the given rational numbers as well as the equivalent fraction for each. Those figures must correspond to the necessary rational figures.
Approach 2:
For the two given rational numbers, determine their respective means. The needed rational number should be the mean value. Repeat the method with the old and the new rational numbers to find further rational numbers.
We hope this article on Rational numbers has been helpful to you. Stay tuned to Embibe for such informative articles.