Basics of Rational Numbers : Key to Acing Math Exams

We all know that numbers can be classified into different types viz- natural numbers, whole numbers, integers, and fractions. But have you ever heard of Rational Numbers? 

In this blog post, we will explain what rational numbers are and some of their basic features, and provide you with an example to help you understand them better.

What are Rational Numbers?

Rational numbers are numbers that can be expressed as a fraction of two integers,  where the denominator is not equal to zero. i.e-  in the form p/q, where q is not equal to zero.

This means that rational numbers are a combination of integers and fractions. For example, 1/2, 2/3, 3/4, and 5/6 are all rational numbers.

Basic Rules of Rational Numbers

• Addition and Subtraction of Rational Numbers: When adding or subtracting rational numbers, we need to make sure that the denominators are the same. We can do this by finding the lowest common multiple (LCM) of the denominators and then converting each fraction to an equivalent fraction with that denominator. For example, to add 1/2 and 1/3, we first find the LCM of 2 and 3, which is 6. Then, we convert each fraction to an equivalent fraction with a denominator of 6. So, 1/2 becomes 3/6 and 1/3 becomes 2/6. Now we can add them: 3/6 + 2/6 = 5/6.

• Multiplication and Division of Rational Numbers: To multiply or divide rational numbers, we simply multiply or divide the numerators and denominators separately. For example, to multiply 1/2 and 2/3, we multiply the numerators (1 × 2 = 2) and the denominators (2 × 3 = 6) separately to get 2/6. We can simplify this by dividing both the numerator and denominator by 2 to get 1/3.

• Ordering Rational Numbers: Rational numbers can be ordered just like whole numbers or integers. We use the same symbols (<, >, ≤, ≥) to indicate the relationship between two rational numbers. For example, 1/2 < 3/4, and 2/3 > 1/2.

Let us consider an interesting Example:

Let's say you have a pizza that is divided into eight equal slices, and you have already eaten two slices. You want to know what fraction of the pizza you have eaten so far. To do this, you can use rational numbers. The whole pizza can be represented by the fraction 8/8, which means eight out of eight slices. The two slices you have eaten can be represented by the fraction 2/8, which means two out of eight slices. To find the fraction of the pizza you have eaten,you can simply add these two fractions: 

8/8 + 2/8 = 10/8.

But this fraction can be simplified because both the numerator and denominator are even numbers. We can divide both by 2 to get 5/4. This means you have eaten five out of the eight slices of the pizza.

Conclusion

Rational numbers are an essential part of mathematics, and they can be used to represent many real-world situations. They have basic rules and features that are easy to understand and apply. We hope this blog post has helped you understand rational numbers better. Remember, practice makes perfect, and the more you work with rational numbers, the easier they will become.

If you have any question you are free to ask in the comments section we are happy to help you.