# Rational Numbers Class 7 Notes: Chapter 9

Chapter 8 Rational Numbers of Class 7 Maths introduces the concept of rational numbers along with their addition, multiplication, subtraction and division operations.

## What is a Rational Number?

The number expressed in the form $\frac{p}{q}$, in which p and q are integers and $q\neq 0$ is known as a rational number. All fractions and integers are rational numbers. –0.1, 2.75, 0.001 and 6 are a few examples of rational numbers. A few characteristics of rational numbers are:

• Rational numbers are of two types: positive and negative rational numbers. When both the numerator and denominator is a positive integer, then it is said to be a positive rational number. When either the numerator or the denominator is a negative integer, then it is said to be a negative rational number.
• The number 0 is neither a negative nor a positive rational number.
• If the numerator and denominator of a rational number are divided or multiplied by a non-zero integer, we get a rational number that is equivalent to the given rational number.
• When a rational number has a denominator that is a positive integer and the numerator and denominator have no common factor other than 1, the rational number is said to be in the standard form.
• While subtracting two rational numbers, the additive inverse of the rational number to be subtracted is added to the other rational number.
• Two rational numbers with the same denominator can be added by adding the numerators keeping the denominators same. Two rational numbers with different denominators are added by taking the LCM of the two denominators first and then converting both the rational numbers to their equivalent forms keeping the LCM as the denominator.
• While subtracting, the additive inverse of the rational number to be subtracted is added to the other rational number.
• Multiplication of two rational numbers is done by multiplying their numerators and denominators separately and the obtained product will be of the form
• $\frac{product \:of \:numerators}{product \:of \:denominators}$
• Division of one rational number by a non-zero rational number is done by multiplying the rational number by the reciprocal of the other.