Introduction to Rational Numbers — lesson. Mathematics CBSE, Class 7.

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A rational number is a number that can be expressed as (\(p / q\) ) of two integers, a numerator \(p\) and a non-zero denominator \(q\). Since \(q\) may be equal to \(1\), every integer is a rational number.

Example:

\begin{array}{l} 15 / 13, where p = 15 and q = 13; q \neq 0. \\ 12 / 20, where p = 12 and q = 20; q \neq 0. \\ 2 / 1, where p = 2 and q = 1; q \neq 0. \end{array}

Difference between a fraction and a rational number:

A number in the rational form

\frac{p}{q}

where \(p\) and \(q\) are whole numbers and \(q ≠ 0\) is known as a fraction, whereas a number in the form

\frac{p}{q}

where \(p\) and \(q\) are integers and \(q ≠ 0\) is known as a rational number.

Example:

\frac{3}{2}

is a fraction as well as the whole number.

\frac{- 3}{2}

is a rational number but not a fraction because \(-3\) is not a whole number.

There are different types of fractions:

i) Proper fractions

ii) Improper fractions

iii) Mixed fraction

iv) Unit fraction

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1. Introduction to Rational Numbers

Theory: