Chapter 4 - Rational Numbers - R D Sharma Solutions for Class 7

Rational numbers are those numbers which can be written in the form of pq where p and q are integers and q≠0. In a rational number pq, p is the numerator of fraction and q is the denominator of the fraction.

For example: 13,57,-3 are rational numbers.

Positive rational numbers are those numbers in which its numerator and denominator are either positive integers or both negative integers.

Negative rational numbers are those in which numerator and denominator are in such a way that one of them is positive and other is negative.

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Useful results:

(1) All natural numbers are rational numbers but a rational number need not be a natural number. Natural numbers are 1, 2, 3….. , all of which can be written in the fraction form as 11,21,31 etc.

If we take a rational number 45 then we see that it is not a natural number.

(2) Zero is a rational number: It is rational number because we can write it as 0=01 where, 0 and 1 are integers and 1≠0

(3) All integers are rational numbers but a rational number need not be an integer.

For example: …,-2, -1, 0, 1, 2…., are integers which can be written in the fraction form. Thus, all are rational numbers also. But if we take a rational number as -12 which can never be an integer.

(4) Each fraction is a rational number but a rational number need not be a fraction.