Whole Numbers are simply the numbers 0, 1,
2, 3, 4, 5, ...
Natural numbers are those used for counting
and ordering i.e. 1, 2, 3, 4, 5, ...
An integer is a whole number (not a
fractional number) that can be positive, negative, or zero.
of integers are: -5, 1, 5 etc.
A number of the form p/q or a number which
can be expressed in the form p/q, where p and q are integers and q≠0, is called
a rational number.
2/3, -3/4 and 13/-7 are rational number.
In the rational number p/q, integer p is
known as the numerator and non-zero integer q is called the denominator.
If the numerator and denominator of a
rational number are of the same sign, then it is said to be positive.
Otherwise, it is negative.
2/11 and -7/-13 are positive numbers
-9/5 and 4/-14 are
A rational number p/q is said to be in the
lowest form or simplest form if p and q have no common factor other than 1.
2/3 is in simplest form as it cannot be further reduced by dividing its
numerator and denominator by common factor.
A rational number p/q is said to be in
standard form, if its denominator q is a positive integer and p and q have no common
divisor other than 1.
Two rational numbers p/q and r/s are equal
if pxs = qxr
Addition of Rational
Numbers With Same Denominators
1 Find the new numerator by adding the numerators of the given fractions.
2 Retain the (common) denominator.
3 Write the new numerator over the denominator.
4 Simplify the fraction if required.
Numbers With Different Denominators
Step 1 Find the LCM (Least Common Multiple) of the denominators of
the given fractions.
Step 2 Convert the given fractions to equivalent fractions with
denominator equal to the LCM (least common multiple) obtained in Step 1.
Step 3 Find the new numerator by adding the
numerators of the given fractions.
Step 4 Retain the (common) denominator.
Step 5 Write the new numerator over the
Step 6 Simplify the fraction if required.