Mathematics - Class ...

Key Points

                           i.        Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, ...

                          ii.        Natural numbers are those used for counting and ordering i.e. 1, 2, 3, 4, 5, ...

                         iii.        An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Examples of integers are: -5, 1, 5 etc.

                         iv.        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.

Example: 2/3, -3/4 and 13/-7 are rational number.

                         v.        In the rational number p/q, integer p is known as the numerator and non-zero integer q is called the denominator.

                        vi.        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.

Example: 2/11 and -7/-13 are positive numbers

-9/5 and 4/-14 are negative numbers

          vii.        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.

Example: 2/3 is in simplest form as it cannot be further reduced by dividing its numerator and denominator by common factor.

          viii.        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.

                           ix.        Two rational numbers p/q and r/s are equal if pxs = qxr

Addition of Rational Numbers

Rational Numbers With Same Denominators

Step 1 Find the new numerator by adding the numerators of the given fractions.

Step 2 Retain the (common) denominator.

Step 3 Write the new numerator over the denominator.

Step 4 Simplify the fraction if required.

Rational 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 denominator.

Step 6 Simplify the fraction if required.