# Mathematics - Class 8 / Grade 8

- Rational Numbers (Recap)
### Rational Numbers (Recap)

Math - Class 8 – Rational Numbers - Key Points/Notes/Worksheets/Explanation/Lesson/Practice Questions Tags: Worksheets and Problems on Rational Numbers for grade VIII, Introduction to Rational Numbers, Practice page and solved example on Rational Numbers for 8th grade, Important Notes on Rational Numbers, Whole Numbers, Natural Numbers, Addition of Rational Numbers, Rational Numbers With Same Denominators, Rational Numbers With Different DenominatorsRational Numbers

**Recapitulation**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.

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