__Comparison of Rational Numbers__- While comparing
**positive rational numbers**with the same denominator, the number with the greatest numerator is the largest. It is easy to compare these numbers if their denominators are the same. Eg: - A positive rational number is always greater than a negative rational number.
- While comparing
**negative rational numbers**with the same denominator, compare their numerators ignoring the minus sign. The number with the greatest numerator is the smallest. - Positive rational numbers lie to the right of 0, while negative rational numbers lie to the left of 0 on the number line.
- To compare rational numbers with different denominators, convert them into equivalent rational numbers with the same denominator, which is equal to the
**LCM**of their**denominators.**You can find infinite rational numbers between any two given rational numbers.

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Application of Algebraic Expressions__

**Operations on Rational Numbers**

- The denominator of the sum or difference of two rational numbers with the same denominator is the same as the common denominator of the given numbers.
- The numerator of the sum of two rational numbers with the same denominator is the sum of the numerators of the given numbers with their correct sign.
- The numerator of the difference of two rational numbers with the same denominator is the difference between the numerators of the given numbers with their correct sign.
- To add or subtract rational numbers with different denominators, we convert them into equivalent rational numbers having common denominator equal to the LCM of the denominators of the given numbers.
- Two rational numbers whose sum is zero are called additive inverse of each other.
- The numerator and denominator of the product of two rational numbers are equal to the product of their individual numerators and denominators.
- Two rational numbers whose product is 1 are called reciprocals of each other.
- A rational number and its reciprocal always have the same sign.
- To divide one rational number by a second rational number, we actually multiply the first number by the reciprocal of the second number.

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