RATIONAL NUMBERS- ESSENTIAL POINTS
- Rational Number: A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0, is called a rational number. The numbers etc. are rational numbers.
- All integers and fractions are rational numbers.
- If the numerator and denominator of a rational number are multiplied or divided by a non-zero integer, we get a rational number which is said to be equivalent to the given rational number.
- For example, -4/7 = (-4 x 2)/(7 x 2) = -8/14 so we say -8/14 is equivalent form of -4/7. Also like -8/14 = (-8 )/(14 ) = -4/7
- Rational numbers are classified as Positive and Negative Rational Numbers.
- A positive rational number has both numerator and denominator positive.
- Negative rational number has either denominator or numerator negative.
- For example, 2/7 is a positive rational number whereas -3/7 is a negative rational number
- Positive rational numbers are greater than negative rational numbers.
- The number 0 is neither a positive nor a negative rational number.
- Standard form of rational number has its denominator as positive integer and there is nothing common factor between numerator and denominator. The numbers 2/5, -4/9 etc. are in standard form
- There are infinite number of rational numbers between two rational numbers.
- Keeping the denominators of rational numbers same, their numerators can be added directly.
- When denominators are different then addition is done by taking the LCM of the two denominators.
- For example, -2/3 + 3/8 = -16/24 + 9/24 = (-16 + 9)/24 = -7/24. Here, LCM of 3 and 8 is 24.
- To subtracting two rational numbers, Additive inverse of number to be subtracted is added to the rational number.
- To multiply two rational numbers, we multiply their numerators and denominators separately, and write the product of rational numbers as (product of numerators)/(product of denominators).
- For division of rational numbers, multiply the rational number by the reciprocal of the other.
- Thus, -7/3 4/5 = -7/2 x (reciprocal of 4/5) = -7/2 x 5/4 = -35/8
- Division by 0 is not defined.
