Rational Numbers - Revision Notes

CBSE Class 8 Mathematics
Revision Notes
Chapter – 01
Rational Numbers

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• Rational numbers are closed under the operations of addition, subtraction and multiplication.
• The operations addition and multiplication are
  (i) commutative for rational numbers.
  (ii) associative for rational numbers.
• The rational number 0 is the additive identity for rational numbers.
• The rational number 1 is the multiplicative identity for rational numbers.
• The additive inverse of the rational number ab$\frac{a}{b}$ is ab$\frac{a}{b}$ and vice-versa.
• The reciprocal or multiplicative inverse of the rational number ab$\frac{a}{b}$ is cd$\frac{c}{d}$ if ab$\frac{a}{b}$xcd$\frac{c}{d}$=1
• Distributivity   of rational numbers: For all rational numbers a, b and c,
  a(b + c) = ab + ac    and  a(b – c) = ab – ac
• Rational numbers can be represented on a number line.
• Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.
• Positive Rationals: Numerator and Denominator both are either positive or negative. Example: 47,−3−4$\frac{4}{7},\frac{-3}{-4}$
• Negative Rationals: Numerator and Denominator both are of opposite signs. Example: −211,4−9$\frac{-2}{11},\frac{4}{-9}$
• Additive Inverse: Additive inverse (negative) ab$\frac{a}{b}$+−ab$\frac{-a}{b}$=−ab$\frac{-a}{b}$+ab$\frac{a}{b}$=0, −ab$\frac{-a}{b}$ is the additive inverse of abandab$\frac{a}{b}and\frac{a}{b}$ is the additive inverse of −ab$\frac{-a}{b}$.
• Mulitiplicative Inverse (reciprocal): ab$\frac{a}{b}$xcd$\frac{c}{d}$=1=cd$\frac{c}{d}$xab$\frac{a}{b}$ where cd$\frac{c}{d}$ is the reciprocal of ab$\frac{a}{b}$. Zero has no reciprocal. The reciprocal of 1 is1 and of -1 is -1.