AP Board Class 8 Maths Chapter 1 Rational Numbers Complete Guide
1. Rational numbers are closed under addition, subtraction, and multiplication.
2. Addition and multiplication are commutative and associative for rational numbers.
3. The additive identity is 0, and the multiplicative identity is 1 for rational numbers.
4. Every rational number has an additive inverse ( -frac{a}{b} ) and a multiplicative inverse ( frac{c}{d} ) such that their product is 1.
5. Rational numbers follow the distributive property and can be represented on a number line, with infinitely many numbers between any two rational numbers.
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AP Board Class 8 Mathematics Chapter 1 – Rational Numbers
Below are the key concepts will cover
1. Rational numbers are closed under the operations of addition, subtraction, and multiplication.
2. The operations addition and multiplication are
(i) commutative for rational numbers.
(ii) associative for rational numbers.
3. The rational number 0 is the additive identity for rational numbers.
4. The rational number 1 is the multiplicative identity for rational numbers.
5. The additive inverse of the rational number \( \frac{a}{b} \) is \( -\frac{a}{b} \) and vice-versa.
6. The reciprocal or multiplicative inverse of the rational number \( \frac{a}{b} \) is \( \frac{c}{d} \) if \( \frac{a}{b} \times \frac{c}{d} = 1 \).
7. Distributivity of rational numbers: For all rational numbers \( a \), \( b \), and \( c \), \( a(b+c) = ab+ac \) and \( a(b-c) = ab-ac \).
8. Rational numbers can be represented on a number line.
9. 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.
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