# VidyaSetu · Class 8 Mathematics · Rational Numbers
## Slides — Rational Numbers: Number Line & Standard Form

### Definition
A number of the form **p/q**, where p, q are integers and **q ≠ 0**.

### Standard form
- Denominator **positive**
- Numerator & denominator **co-prime**
- 8/(−12) = −2/3 · (−15)/(−25) = 3/5

### Number line
To plot a/b:
1. Mark 0 and 1 (left side for negatives)
2. Divide the unit interval into |q| equal parts
3. Count |p| parts from the anchor

### Inverses & identities
- Additive inverse: −a (a + (−a) = 0)
- Multiplicative identity: 1
- Reciprocal: q/p (does not exist for 0)

### Properties checklist
Closure · Commutative (add/mul) · Associative (add/mul) · Distributive
**Not commutative:** subtraction, division

### Infinitely many between any two
Mean of a/b and c/d lies between them: (a/b + c/d) ÷ 2