Mathematics · Class 7
Rational Numbers
Rational numbers on the number line, standard form, and operations.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Rational numbers are numbers that can be written as p/q where p, q are integers and q ≠ 0. Class 7 covers representation on number line, standard form, and operations.
Definition and Standard Form
- Every integer and fraction is rational
- Standard form: denominator positive, HCF(p,q)=1
- 0 is rational (0/1)
Number Line
Between any two rational numbers, infinitely many rationals exist. Use common denominator to compare and plot.
Operations
- Add/subtract: common denominator
- Multiply: (a/b)×(c/d) = ac/bd
- Divide: multiply by reciprocal
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Add Rationals
Find −3/4 + 1/3.
- 1LCM = 12
- 2−9/12 + 4/12
Answer
−5/12
Example 2: Standard Form
Write 12/−18 in standard form.
- 1Move sign to numerator: −12/18
- 2HCF=6 → −2/3
Answer
−2/3
Key Points to Remember
- ✓ Denominator cannot be zero
- ✓ Rational numbers closed under +, −, ×
- ✓ Division by zero undefined
Exam Tips
- • Reduce to standard form in final answer
- • Use LCM for addition of unlike fractions
Practice MCQs — Rational Numbers
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Which is rational?