Questions
3 questions per paper
Difficulty
Medium
Importance
High yield for CTET/DSSSB
Overview
The Number System is the fundamental building block for quantitative aptitude in teaching exams like CTET and DSSSB. Mastery of this topic is essential because it serves as the base for all advanced arithmetic and algebraic problem-solving, ensuring you can handle numerical logic questions with speed and accuracy.
Integers and Number Properties
Integers include all whole numbers, their negative counterparts, and zero, forming the base of the number line. Understanding divisibility rules and properties of operations is critical for solving number sequence and series problems common in teaching entrance exams.
- Natural numbers (N) start from 1, Whole numbers (W) include 0.
- Prime numbers have exactly two factors: 1 and itself.
- Composite numbers have more than two factors.
- Divisibility rule for 3: Sum of digits must be divisible by 3.
- Divisibility rule for 11: Difference between sum of odd and even position digits is 0 or multiple of 11.
Fractions and Decimals
Fractions and decimals are frequently tested through simplification and comparative analysis. Candidates must be comfortable converting repeating decimals into p/q form and performing operations on mixed and improper fractions.
- Proper fraction: Numerator < Denominator.
- Improper fraction: Numerator ≥ Denominator.
- Converting 0.abc (bar) to fraction: (abc - a)/990.
- Addition requires common denominators (LCM).
- Multiplication: Multiply numerators and denominators independently.
Rational Numbers
Rational numbers are any numbers that can be expressed as p/q where q ≠ 0. Exams often test the density property—finding rational numbers between two given values—and identifying terminating vs. non-terminating repeating expansions.
- Terminating decimals have denominators with prime factors of only 2 or 5.
- Rational + Irrational = Irrational.
- Multiplicative inverse: a/b becomes b/a.
- Additive inverse: x becomes -x.
- Commutative property: a + b = b + a.
Exponents and Powers
Exponents follow specific laws that simplify complex arithmetic expressions. These questions often appear in 'simplification' sections where the candidate must apply base-matching techniques.
- Product Law: a^m × a^n = a^(m+n).
- Quotient Law: a^m / a^n = a^(m-n).
- Power of a Power: (a^m)^n = a^(mn).
- Zero Exponent: a^0 = 1 (where a ≠ 0).
- Negative Exponent: a^(-n) = 1/a^n.
Formula Sheet
p/q conversion for recurring decimals
a^m × a^n = a^(m+n)
(a^m)^n = a^(mn)
Divisibility rules for 2, 3, 4, 5, 8, 9, 11
Exam Tip
Always convert repeating decimals to fractions before solving expressions; it turns an impossible-looking multiplication into a simple fraction simplification.
Common Mistakes
- Miscalculating negative signs during integer subtraction or exponentiation.
- Forgetting to simplify fractions to their lowest terms before performing operations.
- Confusing the divisibility rules for prime numbers like 7 or 13 with those for 3 or 9.
More Revision Notes
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