Questions
3 questions per paper
Difficulty
Easy
Importance
High yield for CTET/DSSSB
Overview
Multiplication and division form the bedrock of quantitative aptitude in teacher eligibility exams like CTET and KVS. Mastering these operations is essential not only for direct numerical computation but also for solving complex word problems related to speed, time, and unitary methods. The core focus is on mental agility and applying inverse relationships between these two operations efficiently.
Multiplication Tables and Properties
Multiplication is essentially repeated addition, and speed here is critical for time management during exams. Familiarity with tables up to 20 allows for rapid factorization and simplification of algebraic expressions.
- Commutative Property: a × b = b × a
- Associative Property: (a × b) × c = a × (b × c)
- Distributive Property: a × (b + c) = (ab) + (ac)
- Identity Element: Any number multiplied by 1 is itself
- Zero Property: Any number multiplied by 0 equals 0
Long Division and Remainder Theorem
Long division is tested through questions involving dividends, divisors, and remainders, often framed as algebraic polynomial division. Understanding the relationship between these components is vital for solving divisibility rule problems.
- Dividend = (Divisor × Quotient) + Remainder
- Remainder must always be less than the Divisor
- Division by 0 is undefined in mathematics
- Divisibility rule for 3: Sum of digits must be divisible by 3
- Divisibility rule for 9: Sum of digits must be divisible by 9
Word Problems and Applied Arithmetic
Word problems typically test your ability to convert linguistic statements into mathematical expressions using multiplication or division. Look for keywords like 'each', 'per', or 'distributed' to identify the required operation.
- Unitary Method: Find the value of one unit first, then multiply
- Average formula: Sum of values divided by count of values
- Inverse relationship: Multiplication by a fraction is equivalent to division
- Percentage application: (Part/Whole) × 100
- Rate problems: Total = Rate × Time
Formula Sheet
Dividend = (Divisor × Quotient) + Remainder
a × (b + c) = ab + ac
Average = Total Sum / Number of Units
Exam Tip
Always verify your division results by quickly multiplying the quotient by the divisor and adding the remainder; it takes five seconds but prevents costly calculation errors.
Common Mistakes
- Swapping the divisor and dividend during long division, leading to reciprocal errors.
- Forgetting to include the remainder when verifying division results.
- Misapplying the Order of Operations (BODMAS) when multiplication and division appear together in a string.
More Revision Notes
Ready to test yourself?
Play topic-wise Multiplication & Division questions in Aspirant Arcade — gamified MCQ practice.
Download Free