Four Operations
Addition, Subtraction, Multiplication and Division with Word Problems
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Overview
The four fundamental operations—addition, subtraction, multiplication and division—form the backbone of primary mathematics. For UTET Paper I, this topic tests both your computational accuracy and your ability to apply these operations to real-life word problems typically encountered in Classes I–V.
Expect questions that assess place value understanding during operations, carrying and borrowing procedures, properties of operations, and the translation of verbal statements into mathematical expressions. Word problems are particularly important as they test whether a candidate can identify the correct operation from contextual clues—a skill essential for primary teachers who must teach children to connect mathematics with everyday situations.
Mastery here is non-negotiable. Errors in basic operations cascade into mistakes in fractions, decimals and higher topics. Focus on speed, accuracy and recognising operation keywords in Hindi and English word problems.
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Key Concepts
- **Addition** combines two or more quantities into a single sum. It follows the commutative property (a + b = b + a) and associative property ((a + b) + c = a + (b + c)).
- **Subtraction** finds the difference between quantities. It is neither commutative nor associative. The number being subtracted is the subtrahend; the number from which we subtract is the minuend.
- **Multiplication** is repeated addition. It follows commutative (a × b = b × a), associative and distributive properties. The distributive property states: a × (b + c) = a × b + a × c.
- **Division** is repeated subtraction or equal sharing. It is neither commutative nor associative. Key terms: dividend ÷ divisor = quotient with remainder.
- **Relationship between operations**: Addition and subtraction are inverse operations. Multiplication and division are inverse operations. This relationship helps in checking answers.
- **Place value alignment** is critical—units under units, tens under tens—especially in vertical addition and subtraction with carrying/borrowing.
- **Word problem keywords** signal operations: "total", "sum", "altogether" suggest addition; "left", "difference", "remaining" suggest subtraction; "times", "product", "each" suggest multiplication; "share equally", "distribute", "per" suggest division.
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Formulas / Key Facts
| Concept | Key Fact | |---------|----------| | Addition identity | a + 0 = a (zero is the additive identity) | | Subtraction check | Difference + Subtrahend = Minuend | | Multiplication identity | a × 1 = a (one is the multiplicative identity) | | Multiplication by zero | a × 0 = 0 | | Division rule | Dividend = Divisor × Quotient + Remainder | | Division by 1 | a ÷ 1 = a | | Division of zero | 0 ÷ a = 0 (where a ≠ 0) | | Division by zero | Undefined—never divide by zero | | Commutative (×, +) | Order does not matter: 3 + 5 = 5 + 3; 4 × 6 = 6 × 4 | | Distributive property | 7 × 23 = 7 × 20 + 7 × 3 = 140 + 21 = 161 |