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.
### Example 2: Subtraction with Borrowing **Problem**: A farmer had 5,003 kg of wheat. He sold 2,478 kg. How much wheat remains?
**Solution**: ``` 5003
2478
------ 2525 ``` Step 1: Units: 3 − 8 (cannot do) → borrow from tens, but tens = 0, so borrow from hundreds, but hundreds = 0, so borrow from thousands. Step 2: 5003 becomes 4000 + 900 + 90 + 13 after borrowing Step 3: 13 − 8 = 5; 9 − 7 = 2; 9 − 4 = 5; 4 − 2 = 2
**Answer**: 2,525 kg
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### Example 3: Multiplication (2-digit by 2-digit) **Problem**: A box contains 36 pencils. How many pencils are in 24 such boxes?
**Solution**: ``` 36 × 24 = 36 × (20 + 4) = 36 × 20 + 36 × 4 = 720 + 144 = 864 ``` Alternatively using standard algorithm: ``` 36 × 24 ---- 144 (36 × 4) 720 (36 × 20, written one place left) ---- 864 ```
**Answer**: 864 pencils
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### Example 4: Division with Remainder **Problem**: 497 sweets are to be distributed equally among 8 children. How many sweets does each child get? How many are left over?
**Answer**: Each child gets 62 sweets; 1 sweet remains.
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### Example 5: Word Problem Requiring Two Operations **Problem**: Ravi bought 5 notebooks costing ₹45 each and 3 pens costing ₹12 each. How much did he spend in total?
**Solution**: Cost of notebooks = 5 × 45 = ₹225 Cost of pens = 3 × 12 = ₹36 Total = 225 + 36 = ₹261
**Answer**: ₹261
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Common Mistakes
| Wrong Thinking | Correct Fix | |----------------|-------------| | **Forgetting to carry/borrow** — Writing 48 + 35 = 73 (ignoring carry from units) | Always check: 8 + 5 = 13, write 3, carry 1; 4 + 3 + 1 = 8. Answer is 83. | | **Misaligning place values** — Adding 456 + 78 by writing 78 under 45 | Align rightmost digits first. Write 78 under 56, not under 45. | | **Confusing operation keywords** — Interpreting "how many more" as addition | "How many more" compares two quantities, requiring subtraction. | | **Writing remainder greater than divisor** — Getting 45 ÷ 7 = 5 remainder 10 | Remainder must always be less than divisor. Correct: 45 ÷ 7 = 6 remainder 3. | | **Ignoring zero in multiplication** — Calculating 305 × 4 as 3 × 4 = 12, then appending 5 | Multiply each digit: 4 × 5 = 20, carry 2; 4 × 0 + 2 = 2; 4 × 3 = 12. Answer: 1,220. | | **Order error in subtraction/division** — Treating 12 − 18 as 18 − 12 | Subtraction and division are not commutative. Respect the order given in the problem. |