चार संक्रियाएँ
Four Operations
Addition, subtraction, multiplication and division are the four basic operations of the primary curriculum. What CTET tests is not speed of calculation but understanding — which operation a situation calls for, what the properties are, and where children go wrong.
Meanings a child must build
| Operation | Meanings the child needs |
|---|---|
| Addition | Putting together, increasing by, comparing to find a total |
| Subtraction | Taking away, finding the difference, finding how many more |
| Multiplication | Repeated addition, equal groups, arrays, times as many |
| Division | Equal sharing (how many each) and equal grouping (how many groups) |
A child who knows subtraction only as 'taking away' cannot solve 'Ravi has 7 marbles, Sita has 12, how many more does Sita have?' Teaching both meanings is a syllabus requirement, not an extra.
Properties to remember
- Commutative — a + b = b + a and a x b = b x a. Subtraction and division are not commutative.
- Associative — (a + b) + c = a + (b + c); the same holds for multiplication.
- Distributive — a x (b + c) = a x b + a x c. This is what makes column multiplication work.
- Identity — 0 is the additive identity, 1 is the multiplicative identity.
- Division by zero is not defined; zero divided by any non-zero number is 0.
Estimation and mental maths
A primary child should be able to say roughly what an answer will be before working it out. Rounding 487 + 312 to 500 + 300 gives about 800, which immediately exposes an answer of 79 or 7,990 as wrong. Estimation is part of the syllabus, not a shortcut, and CTET treats the ability to judge the reasonableness of an answer as a mark of real number sense.
Order of operations
Brackets → Of / Order → Division → Multiplication → Addition → Subtraction
The BODMAS order applies within each level from left to right; division and multiplication rank equally, as do addition and subtraction. So 12 - 4 + 3 equals 11, not 5.
The division facts
Dividend = Divisor x Quotient + Remainder
If 47 is divided by 5, the quotient is 9 and the remainder is 2, since 5 x 9 + 2 = 47. The remainder is always less than the divisor — a check that catches most errors.
Where children go wrong
✗ 42 - 17 = 35, subtracting the smaller digit from the larger in each column. | ✓ 42 - 17 = 25, regrouping one ten so that 12 - 7 = 5.
✗ 305 x 1 = 3050 | ✓ 305 x 1 = 305; multiplying by one leaves a number unchanged.
संकेत: जोड़ और गुणा में क्रमविनिमेय (commutative) नियम लागू होता है, घटाव और भाग में नहीं।
The Maths section asks 2-3 questions from the four operations, usually as word problems at Class 4-5 level or as a property-identification item. The most repeated trap is a BODMAS expression where addition appears before subtraction, and the second is a word problem in which the phrase 'how many more' has to be read as subtraction. Remember also the division algorithm, because remainder questions are a standing favourite.
Frequently asked questions
Which operations are commutative?
Addition and multiplication. Changing the order of the numbers does not change the result. Subtraction and division are not commutative, since 7 minus 4 is not the same as 4 minus 7.
What is the rule for the remainder in division?
The remainder must always be less than the divisor, and the relation dividend equals divisor times quotient plus remainder must hold. Checking this catches most division errors immediately.
Why can we not divide by zero?
Because division asks how many times the divisor fits into the dividend, and zero fits any non-zero number an unlimited number of times, giving no single answer. Division by zero is therefore undefined.
60-second recap
- Each operation has more than one meaning; subtraction includes difference, not only take away.
- Commutative and associative hold for addition and multiplication only.
- Distributive property is the basis of column multiplication.
- BODMAS: brackets, of, division and multiplication, addition and subtraction, left to right.
- Dividend = divisor x quotient + remainder, remainder less than divisor.