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MathematicsClass 7Operations

Operations | Class 7 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 4 min read

Operations – this guide gives you a concise, exam-ready overview of Operations from Class 7 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Division of Integers

This section introduces division of integers by relating it to multiplication. Division is understood as finding a number which, when multiplied by the divisor, gives the dividend. For example, (-100) ÷ 25 asks for a number which multiplied by 25 equals -100, which is -4. Similarly, (-100) ÷ (-4) asks for a number which multiplied by -4 equals -100, which is 25. The section generalizes the rules for division of integers: dividing two integers with the same sign results in a positive quotient, while dividing integers with opposite signs results in a negative quotient. The section provides several examples for practice, including word problems involving temperature changes and profit/loss scenarios, reinforcing the application of integer division in real life. Students are encouraged to summarize the rules for integer division based on patterns observed in examples. The section also includes exercises to find missing integers in multiplication and division statements, enhancing problem-solving skills. The connection between multiplication and division is emphasized, helping students understand the inverse relationship between these operations.

📊 Diagram: No specific diagrams, but tables and examples illustrate division as inverse of multiplication with positive and negative integers.

🧪 Activity: Exercises include finding values of integer division expressions and solving real-life problems involving temperature and profit/loss using integer division.

🔗 Connection: This section leads into exploring properties of integer multiplication and division, including commutativity, associativity, and distributive properties.

Frequently asked questions

2. Find the values of the following expressions: (a) (-27) ÷ 9 (b) 84 ÷ (-4) (c) (-56) ÷ (-2)

(a) (-27) ÷ 9 = -3

Explanation: Dividing a negative integer by a positive integer gives a negative quotient. 27 ÷ 9 = 3, so the answer is -3.

(b) 84 ÷ (-4) = -21

Explanation: Dividing a positive integer by a negative integer gives a negative quotient. 84 ÷ 4 = 21, so the answer is -21.

(c) (-56) ÷ (-2) = 28

Explanation: Dividing a negative integer by a negative integer gives a positive quotient. 56 ÷ 2 = 28, so the answer is 28.

3. Find the integer whose product with (-1) is: (a) 27 (b) -31 (c) -1 (d) 1 (e) 0

(a) Let the integer be x.

x × (-1) = 27

=> x = 27 ÷ (-1) = -27

(b) x × (-1) = -31

=> x = -31 ÷ (-1) = 31

(c) x × (-1) = -1

=> x = -1 ÷ (-1) = 1

(d) x × (-1) = 1

=> x = 1 ÷ (-1) = -1

(e) x × (-1) = 0

=> x = 0 ÷ (-1) = 0

4. If 47 - 56 + 14 - 8 + 2 - 8 + 5 = -4, then find the value of -47 + 56 - 14 + 8 - 2 + 8 - 5 without calculating the full expression.

Given: 47 - 56 + 14 - 8 + 2 - 8 + 5 = -4

We need to find: -47 + 56 - 14 + 8 - 2 + 8 - 5

Notice that the second expression is the negative of the first expression:

  • (47 - 56 + 14 - 8 + 2 - 8 + 5) = -(-4) = 4

Therefore, the value is 4.

5. Do you remember the Collatz Conjecture from last year? Try a modified version with integers. The rule is — start with any number; if the number is even, take half of it; if the number is odd, multiply it by -3 and add 1; repeat. An example sequence is shown below. Try this with different starting numbers: (-21), (-6), and so on. Describe the patterns you observe.

This is an exploratory question. For example:

Starting with -21 (odd):

  • Multiply by -3 and add 1: (-21) × (-3) + 1 = 63 + 1 = 64
  • 64 is even, so take half: 64 ÷ 2 = 32
  • 32 is even, half: 16
  • 16 is even, half: 8
  • 8 is even, half: 4
  • 4 is even, half: 2
  • 2 is even, half: 1
  • 1 is odd, multiply by -3 and add 1: 1 × (-3) + 1 = -3 + 1 = -2
  • -2 is even, half: -1
  • -1 is odd, multiply by -3 and add 1: (-1) × (-3) + 1 = 3 + 1 = 4
  • Then the sequence continues.

Patterns observed include oscillat

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