Operations with Integers - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Integers help describe temperatures below zero, debts, lifts below ground level, losses, and direction. The chapter becomes easy when students connect operations to movement on a number line and to real-life gain/loss situations.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Integers

Integers include positive whole numbers, zero, and negative whole numbers. They extend counting numbers in both directions.

Addition and subtraction

Adding a positive moves right; adding a negative moves left. Subtracting a number means adding its opposite.

Multiplication signs

Same signs give positive; different signs give negative. This pattern must be practised until it becomes fluent.

3. Rules and formulas to remember

• Additive inverse: a + (-a) = 0. A number and its opposite cancel.
• Subtract integer: a - b = a + (-b). Change subtraction to addition of opposite.
• Same sign product: (+) x (+) = + and (-) x (-) = +. Same direction effect.
• Different sign product: (+) x (-) = - and (-) x (+) = -. Opposite signs give negative.

4. Worked examples

Example 1: Evaluate -7 + 12.

Move 12 steps right from -7, or subtract magnitudes: 12 - 7 = 5. Answer = 5.

Example 2: Evaluate -9 - 4.

-9 - 4 = -9 + (-4) = -13.

Example 3: Evaluate (-6) x (-8).

Same signs give positive. 6 x 8 = 48, so answer = 48.

Example 4: A diver is at -18 m and rises 7 m. What is the new position?

-18 + 7 = -11 m.

5. Activity corner

Make a floor-number line from -5 to +5. Students physically move right for positive and left for negative. This reduces sign confusion.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Thinking negative always means smaller answer after every operation Fix: Multiplying two negatives gives a positive.
• Mistake: Forgetting to change sign in subtraction Fix: a - b is a + opposite of b.
• Mistake: Dropping brackets around negative numbers Fix: Write (-4) x (-3), not -4 x -3 in unclear working.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Find -15 + 6.
2. Find 8 - (-5).
3. Find (-7) x 9.
4. Find (-48) / (-6).
5. A temperature changes from -3 C to 5 C. What is the rise?
6. Why is -2 x -3 positive?

9. Answer key

1. Find -15 + 6. Answer: -9.

2. Find 8 - (-5). Answer: 13.

3. Find (-7) x 9. Answer: -63.

4. Find (-48) / (-6). Answer: 8.

5. A temperature changes from -3 C to 5 C. What is the rise? Answer: 8 C.

6. Why is -2 x -3 positive? Answer: Repeated sign patterns and integer rules show same signs give positive.

10. Quick revision

• Main themes: integers, negative numbers, addition, subtraction, multiplication, division.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.