Division of Integers

Class 7 Maths · Chapter 10: Operations with Integers · NCERT Ganita Prakash section P2 2.2

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Division asks a multiplication question. (−100) ÷ 25: what times 25 gives −100? 25 × (−4) = −100, so the answer is −4. (−100) ÷ (−4): (−4) × 25 = −100, so the answer is 25. And 50 ÷ (−25) = −2.

(−100) ÷ 25 = −4 · (−100) ÷ (−4) = 25

Same sign rules as multiplication: a ÷ (−b) = −(a ÷ b), (−a) ÷ b = −(a ÷ b), and (−a) ÷ (−b) = a ÷ b. A room cooled from 32°C by 5°C every hour is at 32 + 10 × (−5) = −18°C after 10 hours.

32 + 10 × (−5) = −18

Many factors: 5 × (−3) × 4 = −60 whichever pair you multiply first: multiplication is associative, and order does not matter. The sign of a long product depends on how many negatives: an even number of negatives gives +, an odd number gives −. (−1) × (−1) × (−1) = −1.

5 × (−3) × 4 = −60

Distributive property still holds: 5 × (4 + (−2)) = 5 × 4 + 5 × (−2) = 20 − 10 = 10. A token rectangle shows why: 4 rows of (2 green + 3 red) is 4 × 2 + 4 × (−3). Pattern machine: if a machine gives a + b − c, then (−10, −12, −9) → −10 − 12 + 9 = −13.

a × (b + c) = a × b + a × c

Explore: positive or negative?

1. Sort the results by sign.

Remember

• Division follows the same sign rules as multiplication.
• In a long product, an odd number of negatives makes it negative.

Quick check

What is (−56) ÷ (−2)?

1. 28
2. −28
3. −58
4. 54

Think about it

If 47 − 56 + 14 − 8 + 2 − 8 + 5 = −4, what is −47 + 56 − 14 + 8 − 2 + 8 − 5?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.