NCERT Solutions for Class 7 Maths Chapter 10: Operations with Integers – Ganita Prakash Part 2

Complete NCERT Solutions for Class 7 Maths Chapter 10 “Operations with Integers” from the Ganita Prakash Part 2 textbook, covering multiplication, division, and real-world applications of integers.

Last Updated: September 23, 2026

A Quick Recap of Integers

Finding number pairs from their sum and difference: if a+b = Sum and a−b = Difference, then a = (Sum+Difference)/2 and b = (Sum−Difference)/2.

• Sum=27, Difference=9 → pair = (18, 9)
• Sum=4, Difference=12 → pair = (8, −4)
• Sum=0, Difference=10 → pair = (5, −5)
• Sum=0, Difference=−10 → pair = (−5, 5)
• Sum=−7, Difference=−1 → pair = (−4, −3)
• Sum=−7, Difference=−13 → pair = (−10, 3)

Multiplication of Integers

Using token models: (a) 3 × (−2) = −6 (b) (−5) × (−2) = 10 (c) (−4) × (−1) = 4 (d) (−7) × 3 = −21

Sign rules for multiplication: multiply the absolute values; if the two integers have different signs, the product is negative; if they have the same sign, the product is positive.

Example: given 123 × 456 = 56088: (a) (−123) × 456 = −56088 (b) (−123) × (−456) = 56088 (c) 123 × (−456) = −56088

More Products

• 4 × (−3) = −12
• (−6) × (−3) = 18
• (−5) × (−1) = 5
• (−8) × 4 = −32
• (−9) × 10 = −90
• 10 × (−17) = −170

Division of Integers

Sign rules for division: same as multiplication — same signs give a positive result, different signs give a negative result.

• 14 × (−15) = −210
• −16 × (−5) = 80
• 36 ÷ (−18) = −2
• (−46) ÷ (−23) = 2

Freezing process: room temperature starts at 32°C and drops 5°C every hour for 10 hours. Total drop = 5×10 = 50°C. Final temperature = 32−50 = −18°C.

Cement company profit/loss: profit of Rs. 8/bag on white cement, loss of Rs. 5/bag on grey cement. (a) Selling 3000 white bags and 5000 grey bags: profit = 3000×8=Rs.24,000; loss = 5000×5=Rs.25,000; net = Rs. 1,000 loss. (b) If 6400 grey bags are sold, white bags needed for break-even: 8x = 6400×5 = 32,000, so x = 4,000 bags.

Fill in the Blank

• (−3) × ___ = 27 → −9
• 5 × ___ = −35 → −7
• ___ × (−8) = −56 → 7
• ___ × (−12) = 132 → −11
• ___ ÷ (−8) = 7 → −56
• ___ ÷ 12 = −11 → −132

Combined Expressions

(a) (−5) × (18 + (−3)) = −5×18 + (−5)×(−3) = −90+15 = −75

(b) (−7) × 4 × (−1) = (−28)×(−1) = 28

(c) (−2)×(−1)×(−5)×(−3) = 2×15 = 30

Division: (a) (−27)÷9 = −3 (b) 84÷(−4) = −21 (c) (−56)÷(−2) = 28

Integer whose product with (−1) equals: (a) 27 → −27 (b) −31 → 31 (c) −1 → 1 (d) 1 → −1 (e) 0 → 0

If 47−56+14−8+2−8+5 = −4, find −47+56−14+8−2+8−5 without recalculating: this is exactly the negative of the first expression, so the answer = −(−4) = 4.

Word Problems and Puzzles

Pattern-machine puzzle (rule: First − [Second × Third]): row values computed as 28, −48, 8, 31, −17, and the final missing value = −70.

Temperature expression: starting at 8°C, dropping 5°C/hour for 4 hours: expression = 8 − (5 × 4) = −12°C.

Three consecutive integers with product: (a) −6 → −3, −2, −1 (check: (−3)×(−2)×(−1)=−6) (b) 120 → 4, 5, 6 (check: 4×5×6=120)

Increasing order of expressions (−348)+(−1064)=−1412; (−348)−(−1064)=716; 348−(−1064)=1412; (−348)×(−1064)=370272; 348×(−1064)=−370272; 348×964=335472. Increasing order: 348×(−1064) < (−348)+(−1064) < (−348)−(−1064) < 348−(−1064) < 348×964 < (−348)×(−1064).

Practice more: Extra Questions for Class 7 Maths Chapter 10

Quick revision: Revision Notes for Class 7 Maths Chapter 10

Frequently Asked Questions

What is the rule for adding integers with the same sign versus different signs?
Adding two integers with the same sign: add their values and keep the common sign; adding integers with different signs: subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value.

Why does subtracting a negative integer give the same result as adding a positive one?
Subtracting a number is the same as adding its additive inverse (opposite); since the additive inverse of a negative integer is positive, subtracting a negative integer is mathematically equivalent to adding the corresponding positive integer.

Written by Satish

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