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NCERT Solutions · Maths Ch 10
Operations with Integers
20 questions · 4 exercises
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Ex 10.1
Ex 10.2
Ex 10.3
Ex 10.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 10.1 · 1 QUESTIONS
Sum and Difference Puzzles
Q1
Find the two numbers from their sum and difference (difference = first number − second number): (a) Sum = 27, Difference = 9 (b) Sum = 4, Difference = 12 (c) Sum = 0, Difference = 10 (d) Sum = 0, Difference = −10 (e) Sum = −7, Difference = −1 (f) Sum = −7, Difference = −13
(5 marks)
2
EXERCISE 10.2 · 5 QUESTIONS
Multiplication of Integers
Q2
Using the token interpretation, find the values of: (a) 3 × (−2) (b) (−5) × (−2) (c) (−4) × (−1) (d) (−7) × 3
(3 marks)
Q3
If 123 × 456 = 56088, without calculating, find the value of: (a) (−123) × 456 (b) (−123) × (−456) (c) 123 × (−456)
(2 marks)
Q4
Try to frame a simple rule to multiply two integers.
(2 marks)
Q5
Find the following products: (a) 4 × (−3) (b) (−6) × (−3) (c) (−5) × (−1) (d) (−8) × 4 (e) (−9) × 10 (f) 10 × (−17)
(5 marks)
Q6
Fill in the blanks: 3 × −4 = −12 and −4 × 3 = −12; −30 × 12 = ___ and 12 × −30 = ___; −15 × −8 = 120 and −8 × −15 = 120; 14 × −5 = −70 and −5 × ___ = −70. What do you notice?
(2 marks)
3
EXERCISE 10.3 · 4 QUESTIONS
Division of Integers
Q7
Find the values of: (a) 14 × (−15) (b) −16 × (−5) (c) 36 ÷ (−18) (d) (−46) ÷ (−23)
(3 marks)
Q8
A freezing process requires that the room temperature be lowered from 32°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?
(2 marks)
Q9
A cement company earns a profit of ₹8 per bag of white cement sold and a loss of ₹5 per bag of grey cement sold. [Represent the profit/loss as integers.] (a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss? (b) If the number of grey cement bags sold is 6,400, how many bags of white cement must it sell to have neither profit nor loss?
(3 marks)
Q10
Replace the blank with an integer to make a true statement: (a) (−3) × ___ = 27 (b) 5 × ___ = (−35) (c) ___ × (−8) = (−56) (d) ___ × (−12) = 132 (e) ___ ÷ (−8) = 7 (f) ___ ÷ 12 = −11
(3 marks)
4
EXERCISE 10.4 · 10 QUESTIONS
Expressions Using Integers
Q11
Find the values of the following expressions: (a) (−5) × (18 + (−3)) (b) (−7) × 4 × (−1) (c) (−2) × (−1) × (−5) × (−3)
(3 marks)
Q12
Find the values of the following expressions: (a) (−27) ÷ 9 (b) 84 ÷ (−4) (c) (−56) ÷ (−2)
(3 marks)
Q13
Find the integer whose product with (−1) is: (a) 27 (b) −31 (c) −1 (d) 1 (e) 0
(3 marks)
Q14
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.
(2 marks)
Q15
Try a modified Collatz rule with integers: 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. Try with starting numbers (−21) and (−6). Describe the patterns you observe.
(5 marks)
Q16
In a test, (+4) marks are given for every correct answer and (−2) marks for every incorrect answer. (a) Anita answered all the questions. She scored 40 marks even though 15 of her answers were correct. How many of her answers were incorrect? How many questions are in the test? (b) Anil scored (−10) marks even though he had 5 correct answers. How many of his answers were incorrect? Did he leave any questions unanswered?
(5 marks)
Q17
Pick the pattern: find the operations done by the machine, which takes three numbers (a, b, c) and gives: (4, 8, −3) → 28; (6, 9, 6) → −48; (2, 3, −2) → 8; (−9, 5, −8) → 31; (7, −4, −6) → −17; (−16, −6, −9) → ?
(3 marks)
Q18
Imagine you're in a place where the temperature drops by 5°C each hour. If the temperature is currently 8°C, write an expression which denotes the temperature after 4 hours.
(2 marks)
Q19
Find 3 consecutive numbers with a product of (a) −6 (b) 120.
(3 marks)
Q20
An alien society uses a currency called 'pibs' with just two coins: a +13 pibs coin and a −9 pibs coin. You have several of these coins. Is it possible to purchase an item that costs +85 pibs?
(5 marks)