CBSE Important Questions Class 7 Maths Chapter 10 Operations with Integers

CBSE Important Questions Class 7 Maths Chapter 10 – Operations with Integers

Class 7 Maths Chapter 10 Operations with Integers is a chapter of Part 2 of the new NCERT (National Council of Educational Research and Training) textbook Ganita Prakash. Integers are whole numbers together with their negatives, such as –3, 0 and 7. Students learn to add, subtract, multiply and use brackets with integers, to find the additive inverse of a number, and to apply the rules of signs and the properties of integers.

These CBSE important questions for Class 7 Maths Chapter 10 include multiple choice questions on sums, differences and products of integers, true or false statements, number patterns, and a real-life problem on a plane and a submarine. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them in class. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 7 Maths Chapter 10 Operations with Integers

Operations with Integers (New NCERT)
Medium
Q.
Find the following products.
(a) 4 × (–3)
(b) (–6) × (–3)
(c) (–5) × (–1)
(d) (–8) × 4
(e) (–9) × 10
(f) 10 × (–17)
Operations with Integers (New NCERT)
Medium
Q.
​Imagine you’re in a place where the temperature drops by 5°C each hour. If the temperature is currently at 8°C, write an expression that denotes the temperature after 4 hours.​
Operations with Integers (New NCERT)
Medium
Q.
Use the numbers 3, –2, 5, –6 exactly once and the operations ‘+’, ‘-’, and ‘×’ exactly once and brackets as necessary to write an expression such that-
(a) The result is the maximum possible
(b) The result is the minimum possible
Operations with Integers (New NCERT)
Medium
Q.
Given that 207 × (–33 + 7) = –5382, write the value of –207 × (33 – 7) = ________​
Operations with Integers (New NCERT)
Medium
Q.
Given that (–548) × 972 = –532656, write the values of:
(a) (–547) × 972
(b) (–548) × 971
(c) (–547) × 971
Operations with Integers (New NCERT)
Medium
Q.
Arrange the expressions given below in increasing order:
(a) (–348) + (–1064)
(b) (–348) – (–1064)
(c) 348 – (–1064)
(d) (–348) × (–1064)
(e) 348 × (–1064)
(f) 348 × 964
Operations with Integers (New NCERT)
Medium
Q.
Find the values of:
(a) (32 × (–18)) ÷ ((–36))
(b) (32) ÷ ((–36) × (–18))
(c) (25 × (–12)) ÷ ((45) × (–27))
(d) (280 × (–7)) ÷ ((–8) × (–35))
Operations with Integers (New NCERT)
Medium
Q.
An alien society uses a peculiar currency called ‘pibs’ with just two denominations of 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? Yes, we can use 10 coins of +13 pibs and 5 coins of -9 pibs to make a total of +85. Using the two denominations, try to get the following totals:
(a) +20
(b) +40
(c) –50
(d) +8
(e) +10
(f) –2
(g) +1
(h) Is it possible to purchase an item that costs 1568 pibs?
Operations with Integers (New NCERT)
Medium
Q.
​Find 3 consecutive numbers with a product of (a) –6, (b) 120.​
Operations with Integers (New NCERT)
Medium
Q.
​Pick the pattern – find the operations done by the machine shown below:
Operations with Integers (New NCERT)
Medium
Q.
Find the values of:
(a) 14 × (-15)
(b) -16 × (-5)
(c) 36 ÷ (-18)
(d) (-46) ÷ (-23)
Operations with Integers (New NCERT)
Medium
Q.
​In a test, (+4) marks are given for every correct answer and (-2) marks are given for every incorrect answer.​
​(a) Anita answered all the questions in the test. 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?​
Operations with Integers (New NCERT)
Medium
Q.
​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.
Operations with Integers (New NCERT)
Medium
Q.
​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.​
Operations with Integers (New NCERT)
Medium
Q.
Find the integer whose product with (-1) is:
(a) 27
(b) –31
(c) –1
(d) 1
(e) 0
Operations with Integers (New NCERT)
Medium
Q.
Find the values of the following expressions:
(a) (–27) ÷ 9
(b) 84 ÷ (-4)
(c) (-56) ÷ (-2)
Operations with Integers (New NCERT)
Medium
Q.
Find the values of the following expressions:
(a) (–5) × (18 + (–3))
(b) (–7) × 4 × (–1)
(c) (–2) × (–1) × (–5) × (–3)
Operations with Integers (New NCERT)
Medium
Q.
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
Operations with Integers (New NCERT)
Medium
Q.
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 bags of grey cement sold is 6,400 bags, what is the number of bags of white cement the company must sell to have neither profit nor loss?
Operations with Integers (New NCERT)
Medium
Q.
(a)  □+□×□=−36 \;\square+\square \times \square=-36​​
(b)  (□−□)×□=12\;(\square-\square) \times \square=12​​
(c)   (□−(□−□))=−1(\square-(\square-\square))=-1​​

CBSE Important Questions Class 7 Maths Chapter 10 Operations with Integers

Q1. Which of the following statements is not true?
(a) p – (–q) = p + additive inverse of (–q)
(b) 24 – 33 = 24 + additive inverse of (–33)
(c) Additive inverse of –21 is 21.
(d) 2 + (–7) – (–3) = 2 – 7 + 3

Answer: (b) 24 – 33 = 24 + additive inverse of (–33)
Subtracting a number is the same as adding its additive inverse. 24 – 33 = 24 + (–33), and –33 is the additive inverse of 33, not of –33. So statement (b) is not true.
(a) p – (–q) = p + q, and q is the additive inverse of –q, true. (c) –(–21) = 21, true. (d) 2 + (–7) – (–3) = 2 – 7 + 3, true.

Q2. The sum of two integers is –25. If one of them is –30, then the other integer will be _______.
(a) –5
(b) 5
(c) 55
(d) –55

Answer: (b) 5
Let the other integer be x. Then –30 + x = –25, so x = –25 + 30 = 5.
Check: (–30) + 5 = –25 ✓

Number line showing (-30) + 5 = -25

Q3. If we subtract –100 from 100, then what shall we get?
(a) –200
(b) 0
(c) 100
(d) 200

Answer: (d) 200
100 – (–100) = 100 + 100 = 200. Subtracting a negative number is the same as adding the positive number.

Q4. Evaluate the following: (–20) × [23 + (–4)]
(a) –180
(b) –280
(c) –380
(d) –480

Answer: (c) –380
Using the distributive property: (–20) × [23 + (–4)] = (–20) × 23 + (–20) × (–4) = –460 + 80 = –380.
Or: 23 + (–4) = 19, and (–20) × 19 = –380.

Q5. In which of the following options is the integer obtained after simplification 20,213?
(a) (–17) × (–14) × 28
(b) (–17) × (–41) × 29
(c) (–17) × (–14) × (–29)
(d) (–17) × 41 × 29

Answer: (b) (–17) × (–41) × 29
(–17) × (–41) = 697 (negative × negative = positive), and 697 × 29 = 20,213.
The others give: (a) 238 × 28 = 6,664; (c) 238 × (–29) = –6,902; (d) (–697) × 29 = –20,213.

Q6. What is the value of the expression (–3) × (–5) × (–8) × 6?
(a) –710
(b) –720
(c) 710
(d) 720

Answer: (b) –720
(–3) × (–5) = 15 (negative × negative = positive). 15 × (–8) = –120 (positive × negative = negative). –120 × 6 = –720.

Q7. A plane is flying at a height of 8750 m above sea level. At a particular point, it is exactly above a submarine floating 1340 m below sea level. What is the vertical distance between them?

Answer: Height of the plane above sea level = +8750 m
Position of the submarine below sea level = –1340 m
Vertical distance = 8750 – (–1340) = 8750 + 1340 = 10,090 m

Plane above sea level and submarine below sea level

Q8. State true or false:
(i) The sum of an integer and its inverse is always zero.
(ii) The sum of two negative integers is positive.
(iii) The sum of a positive integer and a negative integer is negative.
(iv) The sum of three different integers can never be zero.
(v) The subtraction of two integers can never be zero.

Answer: (i) True. Example: 5 + (–5) = 0
(ii) False. The sum of two negative integers is negative. Example: (–2) + (–3) = –5
(iii) False. It can be positive too. Example: (–2) + 3 = 1
(iv) False. Example: (–3) + 2 + 1 = 0
(v) False. Example: 5 – 5 = 0

Q9. Which of the following numbers complete this pattern? –7, –3, 1, 5, ___, ___
(a) 8 and 11
(b) 9 and 13
(c) 8 and 12
(d) 9 and 12

Answer: (b) 9 and 13
Each number is 4 more than the one before it: (–7) + 4 = –3, (–3) + 4 = 1, 1 + 4 = 5. So the next numbers are 5 + 4 = 9 and 9 + 4 = 13.

Pattern increasing by 4 each time

Q10. What is the value of 4[14 + (14 – 7) + 5 + (–8)]?
(a) 16
(b) 136
(c) 72
(d) 4

Answer: (c) 72
4[14 + (14 – 7) + 5 + (–8)] = 4[14 + 7 + 5 + (–8)] = 4[14 + 7 + (–3)] = 4[18] = 72

Q11. (–5) + (……) = (–8) + (……)
(a) 8, 5
(b) –8, –5
(c) –5, –8
(d) 0, 0

Answer: (b) –8, –5
(–5) + (–8) = –13 and (–8) + (–5) = –13. Both sides are equal, so the blanks are –8 and –5. This shows the commutative property of addition: changing the order of the integers does not change the sum.

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