Important Questions
Multiple Choice questions:
1. Write numbers with appropriate signs: 40°C below 0°C temperature.
(A) 30
(B) 40
(C) -40
(D) None of these
2. 2 subtracted from 7 gives
(A) -5
(B) 5
(C) -9
(D) 9
3. Fill in the blanks with >, < or = sign. (- 3) + (- 6) ______ (- 3) - (- 6)
(A) <
(B) >
(C) None of these
(D) =
4. The number of integers between -2 and 2 is:
(A) 3
(B) 5
(C) 4
(D) 2
5. Sum of (- 9) and 15.
(A) 90
(B) -6
(C) 6
(D) 20
6. o is:
(A) a positive integer
(B) a negative integer
(C) neither positive nor negative
(D) none of these
7. What is opposite of ’50 km of south’?
(A) 50 km of east
(B) 50 km of west
(C) 50 km of north
(D) None of these
8. Sum of – 30 and – 12 is:
(A) -42
(B) 42
(C)-18
(D) 18
9. Compare pairs of numbers using > or <: 0 _____ -15.
(A) <
(B) =
(C) >
(D) None of these
10. 10 – (-6) is:
(A) 16
(B) 4
(C) 60
(D) 6
11. What must be added to -35 to get 35?
(A) 40
(B) 70
(C) 0
(D) 100
12. The absolute value of -10 is:
(A) -10
(B) 10
(C) -11
(D) -9
13. Absolute value of – 11 is:
(A) 0
(B) 11
(C) 1
(D) -11
14. Product of -140 and +8 is:
(A) 1120
(B) 3200
(C) −1120
(D) −3200
15. (– 4) + (+ 3) = _____
(A) 7
(B) -1
(C) 6
(D) None of these
Match The Following:
Fill in the blanks:
1. When we subtract -10 from 18 we get ______.
2. _____ is an integer which is neither positive nor negative.
3. 272 - 198 - ______ = 0.
4. 15 + _____ =0
True /False:
1. If a and b are any two integers such that a > b, then -a > – b.
2. If the sum of an integer and its opposite is zero, then they are called additive inverses of each other.
3. The negative of 0 is -0.
4. The sum of positive and negative integers is always negative.
Very Short Questions:
1. Write four negative integers less than -20.
2. Write all the integers between -8 and -15. (Write them in the increasing order.)
3. Find the solution of the following:(-9) + (+13)
4. Subtract: (-20) - (-13)
5. Find the value of:(-7) + (-9) + 4 + 16
6. Using number line, add the following integers: 9 + (-6).
7. The temperature on a certain morning is -11℃ at 5 a. m. If the temperature drops 3 degree at 6 a.m.
and rises 5 degree at 8 a.m. and again drops 3 degree at 9 a.m. What is the temperature at 9 a.m.?
8. Represent the following on number line:
(a) -5
(b) 4
9. Identify the negative integers from the given numbers.
– 5, 3, 0, 5, – 6, 7, 3, 4, – 4, – 7
10. What is the additive identity of – 20?
Short Questions:
1. Write the following integers in their increasing order.
– 3, 0, – 6, 5, – 4, 6, 3, – 8
2. Comparing the following pairs of number use > or < .
3. Write all the integers between the following pair of integers:
(а) 0 and – 4
(B) – 5 and 5
(c) – 8 and – 13
(d) 3 and 6
4. Find the solution of the following additions using number line:
(a)(- 3) + 5
(B) (- 5) + (-2)
5. Find the sum of the following integers:
(a) (- 8) + (+ 5) + (- 3) + (- 2)
(B) (- 7) + (- 9) + (+ 4) + (+ 3)
Long Questions:
1. Ramesh thinks of an integer. He subtracts 12 from it and gets the result as – 6.
What was the integer he thought of?
2. Determines:
(a) |5| – |- 3|
(b) |5 – 6|+ |-1|
(c) – 7 + |– 3|
(d) |5| + |– 12|
3. If * is an operation such that for two integers p and q, p * q = p + q – 2, then find:
(a) 6 * 2
(b) (- 2) * (- 3)
(c) (- 2) * (4)
(d) (+ 3) * (- 1)
Assertion and Reason Questions:
(1.) Assertion (A) – David and Mohan have started walking from zero position inopposite directions.
Let the steps to the right of zero be represented by ‘+’sign and to the left of zero represented by ‘–’ sign.
If Mohan moves 5 stepsto the right of zero it can be represented as +5 and if David moves 5 steps tothe
left of zero it can be represented as – 5.
Reason (R) – a movement to the right is made if the number by which we have to move is positive and
A movement to the left is made if the number by which the token has tomove is negative.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
(2.) Assertion (A) – The first numbers to be discovered were natural numbers i.e. 0,1, 2, 3, 4,…
Reason (R) – this collection of numbers is known as Integers
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
ANSWER KEY -
Multiple Choice questions:
1. C. -40
Explanation: below means less than 0 so it is – 40
2. B. 5
Explanation: 7 - 2 = 5
3. A.<
Explanation: -3 -6 = -9
-3 - (-6) = - 3 + 6 = 6 - 3 = 3
so - 9 < 3
4. A. 3
Explanation: integers between -2 and 2 are -1,0, 1 so 3 integers
5. C. 6
Explanation: -9 + 15 = 15 - 9 = 6
6. C. neither positive nor negative
7. C. 50 km of north
8. A. -42
9. C. >
10. A. 16
11. B. 70
12. B. 10
13. B. 11
14. C. −1120
15. B. -1
Match The Following:
Fill in the blanks:
1. When we subtract -10 from 18 we get 28.
2. 0 is an integer which is neither positive nor negative.
3. 272 - 198 - 74 = 0.
4. 15 + -15 =0
True /False:
1. False
2. True
3. False. zero is neither negative nor positive
4. False
Very Short Answer:
1. Four negative integers less than -20 are -21, -22, -23 and -24.
2. The integers between -8 and -15 in increasing order are -14, -13, -12, -11, -10 and -9.
3. (-9) + (+13)
= (-9) + (+9) + (+4)
= 0 + (+4) = +4
4. (-20) - (-13)
= (-20) + (additive inverse of -13)
= (-20) + (13) = -7
5. (-7) + (-9) + 4 + 16
= (-16) + 20
= (-16) + 16 + 4
6. On the number line we first move 9 steps to the right from 0 reaching 9 and then
we move 6 steps to the left of 9 and reach 3.
Thus, 9 + (-6) = 3
7. Temperature at 5 a.m. = -11℃
Temperature decreased at 6 a.m. = 3℃ = -3
Temperature raised at 8 a.m. = 5℃ = +5
Temperature decreased at 9 a.m. = 3℃ = -3
Final temperature at 9 a.m. = (-11) + (-3) + (+5) + (-3)
= -11 - 3 + 5 - 3
= -17 + 5
= -12℃.
8. (a) – 5
(b) 4
9. Negative integers are – 5, – 6, – 4 and – 7 .
10. Additive identity of – 20 is 20.
Short Answer:
1. The required increasing order is:
– 8, – 6, – 4, – 3, 0, 3, 5, 6
2.(a) 0 > – 6
(b) – 10 < – 2
(c) – 100 < 100
(d) 2 > – 2
3. (a) Integers between 0 and – 4 are: -3, -2, -1
(B) Integers between – 5 and 5 are: -4, -3, -2, -1, 0, 1, 2, 3, 4.
(c) Integers between – 8 and – 13 are: -12, -11, -10, -9
(d) Integers between 3 and 6 are: 4 and 5
4. (a)(- 3) + 5
∴ (-3) + 5 = 2
(b) (- 5) + (-2)
∴ (-5) + (-2) = (-7)
5. (a) (- 8) + (+ 5) + (- 3) + (- 2)
= (- 8) + (+ 5) – (3 + 2)
= (- 8) + (+ 5) – (5)
= (- 8) + 0 = – 8 [ ∵ (+ a) + (- a) = 0]
(b) (- 7) + (- 9) + (+ 4) + (+ 3)
= (- 7) + (- 9) + (4 + 3)
= (- 7) + (- 9) + (+ 7)
= (- 7) + (+ 7) + (- 9)
= 0 + (- 9) = – 9 [ ∵ (- a) + (+ a) = 0]
Long Answer:
1. The given sum can be written as under.
(___) – (12) = – 6
The required integer is 12 – 6 = 6.
2. (a) | 5 | – | – 3 | = 5 – 3 = 2 [∵ |a| = a and |- a| = a]
(b) |5 – 6 | + |- 1| = |- 1| + |-1| = 1 + 1 = 2
(c) – 7 + |– 3| = -7 + 3 = -4
(d) |5| + |– 12| = 5 + 12 = 17
3. (a) Given that: p * q = p + q – 2
⇒ 6 * 2 = 6 + 2 – 2 = 6 + 0 = 6
Thus, 6 * 2 = 6.
(b) Given that: p * q = p + q – 2
⇒ (- 2) * (- 3) = (- 2) + (- 3) – 2
= -5 – 2 = -7.
Thus, (- 2) * (- 3) = – 7.
(c) Given that: p * q = p + q – 2
⇒ (- 2) * (4) = (- 2) + (4) – 2 = 2 – 2 = 0.
Thus, (- 2) * (4) = 0.
(d) Given that p*q – p + q – 2
⇒ (+ 3) * (- 1) = (+ 3) + (- 1) – 2 = 2 – 2 = 0
Thus, (+ 3) * (- 1) = 0.
Assertion and Reason Answers:
(1)(a) Both A and R are true and R is the correct explanation of A
(2)(d) A is false but R is true