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Ques 1: Fill in the blanks:
(a) 30 ÷ ________ = 3
(b) – 89 ÷ ________ = 89
(c) ________ ÷ 1 = – 205
(d) ________ × (–12) = 120
(e) 24 + 12 ÷ 4 – 5 × 3 = ________
Ans:
(a) 10
Solution:
30/10 = 3
(b) –1
Solution:
– 89 ÷ 1 = 89
(c) –205
Solution:
When a number is divided by 1, the quotient is the number itself.
(d) –10
Solution:
let blank be X
X x(12)=120
X=120/12
X=120/12
X=10
= 10
(e) 12
Solution:
24+12 ÷ 45×3
=24+35×3
=24+315
=2715
=12
Ques 2: Find the value of P, if p × (–9) = 135
Ans: P = –15
Solution:
We can simply find the value of p by solving the linear equation by transposing the terms.
p× (9) = 135
Transposing 9 from LHS to RHS, we get
p = 135/ (9)
Simplifying 135/(9), we get
p = 15
∴ The value of p is (15).
Hence, the value of p if p× (9) = 135 is (15).
Ques 3: The additive inverse of zero (0) is ________.
Ans: 0
Solution: The additive inverse of a number is an integer that gives 0 as the sum when added.
E.g.  Let the required number be 3.
Then its additive inverse is 3.
since, 3 + 3 = 0
The additive inverse of 0 would be 0.
As, 0 + 0 = 0.
Ques 4: Match the properties of Integers:
(a) Distributive law over addition  (i) a + 0 = a = 0 + a 
(b) Associative law for multiplication  (ii) a + b = b + a 
(c) Additive Identity  (iii) (a × b) × c = a × (b × c) 
(d) Commutative law over addition  (iv) a × 1 = 1 × a = a 
(e) Multiplicative Identity  (v) a × (b + c) = a × b + a × c 
Ans: (a) (v)
(b) (iii)
(c) (i)
(d) (ii)
(e) (iv)
Ques 5: Use the sign of >, < or = in the box to make the statement true.
(a) 25 – 40 + 10 25 – 40 – 10
1. 25  40 + 10
Ans: >
Sol:
We work from left to right:
25  40 + 10
25  40 = 15
So now we have 15 + 10
15 + 10 = 5
Solving, 25 – 40 – 10
We work from left to right:
25  40 = 15
So now we have 15  10
=  25
5 >  25
(b) (–9) + (–6) (–9) – (–6)
Ans: <
Sol:
(–9) + (–6) = 15
(–9) – (–6) = 3
15< 3
(c) 35 + (–70) – (–35) (–24) – (15) + 39
Ans: =
Sol:
We work from left to right:
35 + (–70) =  35
So,
 35  (35) = 0
Solving, (–24) – (15) + 39
(–24) – (15)= 39
39+ 39 = 0
Ques 6: Evaluate :
(a) (–1) × (–2) × (–3) × (–4) × (–5)
(b) 795 × (–25) + (–795) × 75
(c) (–59) × (–19) + 59
Ans:
(a) –120
Sol:
1×(2)×(3)×(4)×(5)
= 2×(12)×(5)
= 24×(5)
= 120
(b) –79500
Sol: 795×(25)+(795)×75
= 19875+(59625)
= 1987559625
= 79500
(c) 1180
Sol: 59×(19)+59
= 1121+59
= 1180
Ques 7: An elevator descends into a mine shaft at the rate of 7m/min. If the descent starts from 5m above the ground level, how long will it take to reach – 205m?
Ans. 30 min.
Sol:
Total distance to be travelled = 5 m + 205 m = 210 m
Speed of descent = 7 m / min
Total Time = Distance / Speed
= 210 m / (7 m/min)
= 30 min
Ques 8: With the help of number line find how much greater is the number 3 than –3.
Ans:
Ques 9: The sum of two integers is –1500. One of the numbers is 599. Find the other number.
Ans: –2099
Sol: Let the number be X
the other number = 599
599 + X = 1500
X = 1500  599
X = 901
Ques 10: Write the answer in True/False :
(a) When 0 is divided by an integer, the quotient is zero.
(b) The product of an integer and 1 is an integer.
(c) When an integer is divided by itself, the quotient is 1.
Ans: (a) True
(b) True
(c) True
Ques 11: The product of two integers is –160. If one of them is 20, find the other.
Ans: –8
Sol:
Let the number be X
X * 20=160
X =160/20
X=8
Ques 12: What integers should be multiplied by (–12) to becomes –300.
Ans: 25
Sol:
Let the integer be "a"
According to question,
(12) × a =  300
a =  300 /  12
a = 300 /12
a = 25
Required number = 25
Ques 13: Pallavi got a scholarship of Rs.1000 from her school. If she gives 550 for the help of flood relief, find the balance amount with her.
Ans: ₹ 450
Sol:
Total Amount = 1000
Rupees given for help = 550
Remaining balance of pallavi= 1000550 = 450
Ques 14: A building has 21m in height. A monkey can climb 3m in one jump. In how many jumps, would the monkey reach at the top of the building?
Ans: 7
Sol: If the monkey could jump 3m once then he would have to jump 7 times to reach at top of the building as 7*3 = 21
Ques 15: Fill in the blanks using different operations :
Operations  18  36  54  72 
+25  
–17  
×6  
÷18 
Ans:
Operations  18  36  54  72 
+25  43  61  79  97 
–17  1  19  37  55 
×6  108  216  324  432 
÷18  1  2  3  4 
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