Ques 1: Fill in the blanks:
(a) 30 ÷ ________ = 3
(b) – 89 ÷ ________ = 89
(c) ________ ÷ 1 = – 205
(d) ________ × (–12) = 120
(e) 24 + 12 ÷ 4 – 5 × 3 = ________
Answer 1:
(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 2: 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 3: 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 4:
(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
Ans6:
(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?
Ans7. 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.
Ans8:
Ques 9: The sum of two integers is –1500. One of the numbers is 599. Find the other number.
Ans9: –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 10: (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 11: –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 12: 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 13: ₹ 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 14: 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: Find solutions for the following problems:
a) Both numbers are less than 10.
The distance between the two numbers on the number line is 14.
b) Both numbers are greater than 15 and less than 5
One number is 6 greater than the other number.
c)The numbers are opposites.
The distance between the two numbers on the number line is 18.
d) One number is 35.
The distance between the two numbers on the number line is 20.
e) The first number is the opposite of 17.
The second number is less than the first number.
The distance between the two numbers on the number line is 9.
Sol: These questions can be easily solved using the number line.
a) There can be many solutions, one solution will be 7 and 7. They both are less 10 and difference is 14
Other solution could be 11 and 3.They both are less 10 and difference is 14
b) There can be many solutions, one solution will be 14 and 8.
Other solution could be 13 and 7.
c) This one will have unique solution. The number will be 9 and 9. Both are opposites and distance between them is 18
d) There can two solutions, one solution will be 55 and another one is 15
e) There can be one solution only. the solution is 17 and 8.
Ques 16: Fill in the blanks using different operations :
Ans16:
76 videos345 docs39 tests

1. What are integers? 
2. How are integers different from natural numbers? 
3. How do you add integers? 
4. Can integers be fractions or decimals? 
5. What is the difference between an integer and a rational number? 

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