Worksheet Question & Answers : Integers - Mathematics (Maths) Class 7

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 ÷ 4-5×3

=24+3-5×3

=24+3-15

=27-15

=12

Ques 2: Find the value of P, if p × (–9) = 135 
Ans: P = –15

Solution:

• p× (-9) = 135 is given.
• We have to find the value of p.

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: 

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)

= -19875-59625

= -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= 1000-550 = 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 16: 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 15: Fill in the blanks using different operations :

Ans: