Integers Worksheet Maths CBSE Class 7 Sample Paper

Integers Worksheet

Multiple Choice Questions

Identify the pair of integers which has their difference equal to one less than –14.
(a) (–12, –3)
(b) (–13, 2)
(c) (8, –7)
(d) (–4, –11)
During summer, it is very important to keep ourselves hydrated. There are 16 houses in a colony and 2 families stay in 1 house. For each house, 1 family require 1100 litres of water and the other require 1200 litres of water. How many litres of water is required in the colony?
(a) 2300 litres
(b) 211200 litres
(c) 1600 litres
(d) 36800 litres
Four friends are returning back to home from the school. As the street near the school is empty, they decide to have a race. Three of them run towards a tree covering 80 m, 90 m and 100 m respectively. The fourth boy runs for 70 m in the opposite direction. What is the product of four numbers (consider the starting point as number ‘0’) obtained after race?
(a) 50400000
(b) –50400000
(c) 720000
(d) –720000
Simmi think of a number which when added to any integer gives the same integer. She then multiply this number with 101. Which of the following number would Simmi get after multiplication?
(a) 1
(b) 0
(c) 101
(d) –1
Vicky has 101 candies with him and he ate 9 of them. After sometime, 5 children enters the room each having the same number of chocolates that Vicky currently has. If the total number of chocolates in the room can be expressed in the form “6 × a – 6 × b” then find the values of a and b and also, find the total number of chocolates.
(a) Total number of chocolates = 560, a = 101 and b = 9
(b) Total number of chocolates = 606, a = 9 and b = 101
(c) Total number of chocolates = 552, a = 101 and b = 9
(d) Total number of chocolates = 505, a = 9 and b = 101
A wave in a sea water move ahead by 5 metres and move back by 7 metres every time. Ravi draws a line at 2 p.m. and measure the movement by 8 p.m. He found that the wave has been moved back by 30 metres from its initial position. How many times did the wave move?
(a) 5
(b) 6
(c) 15
(d) 30
Temperature of a machine room is 20°C. Every time Neeraj enters the room, he decrease the temperature by 4°C. If the temperature of the room is now 12°C below zero, how many times did Neeraj enter the room?
(a) Twice
(b) Four times
(c) Six times
(d) Eight times
Anu takes a number which is 15 times her height. Her brother Dheeraj takes a number which is 40 less than twice his height. The number chosen by Anu is then subtracted from the number chosen by Dheeraj. If Anu’s height is 5 feet and that of Dheeraj’s is 6 feet, find the number obtained after subtraction.
(a) 0
(b) 15
(c) –97
(d) –40
If (–18) × (–5) × ? = –360. Find the number which replaces the question mark.
(a) 4
(b) –4
(c) 32400
(d) –32400
Neeru takes a number and multiply it by –7. She then subtract it from 30 and again multiplies the number obtained by 15. The result is then divided by 0. What is the number obtained after division?
(a) 0
(b) 555
(c) 210
(d) Not defined

Subjective Questions
Move 2 less than 0 and do the same for 17 times. Divide 0 by the number obtained. Find the number obtained after division.
Refer the following figure:

A diver goes until the light blue layer deep in the aquarium every time he dives in the aquarium. He repeated the same 18 times. How deep would he go if he came out only after completing the 18 times distance at once?
Raj’s father runs a shopping centre. He conclude that selling a dress incurs a profit of Rs. 200 whereas, selling a pant incurs a loss of Rs. 50. If the total loss incurred is Rs. 400 and number of dresses sold is 150, how many pants did he sell?
Mango is the national fruit of India. 1 dozen of mangoes costs Rs. 360. If Raj has Rs. 720, how many mangoes can he buy spending the total money?
Find the missing integer in the following:
16 × [? + (–9) ÷ (–3)] = 16 × 3 + 16 × 3
On the number line, move 14 steps on the left of zero and then 7 steps on the right of zero. What is the difference between the numbers obtained on the left and right sides?
Find the additive inverse and multiplicative identity of (–19).
What is the product of multiplicative identity and additive identity of –37?
A building has ten underground floors for parking where the ground floor is considered 0. Radhika stays on the 19th floor. How many floors are there between Radhika’s house and the last underground floor?
Rohan set the temperature of a freezer at 7°C below zero. Reena keeps on decreasing the temperature by 2°C every half an hour. After how many hours temperature would be 31°C below zero?

Multiple Choice Questions

Identify the pair of integers which has their difference equal to one less than –14.
(a) (–12, –3)
(b) (–13, 2)
(c) (8, –7)
(d) (–4, –11)
Correct Option: (c) (8, –7)
Solution:
(–12, –3)
Difference = –12 – (–3) = –9
(–13, 2)
Difference = –13 – 2 = –15
(8, –7)
Difference = 8 – (–7) = 15
(–4, –11)
Difference = –4 – (–11) = 7
So, the pair (–13, 2) has their difference equal to one less than –14.
During summer, it is very important to keep ourselves hydrated. There are 16 houses in a colony and 2 families stay in 1 house. For each house, 1 family require 1100 litres of water and the other require 1200 litres of water. How many litres of water is required in the colony?
(a) 2300 litres
(b) 211200 litres
(c) 1600 litres
(d) 36800 litres
Correct Option: (d) 36800 litres
Solution:
Litres of water required in the colony = 16 × (1100 + 1200)
= 16×1100 + 16×1200
= 17600 + 19200
= 36800
Four friends are returning back to home from the school. As the street near the school is empty, they decide to have a race. Three of them run towards a tree covering 80 m, 90 m and 100 m respectively. The fourth boy runs for 70 m in the opposite direction. What is the product of four numbers (consider the starting point as number ‘0’) obtained after race?
(a) 50400000
(b) –50400000
(c) 720000
(d) –720000
Correct Option: (b) –50400000
Solution:
As the fourth boy runs in the opposite direction, the number obtained will be –70.
The four numbers are 80, 90, 100 and –70.
Product = 80 × 90 × 100 × (–70) = –50400000
Simmi think of a number which when added to any integer gives the same integer. She then multiply this number with 101. Which of the following number would Simmi get after multiplication?
(a) 1
(b) 0
(c) 101
(d) –1
Correct Option: (b) 0
Solution:
‘0’ is the number which when added to any integer gives the same integer.
Now, 0 × 101 = 0
So, after multiplication, Simmi will get the product as ‘0’.
Vicky has 101 candies with him and he ate 9 of them. After sometime, 5 children enters the room each having the same number of chocolates that Vicky currently has. If the total number of chocolates in the room can be expressed in the form “6 × a – 6 × b” then find the values of a and b and also, find the total number of chocolates.
(a) Total number of chocolates = 560, a = 101 and b = 9
(b) Total number of chocolates = 606, a = 9 and b = 101
(c) Total number of chocolates = 552, a = 101 and b = 9
(d) Total number of chocolates = 505, a = 9 and b = 101
Correct Option: (c) Total number of chocolates = 552, a = 101 and b = 9
Solution:
Number of chocolates left with Vicky = 101 – 9 = 92
Each of the 5 children has 93 chocolates.
Total number of chocolates = 6 × 92 = 552
Also, total number of chocolates = 6 × (101 – 9) = 6 × 101 – 6 × 9
Thus, a = 101 and b = 9.
A wave in a sea water move ahead by 5 metres and move back by 7 metres every time. Ravi draws a line at 2 p.m. and measure the movement by 8 p.m. He found that the wave has been moved back by 30 metres from its initial position. How many times did the wave move?
(a) 5
(b) 6
(c) 15
(d) 30
Correct Option: (c) 15
Solution:
Every time the wave move ahead by 5 metres and move back by 7 metres.
Movement in the wave every time = 5 metres ahead and 7 metres back = 5 – 7 = –2
So, every time the wave move back by 2 metres.
Now, it is given that the wave moved back by 30 metres.
Total movement in the wave = –30
Number of movements = (–30) ÷ (–2) = 15
Temperature of a machine room is 20°C. Every time Neeraj enters the room, he decrease the temperature by 4°C. If the temperature of the room is now 12°C below zero, how many times did Neeraj enter the room?
(a) Twice
(b) Four times
(c) Six times
(d) Eight times
Correct Option: (d) Eight times
Solution:
Initially the temperature of the room was 20°C and now it is –12°C.
Difference in the temperature 20 – (–12) = 32
As every time the temperature decreases by 4°C.
Number of times the temperature changes = 32 ÷ 4 = 8
Thus, Neeraj entered the room 8 times.
Anu takes a number which is 15 times her height. Her brother Dheeraj takes a number which is 40 less than twice his height. The number chosen by Anu is then subtracted from the number chosen by Dheeraj. If Anu’s height is 5 feet and that of Dheeraj’s is 6 feet, find the number obtained after subtraction.
(a) 0
(b) 15
(c) –97
(d) –40
Correct Option: (c) –97
Solution:
Anu’s height is 5 feet.
So, the number chosen by Anu is 15×5 = 75
Dheeraj’s height is 6 feet.
So, the number chosen by Dheeraj is (2×6 – 40) = –32
Number obtained after subtraction = –32 – 75 = –97
If (–18) × (–5) × ? = –360. Find the number which replaces the question mark.
(a) 4
(b) –4
(c) 32400
(d) –32400
Correct Option: (b) –4
Solution:
(–18) × (–5) × ? = –360
? = –360 ÷ [(–18) × (–5)]
? = –360 ÷ 90
? = –4
So, –4 replaces question mark.
Neeru takes a number and multiply it by –7. She then subtract it from 30 and again multiplies the number obtained by 15. The result is then divided by 0. What is the number obtained after division?
(a) 0
(b) 555
(c) 210
(d) Not defined
Correct Option: (d) Not defined
Solution:
When any number is divided by 0, it is not defined.

Subjective Questions
Move 2 less than 0 and do the same for 17 times. Divide 0 by the number obtained. Find the number obtained after division.
Solution:
2 less than 0 is –2.
Doing this for 17 times, we get the result as 17 × (–2) = –34
Dividing 0 by –34, we get
0 ÷ (–34) which gives us the result as 0
Refer the following figure:

A diver goes until the light blue layer deep in the aquarium every time he dives in the aquarium. He repeated the same 18 times. How deep would he go if he came out only after completing the 18 times distance at once?
Solution:
Diver dives –200 metres deep in the water every time.
So, he dives for 18 × (–200) metres = –3600 metres after 18 times.
Thus, he would go –3600 metres deep.
Raj’s father runs a shopping centre. He conclude that selling a dress incurs a profit of Rs. 200 whereas, selling a pant incurs a loss of Rs. 50. If the total loss incurred is Rs. 400 and number of dresses sold is 150, how many pants did he sell?
Solution:
Total loss incurred = Rs. 400 i.e. –400 Rs.
Profit earned = 200×150 = Rs. 30000
Loss incurred = Total loss – Profit earned = – 400 – 30000 = Rs. –30400
One pant incurs a loss of Rs. 50 i.e. –50 Rs.
Number of pants sold = (–30400) ÷ (–50) = 608
Mango is the national fruit of India. 1 dozen of mangoes costs Rs. 360. If Raj has Rs. 720, how many mangoes can he buy spending the total money?
Solution:
1 dozen mangoes = 12 mangoes
Now, 720 ÷ 360 = 2
So, Raj can buy 2 dozens of mangoes.
Thus, the number of mangoes Raj can buy = 2×12 = 24.
Find the missing integer in the following:
16 × [? + (–9) ÷ (–3)] = 16 × 3 + 16 × 3
Solution:
Distributive property: a × (b + c) = a × b + a × c
Now, (–9) ÷ (–3) = 3
⇒ 16 × [? + (–9) ÷ (–3)] = 16 × [? + 3]
By distributive property, we have
16 × 3 + 16 × 3 = 16 × [3 + 3]
So, the missing number is 3.
On the number line, move 14 steps on the left of zero and then 7 steps on the right of zero. What is the difference between the numbers obtained on the left and right sides?
Solution:
Number obtained on moving 14 steps on the left of zero is –14.
Number obtained on moving 7 steps on the right of zero is 7.
Difference between the numbers is = –14 – 7 = –21
Find the additive inverse and multiplicative identity of (–19).
Solution:
Additive inverse is obtained when we multiply a number by (–1).
Therefore, additive inverse of –19 is 19.
Its multiplicative identity is 1.
What is the product of multiplicative identity and additive identity of –37?
Solution:
For any integer, its multiplicative identity is 1 and additive identity is 0.
So, the multiplicative identity of –37 is 1 and its additive identity is 0.
Their product = 1 × 0 = 0
A building has ten underground floors for parking where the ground floor is considered 0. Radhika stays on the 19th floor. How many floors are there between Radhika’s house and the last underground floor?
Solution:
Bottom underground floor is –10.
Ground floor is 0.
Radhika’s house is consider as 19.
Floors between Radhika’s house and the bottom underground floor = 19 + 10 – 1 = 28
Rohan set the temperature of a freezer at 7°C below zero. Reena keeps on decreasing the temperature by 2°C every half an hour. After how many hours temperature would be 31°C below zero?
Solution:
Temperature was set 7°C below zero = –7°C
It reaches 31°C below zero i.e. –31°C
Now, –7°C – (–31°C) = 24°C
So, temperature decreases by 24°C.
As the temperature decreases by 2°C every half an hour.
Time required to get the temperature at –31°C is 24 ÷ 2 = 12 half hours which is 6 hours.

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