Class 7 Maths Chapter 1 Practice Question Answers - Integers

Ans: (b)
Sol: 52−27=25

Ans: (a)
Sol:  Given,  

As there are 2 negative numbers in the numerator and 1 in the denominator, the answer will be negative.
Cancelling out the common factors and simplifying we get

= -4 x 2
= -8

Ans: (a)
Sol: (−87)+(−35)
Two different signs (+ and − in either order) ( + and − in either order ) become a negative sign (−)
(−87−35)
Two of the same signs (+ and + or − and −) ( + and + or − and − ) become a positive sign (+) but the sign remains the original one
=−122

Ans: (a)
Sol: 96×(−25)÷(−75)×(−16)
The rule for multiplying positive and negative numbers with the same sign (two positive or two negative) is that the product will always be positive.
When multiplying a positive and a negative, the product will always be negative. It doesn't matter what order the signs are in.
=−2400÷1200
=−2

Ans: (a)
Sol: When multiplying a positive and a negative, the product will always be negative. It doesn't matter what order the signs are in.
(−5) × 8 = −40
3 × (−2) = −6
The rule for multiplying positive and negative numbers with the same sign (two positive or two negative) is that the product will always be positive.
Hence, ((−5) × 8) × (3 × (−2)) = −40 × − 6
= 240

Ans: (a)
Sol: When multiplying a positive and a negative, the product will always be negative. It doesn't matter what order the signs are in.
4 × (−3) × (−2) × 6 × (−5)
= 24 × −30
= −720

Ans: (a)
Sol: 29 + 729 = 758

Ans: (b)
Sol:  Given,

As there are 3 negative numbers in the numerator and 1 in the denominator, the answer will be positive.
Canceling out the common factors and simplifying we get:

 = 18

Ans: (c)
Sol:  Multiplication 2 times: (−2) × (−2)=4
Multiplication 4 times: (−3) × (−3) × (−3) × (−3) = 9 × 9 = 81
Multiplication 6 times: (−1) × (−1) × (−1) × (−1) × (−1) × (−1) = 1 × 1 × 1 = 1
Hence, when a negative integer is multiplied even number of times, the result is a positive integer.

Ans: (b)
Sol: We can observe that,
27 × 3 = 81 and 81 × 3 = 243
Similarly,
5 × 4 = 20 and 20 × 4 = 80
Hence,
3 × 7 = 3 × 7 × 7 = 147

Ans: (d)
Sol: 42(4 + 2) = (42 × 4) + (42 × 2) is an example of distributive property.
a(b + c) = (a × b) + (a × c) is the basic form of distributive property.

Ans: (a)
Sol: Since 231 is an odd number, the product of 231 negative integers will be negative. The product of all positive integers is a positive number. Hence, the product of 9 positive integers will be a positive integer.
Therefore, the product of the two integers (231 negative and 9 positive) of unlike signs will be negative.

Ans: (c)
Sol: Observe −1×−1=1
Product of a pair of negative numbers is positive.
When even number of negative numbers are multiplied, the result is a positive number because every pair of negative terms will give a positive number.

Ans: (c)
Sol: As there are 2 negative numbers in the numerator and 2 in the denominator, the answer will be positive.
Canceling out the common factors and simplifying we get

Ans: (d)
Sol: Clearly the first 3−digits of each number are same.
So, let us compare rest of the remaining 5−digits of each number.
For option A, we have
68788,78688,88687
Clearly, 88687>78688>68788
So, option A is wrong.
Now, check for option D
We have, 88687,78688,68788
Clearly, 88687>78688>68788$$
So, option D is correct.

Ans: (d)
Sol: Since, the elevator going down, so the distance covered by it will be represented by a negative integer.
Change in position of elevator in one minute = −5 m
Position of the elevator after 60 minutes
= (−5) × 60

= −300  m
That means the position of the elevator will be 300 m below ground level.

Ans: (b)
Sol: We are given that −13+(−3)=−16.
The LHS is the sum of the negative integers and the RHS is a negative integer. Thus, the correct answer is option B

Ans: (c)
Sol: As there are 4 negative numbers, which is an even number, the product will be positive.
So, −5×− 2×− 2×− 3
= 60

Ans: (a)
Sol: 96 × (−25) ÷ (−75) × (−16)
The rule for multiplying positive and negative numbers with the same sign (two positive or two negative) is that the product will always be positive.
When multiplying a positive and a negative, the product will always be negative. It doesn't matter what order the signs are in.
The answer will be positive if the product or quotient is positive (two positives or two negatives in the equation) or negative (one positive and one negative in the equation).
= −2400 ÷ 1200
= −2

Ans: (b)
Sol: As there are 3 negative numbers, which is an odd number, the product will be negative.
So, −5×−12 × 2×−3
=−360

Ans: (a)
Sol: (−54) × (64) ÷ (−27) × (−128)
The rule for multiplying positive and negative numbers with the same sign (two positive or two negative) is that the product will always be positive.
When multiplying a positive and a negative, the product will always be negative. It doesn't matter what order the signs are in.
The answer will be positive if the product or quotient is positive (two positives or two negatives in the equation) or negative (one positive and one negative in the equation).
= −3456 ÷ 3456
= −1

Ans: (b)
Sol: (+48)+(−53)
Two different signs (+ and − in either order) ( + and − in either order ) become a negative sign (−) 
=53−48
=−5

Ans: (c)=
Sol: 68×(−1)=−68

Ans: (d)
Sol: Multiplying them in pairs.
There are 3 negative signs. So, the resultant of 3 multiplications would be negative.
Consider,
(−12) × (−3) × (+4) × (−6) = (−12×−3) × (4×−6)
=36×(−24)
=−864
Hence, Option D is correct.

Ans: (c)
Sol: −112×(−1)
= +112

Ans: (a)
Sol: (+13) + (−12)
Two different signs (+ and − in either order) ( + and − in either order ) become a negative sign (−) 
= +1

Ans: (d)
Sol: (132) ÷ (−12)
The answer will be positive if the product or quotient is positive (two positives or two negatives in the equation) or negative (one positive and one negative in the equation).
= 132 / -12
= 12 x 11 / -12
=  -1 x 11
= - 11
Option D is correct.

Ans: (a)
Sol: If the dividend and divisor have same  signs then the quotient will be positive.
For eg. 132/12 = 11
and -132/-12 = 11

Ans: (a)
Sol: Positive of a negative integer is negative.
Example: +(−40) = −40

Ans: (b)
Sol: The product of any number and zero is zero.
Theorem: 0 × a = 0 for any integer a.
So option B is the correct answer.