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: It is given the expression, (-87) + (-35).

on solving brackets we get,

 = -87 - 35 (Both numbers are negative, so we add their absolute values, and the result remains negative.)

⇒ -122

So, the value of -87 + (-35) is -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: (−5) × 8 = −40
3 × (−2) = −6
(W hen multiplying a positive and a negative number, the product will always be negative, regardless of the order of the signs.)
Hence, {(−5) × 8) × (3 × (−2)} = −40 × − 6
= 240

Ans: (a)
Sol: 4 × (−3) × (−2) × 6 × (−5)
Note: (When multiplying a positive and a negative number, the product will always be negative, regardless of the order of the signs.)

= 24 × −30
= −720

Ans: (a)
Sol: 29 + 729 = 758

Ans: (b)
Sol:

Simplify the expression:  (-16) × (-8) × (-81)(-18) × 32

The negative signs cancel each other, so we get: 
= 16 × 8 × 8118 × 32

Now simplify: 16 × 832 = 4, 
we get : 4 × 8118 = 4.5 × 4 = 18

Ans: 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)

Step 1: Simplify using the distributive property.

(-4) × (6 + 7) = (-4) × 13 = -52

Step 2: Break it down using the distributive property.

(-4) × (6 + 7) = [(-4) × 6] + [(-4) × 7]

= (-24) + (-28) = -52

Thus, the result is the same using both methods: -52.

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: 

Simplifying the expression: 5 × (-144) × (-27)(-15) × 18 × (-16)

The negative signs cancel out, leaving:

5 × 144 × 2715 × 18 × 16

First, simplify:

515 = 1/3

Now the expression becomes:

1 × 144 × 273 × 18 × 16

Simplify:

14418 = 8

Now the expression is

8 × 273 × 16

Simplify:

273 = 9

Now the expression is:

8 × 916 = = 92

Ans: (d)
Sol: 

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)
Note: When multiplying two numbers with the same sign (both positive or both negative), the result is always positive. If one number is positive and the other is negative, the product is always negative, regardless of the order.
= −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)

To evaluate $(+48)+(-53)$, subtract the absolute values because the signs are different:

So, the result is $-5-5$

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.