Unit 3 (Integers)

Q.1 The smallest natural number is zero.

Ans.
False.
We know that, natural numbers start from 1, so the smallest natural number is 1.

Q.2 Zero is not an integer, as it is neither positive nor negative.

Ans.
False.
Zero is an integer, even though it is neither positive nor negative.

Q.3 The sum of all the integers between –5 and –1 is –6.

Ans.
False.
The sum of all integers between -5 and -1 = -4 -3 -2
= -9

Q.4 The successor of the integer 1 is 0.

Ans.
False.
The successor of a whole number is the number obtained by adding 1 to it.
Successor of 1 = 1 + 1
= 2

Q.5 Every positive integer is larger than every negative integer.

Ans.
True.
Every positive integer is always larger than every negative integer.
Positive integers are always coming right to 0, so positive integers are always greater than 0.

Q.6 The sum of any two negative integers is always greater than both integers.

Ans.
False.
In negative integer = -4 + (-6)
= – 4 – 6
= – 10
In a negative integer, the sum is less than both integers.

Q.7 The sum of any two negative integers is always smaller than both integers.

Ans.
True.
In negative integer = -6 + (-7)
= – 6 – 7
= – 13
In a negative integer, the sum is less than both integers.

Q.8 The sum of any two positive integers is greater than both integers.

Ans.
True.
Example: consider the two positive integers 11 and 21
Sum of two integers = 11 + 21
= 32
Therefore, the sum of any two positive integers is greater than both integers.

Q.9 All whole numbers are integers.

Ans.
True.
Whole numbers start from 0, 1, 2, 3…. so it contains 0 and positive integers.
Hence, all whole numbers are integers.

Q.10 All integers are whole numbers.

Ans.
False.
Whole numbers start from 0, 1, 2, 3….
Whole numbers are not containing negative integers, but integers contain both positive and negative numbers.
Therefore, all integers are not whole numbers.

Q.11 Since 5 > 3, therefore –5 > –3

Ans.
False.
In the case of a negative integer, the big number is smaller.
So, – 5 < -3

Q.12 Zero is less than every positive integer.

Ans.
True.

Zero is always less than a positive integer and greater than a negative integer.

Q.13 Zero is larger than every negative integer.

Ans.
True.
Zero is always less than a positive integer and greater than a negative integer.

Q.14 Zero is neither positive nor negative.

Ans.
True.
Zero is neither positive nor negative.

Q.15 On the number line, an integer on the right of a given integer is always larger than the integer.

Ans.
True.
By observing the number line below, we can say that an integer on the right of a given integer is always larger than the integer.

Q.16 –2 is to the left of –5 on the number line.

Ans.
False.
-2 is to the right of the number line.

Q.17 The smallest integer is 0.

Ans.
False.
As we know, 0 is greater than negative integers.
So, 0 is not the smallest integer.

Q.18 6 and –6 are at the same distance from 0 on the number line.

Ans.
True.

From the above number line, we can say that, 6 and –6 are at the same distance of 6 units from 0 on the number line.

Q.19 The difference between an integer and its additive inverse is always even.

Ans.
True.
Example:
Consider an integer 5.
Its additive inverse is -5
Difference between an integer and its additive inverse = 5 – (-5)
= 5 + 5
= 10

Q.20 The sum of an integer and its additive inverse is always zero.

Ans.
True.
Example:
Consider an integer 8.
Its additive inverse is -8
Sum of an integer and its additive inverse = 8 + (-8)
= 8 – 8
= 0

Q.21 The sum of two negative integers is a positive integer.

Ans.
False.
The sum of two negative integers is always negative.
Example:
Consider two negative integers – 8 and – 10.
Sum of two negative integers = – 8 + (-10)
= – 8 – 10
= – 18

Q.22 The sum of three different integers can never be zero.

Ans.
False.
Example:
Consider 3 different integers 5, 10 and -15.
Sum of 3 integers = 5 + 10 + (-15)
= 5 + 10 – 15
= 15 – 15
= 0
Therefore, the sum of three different integers can be zero.