Integers

Q1: Write all integers between:

i. -9 and -3

Integers between -9 and -3:
-8, -7, -6, -5, -4

ii. -33 and -26

Integers between -33 and -26:
-32, -31, -30, -29, -28, -27

iii. -5 and 2

-4, -3, -2, -1, 0, 1

iv. -1 and 6

0, 1, 2, 3, 4, 5

Q2: Compare the integers:

i. -16 and -61

-16 > -61, because -16 is closer to zero.
-16 > -61

ii. -39 and 13

A negative number is always less than a positive.
-39 < 13

iii. -236 and -362

-236 is greater as it’s less negative.
-236 > -362

iv. -2 and 0

Zero is greater than all negative integers.
-2 < 0

Q3: Evaluate:

i. 20 – |-11|

= 20 – 11 = 9

ii. |-23| – |-16|

= 23 – 16 = 7

iii. |-137| + |13|

= 137 + 13 = 150

iv. 6 – |-4|

= 6 – 4 = 2

Q4: Arrange the following integers in ascending order:

i. -9, 11, -23, 41, -37, 0, -5

= -37, -23, -9, -5, 0, 11, 41

ii. -31, 19, -50, -8, -23, 3, 8

= -50, -31, -23, -8, 3, 8, 19

iii. -2, 12, -43, 31, 7, -35, -10

= -43, -35, -10, -2, 7, 12, 31

Q5: Arrange the following integers in descending order:

i. -24, 16, -40, -5, -13, 6, -1

= 16, 6, -1, -5, -13, -24, -40

ii. 0, -7, 19, -23, -3, 8, 46

= 46, 19, 8, 0, -3, -7, -23

iii. -31, -13, -49, 4, 37, -9, -52

= 37, 4, -9, -13, -31, -49, -52

Q6: Fill in the blanks

i. 0 is greater than every _______ integer.

Step 1: Negative integers are less than 0.
Step 2: Therefore, 0 is greater than any negative integer.
Answer: negative

ii. Every negative integer is less than every ________ integer.

Step 1: Negative integers are always less than 0.
Step 2: Positive integers are greater than 0.
Step 3: Hence, every negative integer is less than any positive integer.
Answer: positive

iii. For any positive integers a and b, if a < b, then -a ________ -b.

Step 1: Given: a < b, and both are positive.
Step 2: Then, -a > -b (as on the number line, the negative of a smaller number is greater).
Example: a = 3, b = 5 ⇒ a < b
Then -a = -3, -b = -5 ⇒ -3 > -5
Answer: greater than

iv. Modulus of a negative integer is always ________.

Step 1: Modulus means absolute value (distance from 0).
Step 2: Modulus of a negative number is its positive value.
Example: |-7| = 7
Answer: positive

v. The largest negative integer is ________.

Step 1: Among all negative integers, -1 is closest to 0.
Step 2: Hence, it is the largest negative integer.
Answer: -1

vi. The smallest positive integer is ________.

Step 1: The first number after 0 in the set of positive integers is 1.
Step 2: So, 1 is the smallest positive integer.
Answer: 1