Integers

Q1: Add the following integer:

i. 64 and 36

64 + 36 = 100

ii. 73 and -37

73 + (-37) = 73 – 37 = 36

iii. -26 and -45

-26 + (-45) = -(26 + 45) = -71
Answer: -71

iv. -51 and 25

-51 + 25 = -26
Answer: -26

v. 100 and -32

100 + (-32) = 100 – 32 = 68

vi. 0 and -21

0 + (-21) = -21
Answer: -21

Q2: Find the additive inverse of:

i. 23

Additive inverse of 23 = -23
Answer: -23

ii. -33

Additive inverse of -33 = +33
Answer: 33

iii. -1

Additive inverse of -1 = +1
Answer: 1

iv. -476

Additive inverse of -476 = +476
Answer: 476

Q3: Evaluate:

i. 6 – 24

= -18
Answer: -18

ii. 18 – (-8)

= 18 + 8 = 26
Answer: 26

iii. (-16) – (-5)

= -16 + 5 = -11
Answer: -11

iv. (-20) – 6

= -20 – 6 = -26
Answer: -26

v. (-1) – (-19)

= -1 + 19 = 18
Answer: 18

vi. 8 – (-23)

= 8 + 23 = 31
Answer: 31

Q4: Verify the following:

i. (-14) + 9 = 9 + (-14)

LHS = -14 + 9 = -5
RHS = 9 – 14 = -5
Verified ✔

ii. (-8) + (-12) = (-12) + (-8)

LHS = -8 -12 = -20
RHS = -12 – 8 = -20
Verified ✔

iii. (-6) + [(-8) + 12] = [(-6) + (-8)] + 12

LHS = -6 + 4 = -2
RHS = -14 + 12 = -2
Verified ✔

iv. [(-9) + (-7)] + (-14) = (-9) + [(-7) + (-14)]

LHS = -16 + (-14) = -30
RHS = -9 + (-21) = -30
Verified ✔

Q5: Fill in the blanks

i. 8 + _____ = 0

Step 1: To get 0 from 8, we need to add its additive inverse.
Step 2: Additive inverse of 8 is -8.
Answer: -8

ii. (-10) + _____ = (-10)

Step 1: To keep the number unchanged, we must add 0.
Answer: 0

iii. (-6) + (-8) = (-8) + _____

Step 1: This is based on the commutative property of addition: a + b = b + a.
Step 2: So, (-6) + (-8) = (-8) + (-6).
Answer: -6

iv. (-6) + _____ = -14

Step 1: Let x be the missing number.
Step 2: (-6) + x = -14
Step 3: x = -14 – (-6) = -14 + 6 = -8
Answer: -8

v. (-11) + 4 = (-7)

Step 1: Let us verify LHS: -11 + 4 = -7
Step 2: This statement is already complete and correct.
Answer: Correct as is

vi. (-9) + _____ = -1

Step 1: Let x be the missing number.
Step 2: (-9) + x = -1
Step 3: x = -1 – (-9) = -1 + 9 = 8
Answer: 8

Q6: Subtract the sum of -137 and -43 from the sum of -103 and 27.

Sum1 = -137 + (-43) = -180
Sum2 = -103 + 27 = -76
Required = -76 – (-180) = -76 + 180 = 104

Q7: Subtract -29 from -53 and add -16 to the result.

-53 – (-29) = -53 + 29 = -24
-24 + (-16) = -40
Answer: -40

Q8: The sum of two integers is 43. If one of them is -27, find the other.

Let the other number be x
So, x + (-27) = 43
x = 43 + 27 = 70

Q9: Find the successor of:

i. 30

→ 30 + 1 = 31
Answer: 31

ii. -70

→ -70 + 1 = -69
Answer: -69

iii. -206

→ -206 + 1 = -205
Answer: -205

iv. -1

→ -1 + 1 = 0
Answer: 0

Q10: Find the predecessor of:

i. 60

→ 60 – 1 = 59
Answer: 59

ii.-351

→ -351 – 1 = -352
Answer: -352

iii. 0

→ 0 – 1 = -1
Answer: -1

iv. -99

→ -99 – 1 = -100
Answer: -100