Exercise: 1-B
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
