Find the sum :
(i) 16 + 21
(ii) (-16) + 21
(iii) 16 + (-21)
(iv) (-25) + (-18)
(v) (-32) + (-47)
(vi) 54 + (-89)
(vii) (-38) + 45
(viii) 96 + (-103)
(ix) (-150) + (-15)
Answer
(i) 16 + 21
= 37
Hence, 16 + 21 = 37.
(ii) (-16) + 21
= -16 + 21
= 5
Hence, (-16) + 21 = 5.
(iii) 16 + (-21)
= 16 - 21
= -5
Hence, 16 + (-21) = -5.
(iv) (-25) + (-18)
= -25 - 18
= -43
Hence, (-25) + (-18) = -43.
(v) (-32) + (-47)
= -32 - 47
= -79
Hence, (-32) + (-47) = -79.
(vi) 54 + (-89)
= 54 - 89
= -35
Hence, 54 + (-89) = -35.
(vii) (-38) + 45
= -38 + 45
= 7
Hence, (-38) + 45 = 7.
(viii) 96 + (-103)
= 96 - 103
= -7
Hence, 96 + (-103) = -7.
(ix) (-150) + (-15)
= -150 - 15
= -165
Hence, (-150) + (-15) = -165.
Write the additive inverse of :
(i) 34
(ii) -58
(iii) 0
(iv) -1
(v) 170
Answer
(i) 34
Let x be additive inverse of 34.
⇒ 34 + x = 0
⇒ x = 0 - 34
⇒ x = -34
Hence, -34 is the additive inverse of 34.
(ii) -58
Let x be additive inverse of -58.
⇒ -58 + x = 0
⇒ x = 0 - (-58)
⇒ x = 58
Hence, 58 is the additive inverse of -58.
(iii) 0
Let x be additive inverse of 0.
⇒ 0 + x = 0
⇒ x = 0 - 0
⇒ x = 0
Hence, 0 is the additive inverse of 0.
(iv) -1
Let x be additive inverse of -1.
⇒ -1 + x = 0
⇒ x = 0 - (-1)
⇒ x = 1
Hence, 1 is the additive inverse of -1.
(v) 170
Let x be additive inverse of 170.
⇒ 170 + x = 0
⇒ x = 0 - 170
⇒ x = -170
Hence, -170 is the additive inverse of 170.
Write the successor of :
(i) 101
(ii) -47
(iii) -1
(iv) -80
(v) -301
Answer
(i) 101
Successor of 101 = 101 + 1 = 102
Hence, 102 is the successor of 101.
(ii) -47
Successor of -47 = (-47) + 1 = -46
Hence, -46 is the successor of -47.
(iii) -1
Successor of -1 = (-1) + 1 = 0
Hence, 0 is the successor of -1.
(iv) -80
Successor of -80 = (-80) + 1 = -79
Hence, -79 is the successor of -80.
(v) -301
Successor of -301 = (-301) + 1 = -300
Hence, -300 is the successor of -301.
Write the predecessor of :
(i) 40
(ii) -32
(iii) -70
(iv) -91
(v) 0
Answer
(i) 40
Predecessor of 40 = 40 - 1 = 39
Hence, 39 is the predecessor of 40.
(ii) -32
Predecessor of -32 = -32 - 1 = -33
Hence, -33 is the predecessor of -32.
(iii) -70
Predecessor of -70 = -70 - 1 = -71
Hence, -71 is the predecessor of -70.
(iv) -91
Predecessor of -91 = -91 - 1 = -92
Hence, -92 is the predecessor of -91.
(v) 0
Predecessor of 0 = 0 - 1 = -1
Hence, -1 is the predecessor of 0.
Find the difference :
(i) (15) - (21)
(ii) (-29) - (9)
(iii) 70 - (-8)
(iv) 24 - (-24)
(v) (-36) - (64)
(vi) 0 - (-20)
(vii) (-63) - (-7)
(viii) (-80) - (-20)
(ix) (-12) - (-71)
Answer
(i) (15) - (21)
= 15 - 21
= -6
Hence, (15) - (21) = -6.
(ii) (-29) - (9)
= -29 - 9
= -38
Hence, (-29) - (9) = -38.
(iii) 70 - (-8)
= 70 + 8
= 78
Hence, 70 - (-8) = 78.
(iv) 24 - (-24)
= 24 + 24
= 48
Hence, 24 - (-24) = 48.
(v) (-36) - (64)
= -36 - 64
= -100
Hence, (-36) - (64) = -100.
(vi) 0 - (-20)
= 0 + 20
= 20
Hence, 0 - (-20) = 20.
(vii) (-63) - (-7)
= -63 + 7
= -56
Hence, (-63) - (-7) = -56.
(viii) (-80) - (-20)
= -80 + 20
= -60
Hence, (-80) - (-20) = -60.
(ix) (-12) - (-71)
= -12 + 71
= 59
Hence, (-12) - (-71) = 59.
Subtract :
(i) -180 from 180
(ii) 75 from -75
(iii) -630 from -70
(iv) -95 from 0
(v) -90 from -1
(vi) -16 from -25
Answer
(i) -180 from 180
= 180 - (-180)
= 180 + 180
= 360.
Hence, final result = 360.
(ii) 75 from -75
= -75 - 75
= -150
Hence, final result = -150.
(iii) -630 from -70
= -70 - (-630)
= -70 + 630
= 560
Hence, final result = 560.
(iv) -95 from 0
= 0 - (-95)
= 0 + 95
= 95
Hence, final result = 95.
(v) -90 from -1
= -1 - (-90)
= -1 + 90
= 89
Hence, final result = 89.
(vi) -16 from -25
= -25 - (-16)
= -25 + 16
= -9
Hence, final result = -9.
Fill in the blanks :
(i) (+23) + (...............) = 0
(ii) (-13) + (...............) = + 20
(iii) (-14) + (...............) = -34
(iv) (-20) + (...............) = -8
(v) (-30) - (...............) = -14
(vi) (...............) - (-25) = 2
Answer
(i) (+23) + (...............) = 0
Let x be the number in blanks,
⇒ 23 + x = 0
⇒ x = 0 - 23
⇒ x = -23
(+23) + (-23) = 0
(ii) (-13) + (...............) = + 20
Let x be the number in blanks,
⇒ -13 + x = 20
⇒ x = 20 - (-13)
⇒ x = 20 + 13
⇒ x = 33
(-13) + (33) = + 20
(iii) (-14) + (...............) = -34
Let x be the number in blanks,
⇒ -14 + x = -34
⇒ x = -34 + 14
⇒ x = -20
(-14) + (-20) = -34
(iv) (-20) + (...............) = -8
Let x be the number in blanks,
⇒ -20 + x = -8
⇒ x = -8 + 20
⇒ x = 12
(-20) + (12) = -8
(v) (-30) - (...............) = -14
Let x be the number in blanks,
⇒ -30 - x = -14
⇒ -x = -14 + 30
⇒ -x = 16
⇒ x = -16
(-30) - (-16) = -14
(vi) (...............) - (-25) = 2
Let x be the number in blanks,
⇒ x + 25 = 2
⇒ x = 2 - 25
⇒ x = -23
(-23) - (-25) = 2
Use number line to find :
(i) 5 + 4
(ii) 4 + (-6)
(iii) (-4) + 8
(iv) (-5) + 3
(v) (-3) + (-5)
(vi) (-6) + (-3)
(vii) 5 - (-2)
(viii) (-4) - 5
(ix) 4 - (-4)
Answer
(i) 5 + 4 = 9
Starting from 0 on the number line, move 5 steps to the right and from there move 4 steps to the right to reach 9 as shown below.
(ii) 4 + (-6) = 4 - 6 = -2
Starting from 0 on the number line, move 4 steps to the right and from there move 6 steps to the left to reach -2 as shown below.
(iii) (-4) + 8 = -4 + 8 = 4
Starting from 0 on the number line, move 4 steps to the left and from there move 8 steps to the right to reach 4 as shown below.
(iv) (-5) + 3 = -2
Starting from 0 on the number line, move 5 steps to the left and from there move 3 steps to the right to reach -2 as shown below.
(v) (-3) + (-5) = -3 - 5 = -8
Starting from 0 on the number line, move 3 steps to the left and from there move 5 steps to the left to reach -8 as shown below.
(vi) (-6) + (-3) = -6 - 3 = -9
Starting from 0 on the number line, move 6 steps to the left and from there move 3 steps to the left to reach -9 as shown below.
(vii) 5 - (-2) = 5 + 2 = 7
Starting from 0 on the number line, move 5 steps to the right and from there move 2 steps to the right to reach 7 as shown below.
(viii) (-4) - 5 = -4 - 5 = -9
Starting from 0 on the number line, move 4 steps to the left and from there move 5 steps to the left to reach -9 as shown below.
(ix) 4 - (-4) = 4 + 4 = 8
Starting from 0 on the number line, move 4 steps to the right and from there move 4 steps to the right to reach 8 as shown below.
State whether the given statement is true or false :
(i) The sum of two integers is always an integer.
(ii) The difference of two integers is always an integer.
(iii) The absolute value of every integer is a positive integer.
(iv) 0 is the smallest positive integer.
(v) Every whole number is an integer.
(vi) The sum of two integers can never be zero.
Answer
(i) The sum of two integers is always an integer.
True
Explanation:
The set of integers is closed under addition. This means that when you add any two integers, the result will always be another integer. For example, 5 + (−3) = 2, and 2 is an integer.
(ii) The difference of two integers is always an integer.
True
Explanation:
The set of integers is also closed under subtraction. When you subtract one integer from another, the result is always an integer. For example, 3−8=−5, and -5 is an integer.
(iii) The absolute value of every integer is a positive integer.
True
Explanation:
The absolute value of an integer is its distance from zero, which is always non-negative.
(iv) 0 is the smallest positive integer.
False
Explanation:
The set of positive integers starts with 1. Zero is an integer that is neither positive nor negative. The smallest positive integer is 1.
(v) Every whole number is an integer.
True
Explanation:
The set of whole numbers is {0, 1, 2, 3, ...}. The set of integers is {..., -2, -1, 0, 1, 2, ...}. All the numbers in the set of whole numbers are also included in the set of integers.
(vi) The sum of two integers can never be zero.
False
Explanation:
The sum of an integer and its additive inverse (its opposite) is always zero. For example, the sum of 5 and -5 is 0.
What should be added to 15 to get (-15)?
Answer
Let the number be x.
∴ 15 + x = -15
⇒ x = -15 - 15
⇒ x = -30
Hence, -30 should be added to 15 to get -15.
What should be subtracted from (-3) to get +18?
Answer
Let the number be x.
∴ -3 - x = 18
⇒ -x = 18 + 3
⇒ -x = 21
⇒ x = -21
Hence, -21 should be subtracted from (-3) to get +18.
The sum of two integers is -23. If one of them is 12, find the other.
Answer
Given, sum of two integers = -23
One of the numbers = 12
Let x be the number.
∴ 12 + x = -23
⇒ x = -23 - 12
⇒ x = -35
Hence, the other number = -35.
While playing children's cards, Amit lost 70 points in the first game, 50 in the second game and 35 in the third game. He gained 60 in the fourth game and 80 in the fifth game. What was his net loss or gain?
Answer
Given,
Amit lost in the first game = -70 points
Amit lost in the second game = -50 points
Amit lost in the third game = -35 points
Amit gained in the fourth game = +60 points
Amit gained in the fifth game = +80 points
Net loss or gain = (-70) + (-50) + (-35) + 60 + 80
= -70 - 50 - 35 + 60 + 80
= -120 - 35 + 60 + 80
= -155 + 60 + 80
= -95 + 80
= -15
Hence, Amit had a net loss of 15 points.
On one day on a hill, the temperature at 8 p.m. was 2°C but at mid-night that day, it fell down to -3°C. By how many degrees did the temperature fall?
Answer
Initial temperature: 2° C
Final temperature: −3° C
Difference = Initial temperature − Final temperature
= 2° C − (−3° C)
= 2° C + 3° C
= 5° C
Hence, the temperature fell by 5° C.
A car travelled east of Delhi by 100 km and then to the west of it by 130 km. How far from Delhi was the car finally?
Answer
Given, travelled east: +100 km
Travelled west: −130 km
Final position = (+ 100) km + (− 130) km
= 100 − 130
= −30 km
The negative sign indicates that the final position is to the west of Delhi. The distance from Delhi is the absolute value of this number.
Distance = ∣−30∣ km
Distance = 30 km
Hence, the car was finally 30 km to the west of Delhi.