Write the opposite of each of the following statements :
(i) Gain of ₹ 90
(ii) 70 m above sea-level
(iii) 200 m due west
(iv) 25% increase
(v) 10°C below freezing point
(vi) 30 m to the left
(vii) Below average
(viii) Gaining a weight of 1 kg
(ix) Depositing ₹ 500 in a bank
(x) +45
(xi) -50
Answer
(i) Gain of ₹ 90
The opposite of "gaining" something (an increase) is "losing" it (a decrease).
Hence, opposite of "gain of ₹ 90" is "loss of ₹ 90".
(ii) 70 m above sea-level
"Above" and "below" are opposite directions on a vertical axis.
Hence, opposite of "70 m above sea-level" is "70 m below sea-level".
(iii) 200 m due west
"West" and "east" are opposite directions on a horizontal axis.
Hence, opposite of "200 m due west" is "200 m due east".
(iv) 25% increase
"Increase" means to get larger, while "decrease" means to get smaller.
Hence, opposite of "25% increase" is "25% decrease".
(v) 10°C below freezing point
"Below" and "above" are opposite directions on a temperature scale.
Hence, opposite of “10°C below the freezing point” is “10°C above the freezing point”.
(vi) 30 m to the left
"Left" and "right" are opposite directions.
Hence, opposite of 30 m to the left is 30 m to the right.
(vii) Below average
"Below" and "above" are used to describe values relative to a reference point (the average).
Hence, opposite of below average is above average.
(viii) Gaining 1 kg of weight
"Gaining" weight is the opposite of "losing" weight.
Hence, opposite of gaining 1 kg of weight is losing 1 kg of weight.
(ix) Depositing ₹ 500 in a bank
"Depositing" money increases a bank balance, while "withdrawing" decreases it.
Hence, opposite of depositing ₹ 500 in a bank is withdrawing ₹ 500 from a bank.
(x) +45
The opposite of a positive number is its negative counterpart.
Hence, opposite of +45 is -45.
(xi) -50
The opposite of a negative number is its positive counterpart.
Hence, opposite of -50 is +50.
Indicate the following using negative sign :
(i) An increase of 8
(ii) Loss of ₹ 300
(iii) Spending ₹ 725
(iv) 53 m below sea-level
(v) 20°C below freezing point
(vi) 4 above average
Answer
(i) An increase of 8
"Increase" means to get larger, while "decrease" means to get smaller.
Hence, an increase of 8 can be indicated using a negative sign as a decrease of -8.
(ii) Loss of ₹ 300
A loss is a negative change. This is represented by -₹ 300.
Hence, loss of ₹ 300 is -₹ 300.
(iii) Spending ₹ 725
Spending money decreases a total amount, so it is a negative change. This is represented by -₹ 725.
Hence, spending ₹ 725 is -₹ 725.
(iv) 53 m below sea-level
"Below" is a negative direction. This is represented by -53 m.
Hence, 53 m below sea-level is -53 m.
(v) 20°C below freezing point
"Below" is a negative value on a temperature scale. This is represented by -20°C.
Hence, 20°C below freezing point is -20°C.
(vi) 4 above average
4 above average is a positive change. Its opposite, 4 below average, is represented by -4.
Hence, negative sign of 4 above average is -4.
Write all integers between :
(i) 3 and 10
(ii) -3 and 6
(iii) -7 and 0
(iv) -12 and -8
(v) -20 and -14
(vi) -8 and 4
Answer
(i) Integers between 3 and 10
4, 5, 6, 7, 8, 9.
(ii) Integers between -3 and 6
-2, -1, 0, 1, 2, 3, 4, 5.
(iii) Integers between -7 and 0
-6, -5, -4, -3, -2, -1.
(iv) Integers between -12 and -8
-11, -10, -9.
(v) Integers between -20 and -14
-19, -18, -17, -16, -15.
(vi) Integers between -8 and 4
-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3.
Write seven integers, each greater than -6.
Answer
Seven integers, each greater than -6 are -5, -4, -3, -2, -1, 0, 1.
Fill in the blanks by using > or < or = in each of the following :
(i) -5 ............... 3
(ii) 0 ............... -4
(iii) -8 ............... -14
(iv) -23 ............... -16
(v) 15 ............... -15
(vi) -1 ............... -12
(vii) 9 ............... (-1)
(viii) (-9) ............... 1
(ix) (-9) ............... (-1)
Answer
(i) -5 ............... 3
A negative number is always less than a positive number.
-5 < 3
(ii) 0 ............... -4
0 is to the right of -4 on the number line.
0 > -4
(iii) -8 ............... -14
On a number line, -8 is to the right of -14, making it the greater number.
-8 > -14
(iv) -23 ............... -16
-16 is closer to zero than -23, so -16 is greater.
-23 < -16
(v) 15 ............... -15
A negative number is always less than a positive number.
15 > -15
(vi) -1 ............... -12
-1 is closer to zero than -12, so -1 is greater.
-1 > -12
(vii) 9 ............... -1
A negative number is always less than a positive number.
9 > -1
(viii) -9 ............... 1
A negative number is always less than a positive number.
(-9) < 1
(ix) -9 ............... -1
-1 is closer to zero than -9, so -1 is greater.
(-9) < (-1)
Evaluate each of the following :
(i) |-17| - |8|
(ii) |-14| + |5|
(iii) |-9| + |-6|
(iv) |-23| - |-12|
(v) |-8| + |-6| - |-10|
(vi) |-6| + |-1| - |-5|
Answer
(i) |-17| - |8|
= 17 - 8
= 9
Hence, |-17| - |8| = 9.
(ii) |-14| + |5|
= 14 + 5
= 19
Hence, |-14| + |5| = 19.
(iii) |-9| + |-6|
= 9 + 6
= 15
Hence, |-9| + |-6| = 15.
(iv) |-23| - |-12|
= 23 - 12
= 11
Hence, |-23| - |-12| = 11.
(v) |-8| + |-6| - |-10|
= 8 + 6 - 10
= 14 - 10
= 4
Hence, |-8| + |-6| - |-10| = 4.
(vi) |-6| + |-1| - |-5|
= 6 + 1 - 5
= 7 - 5
= 2
Hence, |-6| + |-1| - |-5| = 2.
Write the following integers in ascending order :
(i) 14, -7, -13, 0, 6, -2, 30
(ii) -18, 14, -25, 32, -5, 2
(iii) -9, -24, 26, -2, -11, 18, 9
(iv) 37, -28, -15, 7, 23, -19, -6
Answer
(i) 14, -7, -13, 0, 6, -2, 30
Ascending order: -13 < -7 < -2 < 0 < 6 < 14 < 30.
(ii) -18, 14, -25, 32, -5, 2
Ascending order: -25 < -18 < -5 < 2 < 14 < 32.
(iii) -9, -24, 26, -2, -11, 18, 9
Ascending order: -24 < -11 < -9 < -2 < 9 < 18 < 26.
(iv) 37, -28, -15, 7, 23, -19, -6
Ascending order: -28 < -19 < -15 < -6 < 7 < 23 < 37.
Write the following integers in descending order :
(i) -16, -21, 8, 0, -7, 14
(ii) -4, 31, -41, -23, 6, 0, -11
(iii) -60, -9, -36, -8, 5, 15, 0
(iv) -10, -43, -2, 1, -14, 6, 22
(v) -8, -53, 53, -100, 62, 16, -82
Answer
(i) -16, -21, 8, 0, -7, 14
Descending order: 14 > 8 > 0 > -7 > -16 > -21.
(ii) -4, 31, -41, -23, 6, 0, -11
Descending order: 31 > 6 > 0 > -4 > -11 > -23 > -41.
(iii) -60, -9, -36, -8, 5, 15, 0
Descending order: 15 > 5 > 0 > -8 > -9 > -36 > -60.
(iv) -10, -43, -2, 1, -14, 6, 22
Descending order: 22 > 6 > 1 > -2 > -10 > -14 > -43.
(v) -8, -53, 53, -100, 62, 16, -82
Descending order: 62 > 53 > 16 > -8 > -53 > -82 > -100.
Represent each of the following on the number line :
(i) All integers from -5 to 3.
(ii) All negative integers greater than -6.
(iii) All non-negative integers less than 6.
(iv) All even positive integers less than 12.
(v) All odd negative integers greater than -8.
Answer
(i) All integers from -5 to 3.
(ii) All negative integers greater than -6.
(iii) All non-negative integers less than 6.
(iv) All even positive integers less than 12.
(v) All odd negative integers greater than -8.
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.
6 more than -3 is
9
-9
3
-3
Answer
Given, 6 more than -3
⇒ (-3) + 6
⇒ -3 + 6
⇒ 3
Hence, option 3 is the correct option.
5 less than -8 is
13
-13
-3
3
Answer
Given, 5 less than -8
⇒ (-8) - 5
⇒ -8 - 5
⇒ -13
Hence, option 2 is the correct option.
8 + |-15| = ?
13
3
-13
none of these
Answer
Given, 8 + |-15|
⇒ 8 + 15
⇒ 23
Hence, option 4 is the correct option.
(-36) + (7) = ?
-29
29
43
-43
Answer
Given, (-36) + (7)
⇒ -36 + 7
⇒ -29
Hence, option 1 is the correct option.
(-28) - (-6) = ?
-34
-22
22
none of these
Answer
Given, (-28) - (-6)
⇒ -28 + 6
⇒ -22
Hence, option 2 is the correct option.
The successor of -16 is
-17
17
-15
15
Answer
The successor of -16 = -16 + 1
⇒ -15.
Hence, option 3 is the correct option.
The predecessor of -13 is
-14
-12
14
12
Answer
The predecessor of -13 = -13 - 1
⇒ -14
Hence, option 1 is the correct option.
The additive inverse of 5 is
-5
0
-4
Answer
Let the additive inverse of 5 be x.
∴ x + 5 = 0
⇒ x = 0 - 5
⇒ x = -5
Hence, option 2 is the correct option.
12 - (-8) = ?
4
-4
20
-20
Answer
Given, 12 - (-8)
⇒ 12 + 8
⇒ 20
Hence, option 3 is the correct option.
On subtracting -7 from 0, we get
-7
7
0
none of these
Answer
Given, subtracting -7 from 0
⇒ 0 - (-7)
⇒ 0 + 7
⇒ 7
Hence, option 2 is the correct option.
(-8) + (-9) + 13 + (-14) = ?
-18
18
0
none of these
Answer
Given, (-8) + (-9) + 13 + (-14)
⇒ -8 - 9 + 13 - 14
⇒ -8 + 4 - 14
⇒ -4 - 14
⇒ -18
Hence, option 1 is the correct option.
The sum of two integers is -22. If one of them is 8, then the other is
-14
14
-30
none of these
Answer
Given, sum of two integers = -22.
One number = 8
Let the other number be x.
∴ 8 + x = -22
⇒ x = -22 - 8
⇒ x = -30
Hence, option 3 is the correct option.
What should be added to 8 to get -15?
-7
23
-23
none of these
Answer
Let the number be x.
∴ 8 + x = -15
⇒ x = -15 - 8
⇒ x = -23
Hence, option 3 is the correct option.
What should be subtracted from (-3) to get 15?
18
-12
12
none of these
Answer
Let the number be x.
∴ (-3) - x = 15
⇒ -x = 15 + 3
⇒ -x = 18
⇒ x = -18.
Hence, option 4 is the correct option.
Answer the following question with respect to the number line shown below.
The change in moving from point P to point Q is :
20
10
-20
4
Answer
Position of P = -10
Position of Q = 10
Change in moving from point P to point Q = Final position - Initial position
= Q - P = 10 - (-10) = 20.
Hence, option 1 is the correct option.
Answer the following question with respect to the number line shown below.
The change in moving from point R to point P is :
-15
-25
5
-5
Answer
Position of R = 15
Position of P = -10
Change = Final position - Initial position
= P - R = (-10) - (15) = -25.
Hence, option 2 is the correct option.
Answer the following question with respect to the number line shown below.
At what number must a point S be placed for the change between points P and S to be 15?
5
-15
-5
15
Answer
Change = Final position - Initial position = S - P
We need,
S - (-10) = 15
S + 10 = 15
S = 15 - 10 = 5.
Hence, option 1 is the correct option.
Answer the following question with respect to the number line shown below.
At what number must a point T be placed for the change between points R and T to be -30 ?
15
-30
-15
30
Answer
Change = Final position - Initial position = T - R = -30
T = -30 + R
T = -30 + 15 = -15.
Hence, option 3 is the correct option.
Fill in the blanks :
(i) -36 + 8 = ...............
(ii) -36 - 8 = ...............
(iii) -46 - (-6) = ...............
(iv) 53 - (-10) = ...............
(v) 0 - (-13) = ...............
(vi) 9 + 1 - 61 = ...............
Answer
(i) -36 + 8 = -28.
(ii) -36 - 8 = -44.
(iii) -46 - (-6) = -40.
(iv) 53 - (-10) = 63.
(v) 0 - (-13) = 13.
(vi) 9 + 1 - 61 = -51.
Write T for true and F for false statement :
0 is a positive integer.
Answer
False
Reason
The number 0 is an integer, but it is neither positive nor negative.
Positive integers are numbers greater than 0 (1, 2, 3, ...).
Negative integers are numbers less than 0 (-1, -2, -3, ...).
Zero (0) is the integer that separates the positive and negative integers.
Write T for true and F for false statement :
10°C below freezing point can be expressed as (-10°C).
Answer
True
Reason
The freezing point of water is 0°C. "10°C below freezing point" means 10 degrees less than 0°C, which is expressed as −10°C.
Write T for true and F for false statement :
-(-15) = + 15
Answer
True
Reason
The negative of a negative number is a positive number. Therefore, −(−15) is equal to +15.
Write T for true and F for false statement :
Predecessor of (- 9) is - 10.
Answer
True
Reason
The predecessor of a number is the number immediately before it.
Predecessor of (−9) = −9 − 1 = −10.
Write T for true and F for false statement :
On subtracting - 40 from 40, we get 80
Answer
True
Reason
The expression "subtracting -40 from 40" can be written as:
⇒ 40 − (−40)
⇒ 40 + 40
⇒ 80
Write T for true and F for false statement :
Successor of -1 is 0.
Answer
True
Reason
The successor of a number is the number that comes directly after it. To find the successor, you add 1 to the number.
Successor of (−1) = −1 + 1 = 0.
Write T for true and F for false statement :
|-15| + 10 = -5
Answer
False
Reason
The absolute value of −15 is 15.
⇒ ∣−15∣ + 10
⇒ 15 + 10
⇒ 25
Assertion (A): The integer which is 2 less than its additive inverse is -1.
Reason (R): For an integer a, (-a) is its additive inverse.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Answer
The reason states that for any integer a, its additive inverse is −a.
This is a fundamental definition in mathematics. The sum of an integer and its additive inverse is always zero [a + (−a) = 0].
∴ Reason (R) is true.
Let the unknown integer be x.
According to the Reason (R), its additive inverse is −x.
The assertion states that the integer x is 2 less than its additive inverse. We can write this as an equation:
⇒ x = (−x) − 2
To solve for x, we can add x to both sides of the equation:
⇒ x + x = −2
⇒ 2x = −2
Dividing both sides by 2 gives:
⇒ x = −1
The integer is indeed −1.
∴ Assertion (A) is true.
∴ Both A and R are true and R is the correct explanation of A.
Hence, option 1 is the correct option.
Assertion (A): All whole numbers are integers.
Reason (R): On the number line, all the integers on the left of 0 are negative.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Answer
According to Assertion: All whole numbers are integers.
By definition, whole numbers are the set {0, 1, 2, 3, ...}. Integers are the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Since all whole numbers are included in the set of integers.
∴ Assertion (A) is true.
According to Reason: On the number line, all the integers on the left of 0 are negative.
This is a fundamental property of the number line; numbers to the left of zero are negative, and numbers to the right are positive.
∴ Reason (R) is true.
Both A and R are true but R is not the correct explanation of A.
Hence, option 2 is the correct option.