Worksheet Solutions: Integers

Q.1. Write 'True' or 'False' for the following :
(i) -20° C represent temperature "above 20°C"
(ii) 8 > (-10)
(iii) (- 2 ) = 2
(iv) (- 4 - 2 )  > (-5) 

Ans.
(i) False
(ii) True
(iii) False 
(iv) False 

Q.2. Fill up the blanks :
(i) Integer which is neither positive nor negative is ____________
(ii) Predecessor of (-99) is ____________
(iii) ( -26-14 ) = ____________
(iv) Successor of (-100) is ____________
(v) Largest 3-digit negative integer is ____________ 

Ans.
(i) 0
(ii) -100
(iii) -26-14= (-40)
(iv) -99
(v) -100

Q.3. Subtract (-25) from the sum of 15 and 35.
Ans. 75

Sol: First, find the sum of 15 and 35:

15 + 35 = 50

Now, subtract (-25) from the sum:

50 - (-25) = 50 + 25 = 75

Q.4. Add the sum of (-2063) and 562 to (-2063).
Ans. -3564

Sol: First, find the sum of (-2063) and 562:

(-2063) + 562 = -1501

Now, add this result to (-2063):

(-1501) + (-2063) = -3564

Q.5. Simplify :
(i) (-50) + (-200) - (-500)
(ii) 23 - (-15) + 12
(iii) (24 + 6) ÷ (-3)
(iv) 19 + {10 ÷ (7 - 9)}
(v) 12 - {16 - (6 + 2 - 6 ÷ 3)} 

Ans.
(i) 250

Sol: (-50) + (-200) - (-500)

= (-50) + (-200) + 500

= 250

(ii) 50

Sol: 23 - (-15) + 12

= 23 + 15 + 12

= 50

(iii) (-10)

Sol: (24 + 6) ÷ (-3)

= 30 ÷ (-3)

= -10

(iv) 14

Solution: 19 + {10 ÷ (7 - 9)}

= 19 + {10 ÷ (-2)}

= 19 + (-5)

= 14

(v) 2

Solution: 12 - {16 - (6 + 2 - 6 ÷ 3)}

= 12 - {16 - (6 + 2 - 2)}

= 12 - {16 - 6}

= 12 - 10

= 2

Q.6. Write additive inverse of :
(i) (-6347)
(ii) 0
(iii) 4231
(iv) 2132 - 132
(v) -10 - 5

Ans.
(i) 6347
(ii) 0
(iii) -4231
(iv) -2000
(v) 15

Q.7.

Observe the number line given above and answer the following :
(i) What is the position of Reeta on the number line?
(ii) What is the position of Seema?
(iii) What is the distance between Reeta and Seema?

Ans.
(i) Position of Reeta = -3
(ii) Position of Seema = 5
(iii)  The distance between Reeta and Seema is calculated as:

Distance = 5 - (-3) = 5 + 3 = 8

Therefore, the distance between Reeta and Seema is 8 units.

Q.8. Represent the following numbers/expressions on a number line?
(i) -7
(ii) 3+ (-4)
(iii) 4 + 6
(iv) 8 - 5
(v) -7 + 7

Ans. 

(i)

(ii)

(iii)

(iv)

(v)

Q.9. Enter the correct symbol >, =, < in the following :
(i) (-7) _________  (2)
(ii) 7 _________  (-12)
(iii) 0 _________  (-2)
(iv) (-16) _________  (9 + 7)
(v) - (10 + 5) _________  (-15) 

Ans.
(i) <
(ii) >
(iii) >
(iv) <

(v) =

Q.10. Find the values of 'a' when :
(i) a + 10 = - 18
(ii) a - 3 = 7
(iii) -13a = 91
(iv) a ÷ 5 = 3

Ans.

(i) a + 10 = -18

Sol: To find 'a', subtract 10 from both sides:

a = -18 - 10

a = -28

(ii) a - 3 = 7

Sol: To find 'a', add 3 to both sides:

a = 7 + 3

a = 10

(iii) -13a = 91

Sol: To find 'a', divide both sides by -13:

a = 91 ÷ (-13)

a = -7

(iv) a ÷ 5 = 3

Sol: To find 'a', multiply both sides by 5:

a = 3 × 5

a = 15

$(2,\; -7)$