integer

Question 1.

Evaluate the following, using the number line:

(i) 4 – (-2)

(ii) -4 – (-2)

(iii) 3 – 6

(iv) -3 – (-5)

Solution:

(i) Start from 4 on the number line.

Move 2 units to the digits we reach at 6

∴ 4 – (-2) = 4 + 2 = 6

 

(ii) Start from -4 on the number line.

Move 2 units to the right, we reach at -2

∴ -4 – (-2) = —4 + 2 = -2

(iii) Start from 3 on the number line.

Move 6 units to the left, we reach at -3

3 – 6 = -3

(iv) Start from -3 on the number line.

Move 5 units to the right, we reach at 2

-3 – (-5) = -3 + 5 = 2

Question 2.

Subtract :

(i) -6 from 9

(ii) 6 from -9

(iii) -6 from -9

(iv) -725 from -63

(v) -376 from 10

(vi) 92 from -620

Solution:

(i) 9 – (-6) = 9 + 6 = 15

(ii) -9 – 6 = -15

(iii) -9 – (-6) = -9 + 6 = -3

(iv) -63 – (-725) = -63 + 725 = +662

(v) 10 – (-376) = 10 + 376 = 386

(vi) -620 – 92 = -712

Question 3.

Evaluate the following:

(i) -237 – (+ 1884)

(ii) -346 – (- 1275)

(iii) -190 – (-3512)

(iv) -2718 – (+ 6827)

Solution:

(i) -237 – (+ 1884)

= -237 – 1884

= -(237 + 1884) = -2121

 

(ii) -346 -(- 1275)

= -346 + 1275

= 1275 – 346 = 929

(iii) -190 – (-3512)

= -190 + 3512

= 3512- 190 = 3322

(iv) 2718 – (+ 6827)

= -2718 – 6827

= -(2718 + 6827) = -9545

Question 4.

The sum of two integers is 17. If one of them is -35, find the other.

Solution:

One number = -35

Sum of two integers =17

Second number = Sum of integers – (The given number)

= 17 – (-35)

= 17 + 35 = 52

Question 5.

What must be added to -23 to get -9?

Solution:

Let the number to be added = x

∴ -23 + x = -9

∴ The required number = -9 – (-23)

= -9 + 23 = 14

Question 6.

Find the predecessor of 0.

Solution:

Predecessor of 0 = 0 – 1 = -1

Question 7.

Find the successor and the predecessor of the following integers:

(i) -31

(ii) -735

(iii) -240

Solution:

(i) Successor of -31 = -31 + 1 = -30

Predecessor of -31 = -31 – 1 = -32

(ii) Successor of -735 = -735 + 1 = -734

Predecessor of-735 = -735 – 1 = -736

(iii) Successor of -240 = -240 + 1 = -239

Predecessor of -240 = -240 – 1 = -241

Question 1.

Find the value of:

(i) 6 – 9 + 4

(ii) -5 – (-3) + 2

(iii) 7 + (-5) + (-6)

(iv) 6 – 3 – (-5)

Solution:

(i) 6 – 9 + 4

= (6 + 4) – 9 = 10 – 9= 1

 

(ii) -5 – (-3) + 2

= -5 + 3 + 2 = -5 + 5 = 0

(iii) 7 + (-5) + (-6)

= 7 – 5 – 6 = 2 – 6 = -4

(iv) 6 – 3 – (-5)

= 6 – 3 + 5 = 8

Question 2.

Evaluate the following:

(i) -77 + (-84) + 318

(ii) 54 + (-218) – (-76)

(iii) -121 – (-78) + (-193) + 576

(iv) -65 + (-76) – (-28) + 32

Solution:

(i) -77 + (- 84) + 318

= -77 – 84 + 318

= -(77 + 84)+ 318

= -(161) + 318

= -161 +318

= 318 – 161 = 157

(ii) 54 + (-218) – (-76)

= 54 – 218 + 76

= (54 + 76) – 218

= 130 – 218 = – 88

(iii) -121 – (-78) + (-193) + 576

= -121 + 78 – 193 + 576

= -121 – 193 + 78 + 576

= -(121 + 193) + 78 + 576

= -(314) + 654

= 654 – 314 = 340

(iv) -65 + (-76) – (-28) + 32

= -65 – 76 + 28 + 32

= -(65 + 76) + 60

= -141 + 60 = -81

Question 3.

Find the value of:

(i) 8 – 6 + (-2) – (-3) + 1

(ii) 31 + (-23) – 35 + 18 – 4 – (-3)

Solution:

(i) 8 – 6 + (-2) – (-3) + 1

= 8 – 6 – 2 + 3 + 1

=-6 – 2 + 8 + 3 + 1

= -6 – 2 + 12

=-8 + 12 = 4

(ii) 31 + (-23) – 35 + 18 – 4 – (-3)

= 31 – 23 – 35 + 18 – 4 + 3

= -23 – 35 – 4 + 31 + 18 + 3

= -23 – 35 – 4 + 52

= -62 + 52 = -10

Question 4.

Rashmi deposited ₹ 4370 in her account on Monday and then withdrew ₹ 2875 on Tuesday. Next day she deposited ₹ 1550. What was her balance on Thursday?

Solution:

Rashmi deposited in her account on Monday = ₹ 4370

Less withdrawal on Tuesday = ₹ 2875

So the Balance on Tuesday

= ₹ 4370 – ₹ 2875

= ₹ 1495

Again she deposited on Wednesday = ₹ 1550

Balance on Thursday

= ₹ 1495 + ₹ 1550 = ₹ 3045

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Question 1.

Use the appropriate symbol < or > to fill in the following blanks:

(i) (-3 + ……… (-6) (-3) – (-6)

(ii) (-21) – (-10) ……. (-31)+ (-11)

(iii) 45 – (-11) ……….. (57) + (-4)

(iv) (-25) – (-42) …………. (-42) – (-25)

Solution:

(i) (-3 + (-6) < (-3) – (-6)

(ii) (-21) – (-10) > (-31) + (-11)

(iii) 45 – (-11) > (57) +(-4)

(iv) (-25 – (-42) > (-42) – (-25)

Question 2.

Find the value of:

(i) 12 + ( -3) + 5 – (-2)

(ii) 39 – 35 + 7-(-4) + 21

(iii) -15- (-2) – 71 – 8 + 6

Solution:

(i) 12 + (-3) + 5 – (-2)

= 12 – 3 + 5 + 2

= 9 + 7= 16

(ii) 39 – 35 + 7 – (-4) + 21

= 39 – 35 + 7 + 4 + 21

= 4 + 11 + 21

= 15 + 21 =36

(iii) -15 – (-2) – 71 – 8 + 6

= -15 + 2 – 71 – 8 + 6

= -13 – 79 + 6

= 92 + 6 = -86

Question 3.

Evaluate:

(i) |-13| – |-15|

(ii) |35 – 41| – |7-(-2)|

Solution:

(i) |-13| – |-15|

= +13 – 15 =-2

(ii) |35 – 41| – |7 – (-2)|

= 6 – 9 = -3

Question 4.

Arrange the following integers in ascending order:

-39, 35, -102, 0, -51, -5, -6, 7

Solution:

-102, -51, -39, -6, -5, 0, 7, 35

Question 5.

Find the successor and the predecessor of -199.

Solution:

Successor = -199 – 1 = -198

Predecessor = -199 – 1 = -200

Question 6.

Subtract the sum of -235 and 137 from -152.

Solution:

Sum of (-235 and 137)

= -235 + 137

= 137 – 235 = -98

Now, subtract the sum of (-235 and 137) from -152

= 152 – (-98)

= -152 + 98 = -54

Question 7.

What must be added to -176 to get -95?

Solution:

Let the number to be added = x

∴ -176 + x = -95

x = -95 + 176 = 81

Question 8.

What is the difference in height between a point 270 m above sea level and 80 m below sea level?

Solution:

Height above sea level = +270 m

Height below sea level = -80 m

Difference = +270 – (-80)

= 270 + 80 = 350 m