Integers - Exercise 1(B)

Add the following integers :

(i) 64 and 36

(ii) 73 and -37

(iii) -26 and -45

(iv) -51 and 25

(v) 100 and -32

(vi) 0 and -21

Answer

(i)

We have

64 + 36

= 100

(ii)

We have

73 + (-37)

Since one integer is positive and the other is negative, we subtract their values and keep the sign of the greater number (73).

73 + (-37)

= 73 - 37

= 36

(iii)

We have

-26 + (-45)

Since both integers are negative, we add their values and keep the negative sign.

-26 + (-45)

= -26 - 45

= -71

(iv)

We have

−51 + 25

Since one integer is negative and the other is positive, we subtract their values and keep the sign of the greater number (−51).

−51 + 25

= −(51 − 25)

= −26

(v)

We have

100 + (−32)

Since one integer is positive and the other is negative, we subtract their values and keep the sign of the greater number (100).

100 + (−32)

= 100 − 32

= 68

(vi)

We have

0 + (-21)

Zero is the additive identity. Adding 0 to any integer does not change its value.

∴ 0 + (-21)

= -21

Find the additive inverse of :

(i) 23

(ii) -33

(iii) -1

(iv) -476

Answer

(i) 23

Since 23 + (−23) = 0

∴ the additive inverse of 23 is -23

(ii) -33

Since (−33) + 33 = 0

∴ the additive inverse of −33 is 33

(iii) -1

Since (−1) + 1 = 0

∴ the additive inverse of −1 is 1

(iv) -476

Since (−476) + 476 = 0

∴ the additive inverse of −476 is 476

Evaluate :

(i) 6 - 24

(ii) 18 - (-8)

(iii) (-16) - (-5)

(iv) (-20) - 6

(v) (-1) - (-19)

(vi) 8 - (-23)

Answer

(i)

We have

6 - 24

= 6 + (-24)

= -18

(ii)

We have

18 - (-8)

= 18 + 8

= 26 $\quad$ [∵ a - (-b) = a + b]

(iii)

We have

(-16) - (-5)

= -16 + 5

= -11

(iv)

We have

(-20) - 6

= (-20) + (-6)

= -26

(v)

We have

(-1) - (-19)

= (-1) + 19

= 18

(vi)

We have

8 - (-23)

= 8 + 23

= 31 $\quad$ [∵ a - (-b) = a + b]

Verify the following :

(-14) + 9 = 9 + (-14)

Answer

We have

(-14) + 9 = 9 + (-14)

LHS = (−14) + 9
= −5

RHS = 9 + (−14)
= −5

Since LHS = RHS,
∴ (-14) + 9 = 9 + (-14)

Verify the following :

(-8) + (-12) = (-12) + (-8)

Answer

We have

(-8) + (-12) = (-12) + (-8)

LHS = (−8) + (−12)
= −20

RHS = (−12) + (−8)
= −20

Since LHS = RHS,
∴ (-8) + (-12) = (-12) + (-8)

Verify the following :

(-6) + [(-8) + 12] = [(-6) + (-8)] + 12

Answer

We have

(-6) + [(-8) + 12] = [(-6) + (-8)] + 12

LHS = (−6) + [−8 + 12]
= (−6) + 4
= −2

RHS = [(−6) + (−8)] + 12
= (−14) + 12
= −2

Since LHS = RHS,
∴ (-6) + [(-8) + 12] = [(-6) + (-8)] + 12

Verify the following :

[(-9) + (-7)] + (-14) = (-9) + [(-7) + (-14)]

Answer

We have

[(-9) + (-7)] + (-14) = (-9) + [(-7) + (-14)]

LHS = [−9 + (−7)] + (−14)
= (−16) + (−14)
= −30

RHS = (−9) + [−7 + (−14)]
= (−9) + (−21)
= −30

Since LHS = RHS,
∴ [(-9) + (-7)] + (-14) = (-9) + [(-7) + (-14)]

Fill in the blanks:

(i) 8 + ............... = 0

(ii) (-10) + ............... = -10

(iii) (-6) + (-8) = (-8) + ...............

(iv) (-6) + ............... = -14

(v) (-11) + ............... = (-7)

(vi) (-9) + ............... = -1

Answer

(i) 8 + (-8) = 0

(ii) (-10) + 0 = -10

(iii) (-6) + (-8) = (-8) + (-6)

(iv) (-6) + (-8) = -14

(v) (-11) + 4 = (-7)

(vi) (-9) + 8 = -1

Subtract the sum of -137 and -43 from the sum of -103 and 27.

Answer

Calculate the sum of -137 and -43:

(-137) + (-43) = -180

Calculate the sum of -103 and 27:

(-103) + 27 = -76

Subtract the first sum from the second sum:

(-180) - (-76)

= -180 + 76

= -104

∴ The answer is -104

Subtract -29 from -53 and add -16 to the result.

Answer

Subtract -29 from -53:
-53 - (-29) = -53 + 29 = -24

Add -16 to the result: -24 + (-16) = -40

Final Answer is -40

The sum of two integers is 43. If one of them is -27, find the other.

Answer

Let the two integers be x and y.

Given that x + y = 43 and x = -27.

Substitute x in the below equation

x + y = 43
-27 + y = 23 $\hspace{2cm}$(Substituting x)
y = 23 + 27 $\hspace{2.2cm}$(Solve for y)
y = 23 + 27
y = 70

∴ The other integer is 70

Find the successor of :

(i) 30

(ii) -70

(iii) -206

(iv) -1

Answer

(i)

The successor of 30 is:

30 + 1 = 31

(ii)

The successor of -70 is:

-70 + 1 = -69

(iii)

The successor of -206 is:

-206 + 1 = -205

(iv)

The successor of -1 is:

-1 + 1 = 0

Find the predecessor of:

(i) 60

(ii) -351

(iii) 0

(iv) -99

Answer

(i)

The predecessor of 60 is:

60 - 1 = 59

(ii)

The predecessor of -351 is:

-351 - 1 = -352

(iii)

The predecessor of 0 is:

0 - 1 = -1

(iv)

The predecessor of -99 is:

-99 - 1 = -100