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(- 20) × (-2) × (-5) × 7 

= (- 20) × [(-2) × (-5)] × 7 

= [(- 20) × 10] × 7 

= – 200 × 7 

= – 1400

(- 20) × (-2) × (-5) × 7 

= (- 20) × [(-2) × (-5)] × 7 

= [(- 20) × 10] × 7 

= – 200 × 7 

= – 1400

B) 4, 2, – 1, – 3

B) Associative under addition

B) – 8, – 5, 1, 2

Correct option is  C) 0

C) Z = {- 3, -2, -1, 0, 1, 2 ………….}

(d) (– 8) × (– 3) – (– 8) × (– 4)

[(– 8) × (– 3)] × (– 4)

= (– 8) × [(– 3) × (– 4)]

= [(– 8) × (– 4)] × (– 3)

= [(– 3) × (– 8)] × (– 4

But, [(– 8) × (– 3)] × (– 4) ≠ [(– 8) × (– 3)] × (– 4)

Correct option is  A) 1

(b) 1

The multiplicative identity of an integer a is 1. 

[As a x 1 = a]

(a) – (-a)

The additive inverse of a is – a

But, – (-a) = a

(d) 43

Using BODMAS rule,

(-10) x (-5) + (-7) 

= 50 – 7 

= 43

Let the integers be 12 and -3 such that 12 × (-3) = -36
and their difference = 12 – (-3) = 12 + 3 = 15

∴ A pair of integers is (-3,12).

(c) (– 11) × (– 7)

We have,

11 x (-7) = -77

– (11 x 7) = -77 and

7 x (-11) = -77

But, (-11) x (-7) = 77

1. Age of child is 8 years. 

2. Five years ago, year was 2012. His/her age is 3 years. 

3. In 2024, he/she will go the Std X. His/her age is 15 years.

Let the integers be -2 and 6 such that (-2) × 6 = -12

∴ A pair of integers is (-2, 6).

And there are seven integers, i.e.,

-1, 0, 1, 2, 3, 4, 5 which lie between -2 and 6.

(b) 0 and 10

The value of 5 ÷ (–1) = -5

As it’s as negative number it doesn’t lie between 0 and 10.

(a) -10

As (-3) x 3 = -9

So, -9 lies to the right to -10.

Product of two integers with same sign is always a positive integer and the product of two integers with opposite signs is always negative integer.

(c) When a positive integer and a negative integer is added we always get a negative integer.

The above statement is false as when a positive and a negative integer is added we may get a positive number or even zero.

The sum of two negative integers is a positive integer.

False

a × (-1) = – 1 × a = – a. 

When an integer is multiplied by – 1, 

the sign of the integer changes from + ve to – ve or – ve to + ve.

The sum of three different integers can never be zero.

False

The product of two integers is zero only when one of them is zero.

(i) (-5) + (-8) = (-8) + (-5)

(ii) -53 + 0 = -53

(iii) 17 + -17 = 0

(iv) [13 + (-12) + (-7) = 13 + [(-12) + (-7)]

(v) (-4) + [15 + (-3)] = [-4 + 15] + -3.

Team A scored = -40 + 10 + 0 = -30
Team B scored = 10 + 0 – 40 = -30
Yes. We can add integers in any order.

Let -2 and 1
-2 – (+1)
-2 – 1 = -3

Let -10 and 5
∴  -10 + 5 = -5

Let -4 and -12 are two negative integers.
∴ -4 – (-12)
-4 + 12 = 8

(a) sum is -7

– 2 + -5 = -7
∴ The two integers be -2 and -5.

(b) difference is -7

-20 – (-10) = -10 (∵ -20 – (-10))
-20 + 10 = -10
∴ The two integers be – 20 and -10.

(c) sum is 0

Any two integers of same number but different sign. 

For eg : 10 + (-10) = 0.

The highest point (above sea level) = 8,848 m

The lowest point (below sea level) = 10,911 m

∴ Total vertical distance between two points

= [8,848 – (-10,911)] m

= [8,848 + 10,911] m = 19,759 m

Elevation relative to the sea level at the end of the ride

= [380 + 540 – 268 + 116 -152 + 490 – 844 + 94]m

= [380 + 540 + 116 + 490 + 94 – 268 – 152 – 844]m

= [1620 – 1264] m = 356 m

(a) Closest location to sea level is C 

(b) Fathest location from sea level is D

(c) A,C,B,D

(i) 14, 27, 15, -14, -9, 0,11, -17

• Separating the positive integers 14, 27, 15, 11 and negative integers -14, -9, -17
• Arranging in descending order we get the positive integers 27,15,14,11 and the negative integers -9, -14, -17.
• ‘0’ is neither positive nor negative and so it stand in middle.
• ∴ The numbers in descending order : 27, 15, 14, 11, 0, -9, -14, -17

(ii) -99, -120, 65, -46, 78, 400, -600

• Separating the positive integers 65, 78, 400 and negative integers -99, -120, -46, -600
• Arranging the positive integers in descending order as 400, 78, 65 and the negative integers in descending order -46, -99, -120, -600.
• The numbers in descending order : 400, 78, 65, -46, -99, -120, -600.

(iii) 111, -222, 333, -444, 555, -666, 7777, -888

• Separating the positive integers 111, 333, 555, 7777 and negative integers -222, -444, -666, -888
• Arranging the positive integers in descending order as 7777, 555, 333, 111 and negative integers in descending order as -222, -444, -666, -888
• The numbers in descending order : 7777, 555, 333, 111, -222, -444, -666, -888

Descending order of given integers is, 0, -1, -3, -4, -6

– 25 × (- 4) × 2 × (- 8) 

= [- 25 × (- 4)] × 2 × (- 8) 

= [100 × 2] × (-8)

= 200 × (-8) 

= – 1600

a × (b + c) = (a × b) + (a × c) 

Distributive over addition property 

18 × (7 – 3) = (126) + (- 54) 

18 × 4= 126 – 54 

72 = 72

a × b = b × a 

2 × (-3) = (-3) × 2

a × (b + c) = (a × b) + (a × c) 

5×[(-6)+9] = 5 × (-6) + [(5 × 9 )]

a × 1 = a = 1 × a 

-6 × ________ = – 6

a + b = b + a (Additive commutative property) 

– 3 + 5 = 5 – 3 

2 = 2

a × 1 = 1 × a = a 

Multiplicative identity property 

– 2 × 1 = 1 × (-2) = – 2

– 2 = – 2

a + (b + c) = (a + b) + c 

= [(-6) + 3] + (- 2)

(a × b) × c = a × (b × c) 

Multiplicative associative property. 

(- 10) × 3 = (- 5) × (6) 

– (10 × 3) = – (5 × 6) 

– 30 = – 30

(- a) × b = – (ab) 

Multiplicative closure property 

– 30 = – 30

1. -666

2. -2, -1, 0, 1, 5

1. + 2500

2. -4000 feet

3. 1