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(- 24) × (- 7) 

We know, (- a) × (- b) = (a × b) 

= 24 × 7 

= 168

i) 40 – (22) = +40 – 22 

= +(18 + 22)-22 

= 18 +(22-22) 

= 18 + 0 

∴ 40-(22) = + 18

ii) 84 – (98) = 84 – 98

= + 84 – 84 – 14 

= (84 – 84) – 14 

= 0 – 14 

∴ 84 – (98) = – 14

iii) (-16) + (-17) = -16 – 17 = – 33 

∴ (-16) + (-17) = -33

iv) (-20) – (13) = – 20 – 13 = -33 

∴ (-20) – (13) = – 33

v) 38 – (-6) = 38 + 6 

We know – (-a) = a = + 44 

∴ 38 – (-6) = + 44

vi) (-17) – (-36) = -17 + 36 

We know – (- a) = a 

= -17 + 17 + 19 

= (-17+17) + 19

= + 19 

∴ (-17) – (-36) = + 19

-2:

( – 40) × (-2) = 80

(- 3) × (-40) 

We know, (- a) × (-b) = (a × b) 

= (- 3) × (- 40) 

= 3 × 40 

= 120

(-2) × 175 

We know, (- a) × b = – (a × b) 

= – (2 × 175) 

= – 350

8 × (-1) 

We know, a × (- b) = – (a × b) 

= – (8 × 1) 

= – 8

7 × 6 – \(\overline {8-4}\) (Vinculum)

= 7 × 6 – 4 (Multiplication) 

= 42 – 4 (Subtraction) 

= 38

6 × 9 – 6 ÷ 3 (Division) 

= 6 × 9 – 2 (Multiplication) 

= 54 – 2 (Subtraction) 

= 52

12 – 36 = 3 (Division) 

= 12 – 12 (Subtraction) 

= 0

6 × (- 7) + (- 3) ÷ 3 

We know, (- a) ÷ b = – (a ÷ b) 

= 6 × (- 7) – 3 ÷ 3 (Division)

We know, a × (-b) = – (a × b) 

= – (6 × 7) – 1 (Multiplication) 

= – 42 – 1 (Subtraction) 

= – 43

7°C temperature at 2:00 pm.

(a) -F

(b) Negative integer (-6)

(c)  -10

(d) E has the least value as it represents -10

(e) D > O > B > A > O > H > G > F > E.

The scores of five successive rounds }
= 25, -5, -10, 15, 10
Total scores of Jack at the end of the event }
= 25 + 15+ 10+ = 50
= -5 -10 = -15
= 35

(a) Increase in size.
(b) Success.
(c) Loss of ₹ 10
(d) 1000 BC
(e) Fall in water level.
(f) 60 km north.
(g) 10 m below the danger mark of river Ganga.
(h) 20 m above the danger mark of the river Brahmaputra.
(i) Losing by a margin of 2000 votes.
(j) Withdrawing ₹ 100 from the Bank account.
(k) 20°C fall in temperature.

(a) Increase in size 

(b) Success 

(c) loss of Rs. 10 

(d) 1000 B.C. 

(e) Fall in water level 

(f) 60 km North 

(g) 10 m below the danger mark of river Ganga. 

(h) 20 m above the danger mark of river Brahmaputra. 

(i) Losing by a margin of 2000 votes. 

(j) Withdrawing Rs 100 from the Bank. 

(k) 20°C fall in temperature.

Given 3 – (5 – 6 ÷ 3)

According to removal of bracket rule firstly remove inner most bracket

We get 3 – (5 – 6 ÷ 3) 

= 3 – (5 – 2)

= 3 – 3

= 0

(i) 9 (2 + 5)

(ii) 12 ÷ (2 + 3)

(iii) 20 ÷ (7 – 2)

(iv) 2 × 3 -8

(v) 40 ÷ [1 + (9 + 10)]

(vi) 2 × [(19 -6) -1]

Given (-3) × (-4) ÷ (-2) + (-1)

According to BODMAS rule we have perform division first then followed by multiplication, addition and subtraction.

(-3) × (-4) ÷ (-2) + (-1) 

= -3 × 2 -1

= – 6 – 1

= -1

Given (-15) + 4 ÷ (5 – 3)

According to BODMAS rule we have perform division first then followed by addition and subtraction.

Therefore, (-15) + 4 ÷ (5 – 3) 

= (-15) + 4 ÷ 2

= -15 + 2

= -13

Given (-3) + (-8) ÷ (-4) -2 × (-2)

According to BODMAS rule we have perform division first then followed by multiplication, addition and subtraction.

(-3) + (-8) ÷ (-4) -2 × (-2) 

= -3 + 2 -2 × (-2)

= -3 + 2 + 4

= 6 – 3

=3

Given (-2) + (-8) ÷ (-4)

According to BODMAS rule we have perform division first then followed by addition and subtraction.

Therefore, (-2) + (-8) ÷ (-4) 

= (-2) + 2

= 0

Given (-40) × (-1) + (-28) ÷ 7

According to BODMAS rule we have perform division first then followed by multiplication, addition and subtraction.

(-40) × (-1) + (-28) ÷ 7 

= (-40) × (-1) – 4

= 40 – 4

= 36

Given 24 + 15 ÷ 3

According to BODMAS rule we have operate division first then we have to do addition

Therefore 24 + 15 ÷ 3 

= 24 + 5 

= 29

Given (-20) × (-1) + (-28) ÷ 7

According to BODMAS rule we have perform division first then followed by multiplication, addition and subtraction.

Therefore, (-20) × (-1) + (-28) ÷ 7 

= (-20) × (-1) – 6

= 20 – 6 

= 16

Given 120 – 20 ÷ 4

According to BODMAS rule we have operate division first then we have to do multiplication

Therefore 120 – 20 ÷ 4 

= 120 – 5 

= 115

Given 28 – 5 × 6 + 2

According to BODMAS rule we have perform multiplication first then followed by addition and subtraction.

Therefore, 28 – 5 × 6 + 2 

= 28 – 30 +2

= 28 – 28 

= 0

Given 32 – (3 × 5) + 4

According to BODMAS rule we have operate in brackets first then we have move to addition and subtraction.

Therefore 32 – (3 × 5) + 4 

= 32 – 15 + 4

= 32 – 11 

= 21

Given 16 + 8 ÷ 4 – 2 × 3

According to BODMAS rule we have perform division first then followed by multiplication, addition and subtraction.

Therefore, 16 + 8 ÷ 4 – 2 × 3 

= 16 + 2 – 2 × 3

= 16 + 2 – 6

= 18 -6

= 12

Given 21 – 12 ÷ 3 × 2

According to BODMAS rule we have perform division first then multiplication and addition.

Therefore, 21 – 12 ÷ 3 × 2 

= 21 – 4 × 2

= 21 – 8 

= 13

Given 3 – (5 – 6 ÷ 3)

According to BODMAS rule we have operate in brackets first then we have move to subtraction.

Therefore 3 – (5 – 6 ÷ 3) 

= 3 – (5 – 2)

= 3 –3 

= 0

2020 ÷ 20 – 100 = 1 (Division) 

101 – 100 = 1 (Subtraction) 

1 = 1 

It is a true statement.

– 11 + 3 × 7 = – 56 (Multiplication) 

– 11 + 21 = – 56 (Subtraction) 

10 ≠ – 56 

It is a false statement.

2 × (-6) = – (2 × 6) = – 12

– 18 + 12 ÷ 3 = – 14 (Division) 

– 18 + 4 = – 14 (Subtraction) 

– 14 = – 14 

It is a true statement.

7 × (-4) = – (7 × 4) = – 28

16 – (4 + 18 ÷ 6 – \(\overline{7-5}\)) x 5 (Vinculum)

= 16 – (4 + 18 + 6 – 2) × 5 (Division) 

= 16 -(4 + 3 – 2) × 5 (Simple bracket) 

= 16 – (7 – 2) × 5 = 16 – 5 × 5 (Multiplication) 

= 16 – 25 (Subtraction) 

= – 9

{6 of 145 ÷ (3 + 2)} ÷ 2 -4 of 20 (Simple Bracket)

= {6 of 145 ÷ 5} ÷ 2 – 4 of 20 (Of) 

= {870 ÷ 5} ÷ 2 – 80 (Curly bracket, Division) 

= 174 ÷ 2 – 80 (Division) 

= 87 – 80 (Subtraction) 

= 7

48 ÷ 6 – 4 = 24 (Division) 

8 – 4 = 24 (Subtraction) 

4 ≠ 24 

It is a false statement.

Correct option is (C) -250

42 x (-5) + (-8) x 5 = -210 - 40 = -250
 

Correct option is  C) – 250

Correct option is D) 0 ÷ (- 5) = 0

Any number which is divided by zero is not defined and any number whih is multiplied with zero gives 0 as product.

\(\therefore\) 

(A) 8 ÷ 0 is not defined

(B) 0 ÷ 11 = 0

(C) (-7) ÷ 0 is not defined

(D) 0 ÷ (-5) = 0

D) 0 ÷ (- 5) = 0

25 + [14 – 18 + {12 of 5 – (- 4 + 14)}] Applying BODMAS Rule 

= 25 + [14 – 18 + {12 of 5 – (10)}] [Removing inner most in bracket] 

= 25 + [14 – 18 + {12 × 5 – 10}] [Replacing of] 

= 25 + [14- 18 + {60 – 10}] = 25 + [- 4 + 50]

= 25 – 4 + 50 = 75 – 4 

= 71

Correct option is (B) -2

(-3/4) x (5/6) x 8/7 x (-14/5)

 = \((\frac{-3}4\times\frac{-5}6)\times(\frac87\times\frac{-14}5)\) 

 = \(\frac58\times\frac{-16}5=-2\)

Correct option is  B) – 2

Given -25 + 14 ÷ (5 – 3)

According to removal of bracket rule firstly remove inner most bracket

We get -25 + 14 ÷ (5 – 3) 

= -25 + 14 ÷ 2

= -25 + 7

= -18

Observe the following and fill the blanks

(iii) 0 + (-14) = – 14,
(iv) (-8) + 0 = -8
(v) 15 +0 = 15,
(vi) (-23) + 1 = -23

Multiplications: 

(i) (- 10) × 6 = – 60 

(ii) (- 4) × (- 9) = 36 

(iii) 12 × 6 = 72 

(iv) 6 × (-4) = – 24 

(v) 8 × 6 = 48 

(vi) 12 × 8 = 96

Divisions: 

(i) (-36) ÷ 6 = – 6

(ii) (-100) ÷ (- 10) = 10 

(iii) 45 ÷ (-9) = – 5 

(iv) 72 ÷ 12 = 6 

(v) (-56) ÷ 8 = – 7 

(vi) (-28) ÷ (-4) = 7

Multiplications: 

(i) (- 10) × 6 = – 60 

(ii) (- 4) × (- 9) = 36 

(iii) 12 × 6 = 72 

(iv) 6 × (-4) = – 24 

(v) 8 × 6 = 48 

(vi) 12 × 8 = 96

Divisions: 

(i) (-36) ÷ 6 = – 6

(ii) (-100) ÷ (- 10) = 10 

(iii) 45 ÷ (-9) = – 5 

(iv) 72 ÷ 12 = 6 

(v) (-56) ÷ 8 = – 7 

(vi) (-28) ÷ (-4) = 7

False.

Sum of two negative integers is always negative.

Example:

Consider two negative integers – 8 and – 10.

Sum of two negative integers = – 8 + (-10)

= – 8 – 10

= – 18

C) Commutative under multiplication