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The values is 2 × (-5)

When a negative integer is multiplied with a positive integer then negative integer is found, it can be verified from following examples –

(i) – 1 x 4 = – 4 = 0 – 4
(ii) – 2 x 4 = – 8 = – 4 – 4
(iii) -3 x 4 = – 12 = – 4 – 4 – 4
(iv) – 5 x 2 = -10 = – 5 – 5
(v) – 6 x 3 = -18 = – 6 – 6 – 6

(i) (-12) x (-15) = 180
(ii) (-25) x (-4) = 100
(iii) (-17) x (-11) = 187

The sum of two integers is 30. If one of the integers is –42, then the other is 72.

(-42) × (-7) = + 294

(-7) × (-42) = + 294 

∴ (- 42) × (- 7) = (- 7) × (- 42) 

It is multiplicative commutative law.

The values is 6 × (-7)

-1× (–93) = 93

Fill in the blanks using <, = or > :

–60 < 50

(- 12) ÷ ( + 6) 

We know, (- a) ÷ (- b) = – (a ÷ b) 

= (- 12) ÷ 6 

= – 2

Pattern is :

(-1) x 5 = -5                (-1) x 2 = -2
(-1) x 4 = -4                (-1) x 0 = 0
(1) x 3 = -3               (-1) x (-1) = + 1

(i) True
(ii) False because division of integers is not closed.
(iii) True
(iv) True
(v) False because division of integers is not distributed on subtraction.

Fill in the blanks using <, = or > :

0 < 1

=

(-2) + (-5) + (-6) = -2 – 5 – 6 

= -13 (-3) + (-4) + (-6) = -3 – 4 – 6—13 

And-13 = -13

(A) – 15

(-3) x 5

= -15

0 > -2 

0 > -2

On the number line, –15 is to the left of zero.

(a) 0 + 1 – 2 + 3 – 4 + 5 – 6 + 7 –8 + 9 = 5 

(b) 0 – 1 – 2 + 3 + 4 – 5 + 6 – 7 + 8 – 9 = –3

(a) –5 

(b) – 25 

(c) 20 

(d) – 60 

(e) – 8 

(f) – 7 

(g) 0 

(h) 0

Correct option is (D) 1

7- {7 - (7 - \(\overline {7-1}\))} = 7[7 - {7 - ( 7 -1)}]

 = 7 - {7 - (7 - 6)}

 = 7 - (7 - 1)

 = 7 - 6 = 1

Correct option is  D) 1

Correct option is  C) -120

-2 x -3 x -20 

= 6 x -20 

= -120 

Correct option is  A) 0

if any number multiplied with 0 then product equals to zero .

∴  (-576) x 1153 x 405 x 0 x 11 = 0

i) -1 < 0 

ii) -3 > -7 

iii) -10 < +10

i) False 

ii) False 

iii) True

iv) True 

v) True

True

(–5) × (–7) is same as (–7) × (–5).

i) +1 is the nearest positive integer to -1.

ii) On the given number line negative numbers to left of zero are -1, -2, -3, -4, -5. So, there are 5 in number. 

iii) On the number line integers between -3 and 7 are -2, -1, 0, 1, 2, 3, 4, 5, 6. So, there are 9 in number. 

iv) Integers less than -2 means numbers left side of -2. They are -3, -4, -5, -6, -7, ……… So, 3 integers lesser than -2 are -3, -4, -5. 

v) Integers more than -2 means numbers right side of -2. They are -1, 0, 1, 2, 3, 4, …….. So, 3 integers more than -2 are -1, 0, 1.

Correct option is  C) 17

\(\frac{-17 \times17}{-17}\)

= \(\frac{-17}{-1}\) 

= 17

Correct option is  C) – 5°

present temperature = -16° c - (-11° c)

= -16° c + 11° c

= (-16 + 11)° c

= - 5° c

False

(– 80) ÷ (4) is not same as 80 ÷ (–4)

Here – 2 × 24 = – 48, 

– 4 × 12 = – 48 and 

– 6 × 8 = – 48

All the pairs i.e. (–2, 24); (–4, 12); (–6, 8) give same answer on multiplication, whereas –3 × 10 = –30, gives a different answer. So, odd one is (b).

Correct option is  B) 0

∵ (-1) ^{odd number} = -1 and (-1) ^{even number} = 1 

∴  (-1) ^{odd number} + (-1)  ^{even number} = -1 + 1 = 0

Here –3 + (–6) = –9, 

+1 + (–10) = –9 and 

–2 + (–7) = –9 

All the above pairs i.e. (–3, –6); (+1, –10); (–2, –7) give same answer on adding, whereas – 4 + (–9) = –13, gives a different answer. So, odd one out is (d).

Since sum of two integers is zero, one integer is the additive inverse of other integer, like – 3, 3; – 4, 4 etc. But the difference has to be 10. So, the integers are 5 and – 5 as 5–(–5) is 10.

False

Since, the sum of any two negative integers is always smaller than both the integers.

There are few pairs of integers whose product is – 15.

e.g. – 1 × 15 

– 3 × 5 

3 × (– 5) 

15 × (– 1) 

but difference of –3 and 5 or –5 and 3 is 8. So the required pair of integers is – 3, 5 and – 5, 3.

Sum of two negative integers always gives a number smaller than both the integers.

True

– 5 and – 4 are smaller than – 3 but their difference is (–4) – (–5) = 1 which is greater than – 3. 

or 

– 6 and –10 are smaller than – 3 but their difference is (–6) – (–10) = 4 which is greater than – 3.

-19, -18, -17, -16

(a) – 6 and – 4 both have negative signs. 

So, – 6 + (– 4) = – (6 + 4) = –10 

(b) + 3 and – 4 have opposite signs. 

As 4 – 3 = 1, therefore + 3 + (– 4) = –1 

(c) + 4 and –2 have opposite signs. 

So, 4 + (–2) = 4 – 2 = 2

(a) The additive inverse of 3 is –3. 

So, – 4 – 3 = – 4 + (–3) = – (4 + 3) = –7 

(b) The additive inverse of –3 is + 3. 

So, – 4 – (–3) = – 4 + (+3) = –1

(A) 0

Positive integers are always coming right to the 0, so positive integers always greater than 0.

The correct option is (A) 0.