Integers Test - 13

By observing the series, difference between two consecutive numbers is 3,

i.e.

11 - 8 = 3

8 - 5 = 3

5 - 2 = 3

So, next number will be

2 - 3 = -1

Similarly, next two numbers are

-1 - 3 = -4

-4 - 3 = -7

By observing the series, difference between two consecutive numbers is 25, i.e.

- 37 - (-62) = -37 + 62 = 25

– 12 – (- 37) = -12 + 37 =25

So, next number will be

-12 + 25 = 13

(a) True, when two positive integers are added, the resultant number is also a positive  integer.

(b) True, while adding integers, if both the numbers have same sign, the resultant number also get that sign.

(c) False, while adding the integers of different signs, the resultant number get the sign of greater number.

(d) True, additive inverse of an integer is the same integer value, with opposite sign.

(-11) x 7 = (-77) (we know, in multiplication, if sign of both numbers are different, then the sign of the resultant is negative and if sign of both numbers are same, then the sign of the resultant is positive.)

Option (a), 11 x (-7) =-77

Option (b), - (11 x 7) = – 77

Option (c), (-11) x (- 7) = 77

Option (d), 7 x(-11) = -77

(-10) x (- 5) + (- 7)

= {(- 10) x (- 5)} + (- 7)

= 50 + (- 7)

= 50 - 7

= 43

Additive inverse of a is (- a).

[additive inverse of an integer is the same integer value, with opposite sign]

So,

Option (a), - (- a) = a

Option (b),a x (-1) = -a

Option (c), – a

Option (d), a + (-1) = -a

Multiplicative identity for an integer a is 1.

[? a multiplicative identity is that identity in which any number is multiplied by that identity, it gives out the same number.]

(- 25) x [6 + 4] = (- 25) x 10

Also, (- 25) x [6 + 4] = – 25 x 6 + (- 25) x 4

[using distributive property, i.e. a x (b + c) = a x b + a x c] = -150 - 100 = -250

Hence, (-25) x (6 + 4) is not same as -25 x 6 x 4.

(- 43) x (- 99) + 43

= (- 1) (43) x (- 99) + 43

= 43 {-(- 99) + 1}  [taking 43 as common]

= 43 (99 + 1)

= 43 x 100

= 4300