Question

1. Verify the property : (a - b) = (b - a) for the
following integers:
(i) 13,-8
(ii) -15, -12
(iii) -18,5
(iv) 6,17
2. Subtract the following integers:
(i) -16 from 12 (ii) -23 from -19
(iii) 61 from 85
(iv) 15 from -73
Write down a pair of:
(i) positive integers whose difference is -6.
(ii) negative integers whose difference is -3.
(iii) a negative and a positive integer who
difference is -5.​

Answer 1

1. We need to verify if the following property is true ⇒ $(a-b)\neq (b-a)$

(i) a = 13, b = (-8)

$(13-(-8)\neq ((-8)-13)$

$(13+8)\neq (-8-13)$

$21\neq (-21)$

∴ $(a-b)\neq (b-a)$

(ii) a = (-15), b = (-12)

$((-15)-(-12)\neq ((-12)-(-15))$

$(-15+12)\neq (-12+15)$

$(-3)\neq 3$

∴ $(a-b)\neq (b-a)$

(iii) a = (-18), b = 5

$((-18)-5) \neq (5-(-18))$

$(-18-5)\neq (5+18)$

$(-23)\neq 23$

∴ $(a-b)\neq (b-a)$

(iv) a = 6, b = 17

$(6-17)\neq (17-6)$

$(-11)\neq 11$

∴ $(a-b)\neq (b-a)$

2. We need to subtract the following integers using the integer law.

(i) 12-(-16)

Here we need to apply this law ⇒ $-(-)=+$

12+16 = 28

(ii) (-19)-(-23)

Here we need to apply this law ⇒ $-(-)=+$

(-19)+23 = 4

(iii) 85-65

Here we can directly subtract.

85-65 = 20

(iv) (-73)+15

Here we can directly subtract.

(-73)+15 = (-58)

3. Here we can write any pair of two numbers that give the following answer.

(i) 4-10 = (-6)

(ii) (-5)-(-3) = (-2)

(iii)  (-3)-2 = 5