(i) Given (-9/12) and (8/-12)

The standard form of (-9/12) is (-3/4) [on diving the numerator and denominator of given number by their HCF i.e. by 3]

The standard form of (8/-12) = (-2/3) [on diving the numerator and denominator of given number by their HCF i.e. by 4]

Since, the standard forms of two rational numbers are not same. Hence, they are not equal.

(ii) Given (-16/20) and (20/-25)

Multiplying numerator and denominator of (-16/20) by the denominator of (20/-25)

i.e. -25.

(-16/20) × (-25/-25) = (400/-500)

Now multiply the numerator and denominator of (20/-25) by the denominator of

(-16/20) i.e. 20

(20/-25) × (20/20) = (400/-500)

Clearly, the numerators of the above obtained rational numbers are equal.

Hence, the given rational numbers are equal

(iii) Given (-7/21) and (3/-9)

Multiplying numerator and denominator of (-7/21) by the denominator of (3/-9)

i.e. -9.

(-7/21) × (-9/-9) = (63/-189)

Now multiply the numerator and denominator of (3/-9) by the denominator of

(-7/21) i.e. 21

(3/-9) × (21/21) = (63/-189)

Clearly, the numerators of the above obtained rational numbers are equal.

Hence, the given rational numbers are equal

(iv) Given (-8/-14) and (13/21)

Multiplying numerator and denominator of (-8/-14) by the denominator of (13/21)

i.e. 21

(-8/-14) × (21/21) = (-168/-294)

Now multiply the numerator and denominator of (13/21) by the denominator of

(-8/-14) i.e. -14

(13/21) × (-14/-14) = (-182/-294)

Clearly, the numerators of the above obtained rational numbers are not equal.

Hence, the given rational numbers are also not equal.