Step-by-step explanation:

To find the quotient for each of these divisions, you can use the rule: "Dividing by a fraction is the same as multiplying by its reciprocal." Here are the solutions:

(i) (15/19) ÷ (5/3)

= (15/19) * (3/5)

= (15 * 3) / (19 * 5)

= 45/95

Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:

= (45 ÷ 5) / (95 ÷ 5)

= 9/19

(ii) (2/9) ÷ (1/3)

= (2/9) * (3/1)

= (2 * 3) / (9 * 1)

= 6/9

Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:

= (6 ÷ 3) / (9 ÷ 3)

= 2/3

(iii) (4 3/7) ÷ (3/5)

First, convert the mixed number to an improper fraction:

= (4 * 7 + 3)/7 ÷ (3/5)

= (31/7) ÷ (3/5)

Now, proceed with the division:

= (31/7) * (5/3)

= (31 * 5) / (7 * 3)

= 155/21

(iv) (12 1/5) ÷ (1/5)

First, convert the mixed number to an improper fraction:

= (12 * 5 + 1)/5 ÷ (1/5)

= (61/5) ÷ (1/5)

Now, proceed with the division:

= (61/5) * (5/1)

= 61/1

= 61

(v) 2 ÷ (3/5)

To divide by a fraction, multiply by its reciprocal:

= 2 * (5/3)

= (2 * 5) / 3

= 10/3

So, the quotients are:

(i) 9/19

(ii) 2/3

(iii) 155/21

(iv) 61

(v) 10/3