Question

Match the following:

Column I	Column II
(i) `a/b ÷ a/b`	(a) `(-a)/b`
(ii) `a/b ÷ c/d`	(b) –1
(iii) `a/b ÷ (-1)`	(c) 1
(iv) `a/b ÷ (-a)/b`	(d) `(bc)/(ad)`
(v) `b/a ÷ (d/c)`	(e) `(ad)/(bc)`

Answer 1

Column I	Column II
(i) `a/b ÷ a/b`	(c) 1
(ii) `a/b ÷ c/d`	(e) `(ad)/(bc)`
(iii) `a/b ÷ (-1)`	(a) `(-a)/b`
(iv) `a/b ÷ (-a)/b`	(b) –1
(v) `b/a ÷ (d/c)`	(d) `(bc)/(ad)`

Explanation:

(i) Given, `a/b ÷ a/b = a/b xx b/a`  ......`[∵ "Reciprocal of " a/b = b/a]`

= 1

(ii) Given, `a/b ÷ c/d = a/b xx d/c`  ......`[∵ "Reciprocal of " c/d = d/c]`

= `(ad)/(bc)`

(iii) Given, `a/b ÷ (-1) = a/b xx (-1)`  ......[∵ Reciprocal of  –1 = –1]

= `(-a)/(b)`

(iv) Given, `a/b ÷ (-a)/b = a/b xx ((-b)/a)`  ......`[∵ "Reciprocal of"  (-a)/b = (-b)/a]`

= –1

(v) Given, `b/a + (d/c) = b/a xx c/d`   ......`[∵ "Reciprocal of " d/c = c/d]`

= `(bc)/(ad)`