Question

Find the reciprocal of the following:

`(1/2 xx 1/4) + (1/2 xx 6)`

Answer 1

Given, `(1/2 xx 1/4) + (1/2 xx 6)`

= `(1 xx 1)/(2 xx 4) + (1 xx 6)/(2 xx 1)` ...`[∵ "Product of rational numbers" = "Product of numerators"/"Product of denominators"]`

= `1/8 + 6/2` 

= `(1 xx 1)/(8 xx 1) + (6 xx 4)/(2 xx 4)`

= `1/8 + 24/8`

= `(1 + 24)/8`

= `25/8`

Hence, the reciprocal of `25/8` is `8/25`.