Question

Simplify the following expression

`(45 ÷ 3 xx 2/3 + 1 1/3  "of"  6 3/8 - 4 1/8)/(1/2[(2 1/4 + 1 1/2) ÷ (1/15 + 1/3 - 9/10)])`

पर्याय

• `-4/9`

• `68/5`

• `-23/6`

• `-8/9`

Answer 1

`-23/6`

Explanation:

`(45 ÷ 3 xx 2/3 + 1 1/3  "of"  6 3/8 - 4 1/8)/(1/2[(2 1/4 + 1 1/2) ÷ (1/15 + 1/3 - 9/10)])`

= `(45 ÷ 3 xx 2/3 + 4/3  "of"  51/8 - 33/8)/(1/2[(9/4 + 3/2) ÷ ((2 + 10 - 27)/30)])`

= `(15 xx 2/3 + 57/2 - 33/8)/(1/2 [(9 + 6)/4 + (-1/2)])`

= `(10 + (68 - 33)/8)/(1/2[15/4 xx -2])`

= `(10 + 35/8)/((-15)/4)`

⇒ `(80 + 35)/8 xx (-4)/15`

= `115/8 xx (-4)/15`

= `23/8 xx (-4)/3`

= `(-23)/6`

So, option (3) is the correct answer.