Question

Simplify
1÷{1/2+1/3+1/6÷(3/4-1/3)

Answer 1

let 3/4-1/3 =A

then A = 5/12

Now let 1/2 + 1/3+1/6= B

then B=1

so B/A=12/5

now 1/(12/5)

=5/12

Answer 2

Given:

1 ÷ {1/2+1/3+1/6 ÷ (3/4-1/3).

To find:

The simplified value of 1 ÷ {1/2+1/3+1/6 ÷ (3/4-1/3).

Solution:

To solve this question, first of all, we open the brackets and then apply the BODMAS rule.

So,

As given,

we have,

$1 ÷ [\frac{1}{2} + \frac{1}{3} + \frac{1}{6} ÷ (\frac{3}{4} - \frac{1}{3} ) ]$

On taking 12 as LCM of 4 and 3 from the denominator of 3/4 and 1/3, we get

$1 ÷ [\frac{1}{2} + \frac{1}{3} + \frac{1}{6} ÷ (\frac{9 - 4}{12} ) ]$

$= 1 ÷ [\frac{1}{2} + \frac{1}{3} + \frac{1}{6} ÷ (\frac{5}{12}) ]$

$= 1 ÷ [\frac{1}{2} + \frac{1}{3} + \frac{1}{6} \times (\frac{12}{5}) ]$

(as a ÷ b = a × 1/b)

Now, using BODMAS, first, we multiply and then add all the terms,

So,

$= 1 ÷ [\frac{1}{2} + \frac{1}{3} + \frac{2}{5} ]$

Taking 30 as LCM, we get

$= 1 ÷ [\frac{15 + 10 + 6}{30} ]$

$= 1 ÷ [\frac{31}{30} ]$

$= 1 \times \frac{30}{31}$

$= \frac{30}{31}$

Hence, the value of 1 ÷ {1/2+1/3+1/6 ÷ (3/4-1/3) is 30/31.