Question

How do you simplify `1/2 - 1/3 times 1/4 + 1/5 1/6 ÷ 1/6`?

Answer 1

See Process below;

Explanation:

Following the rule of PEDMAS

`1/2 - 1/3 xx 1/4 + 1/5 1/6 div 1/6`

`1/5 1/6 = 1/5 cdot 1/6` since there is no symbol attached!

Hence;

`1/2 - 1/3 xx 1/4 + 1/5 cdot 1/6 div 1/6`

`1/2 - 1/3 xx 1/4 + 1/5 xx 1/6 div 1/6`

So we'll take it step wise..

Since there are Parenthesis, Exponents.. we'll go to;

Division

`1/2 - 1/3 xx 1/4 + 1/5 xx color(red)(1/6 div 1/6)`

`1/2 - 1/3 xx 1/4 + 1/5 xx (color(red)(1/6 xx 6/1)) -> "Transposed!"`

`1/2 - 1/3 xx 1/4 + 1/5 xx color(red)(1/cancel6 xx cancel6/1)`

`1/2 - 1/3 xx 1/4 + 1/5 xx 1/1`

Multiplication

`1/2 - color(blue)(1/3 xx 1/4) + color(blue)(1/5 xx 1/1)`

`1/2 - 1/12 + 1/5`

Addition

`1/2 - color(orange)(1/12 + 1/5)`

Note, Addition and Subtraction deals with finding the LCM..

LCM of `12 and 5 = 60`

`1/2 - color(orange)((5 + 12)/60)`

`1/2 - 17/60`

Subtraction

`color(green)(1/2 - 17/60)`

LCM of `2 and 60 = 60`

`color(green)((30 - 17)/60)`

`13/60`