Question

How do you evaluate `\frac { 2\cdot 6- ( 4+ 2) } { ( 2- 4- 6) \div ( 2- 1) }`?

Answer 1

`-3/4`

Explanation:

Solve in order of PEMDAS. Start inside the parentheses:

`4+2=6`

`2-4-6=-8`

(You go left to right on this one since they're are equal in precedence)

`2-1=1`

Rewrite what we have:

`(2**6-6)/(-8-:1)`

There are no exponents. Continue on with multiplication and division:

`2**6=12`

`-8 -: 1 = -8`

Rewrite what we have:

`(12-6)/(-8)`

Solve for the numerator first:

`12-6=6`

So now we have:

`6/-8`

Factor out a 2 from both top and bottom and cancel them. So we're left with:

`-3/4`

Answer 2

`(2*6-(4+2))/((2-4-6) -: (2-1)) = -3/4`

Explanation:

Given: `(2*6-(4+2))/((2-4-6) -: (2-1))`

First we have to simplify all the brackets in the expression to get rid of them:

`(4 + 2) = 6`
`(2-4-6) = -8`
`(2-1) = 1`
`2*6 = 12`

Make sure to keep track of the signs, remember:

`-( ...) = -`(everything inside)

Then:

`(2*6-(4+2))/((2-4-6) -: (2-1)) = (2*6-6)/(-8-:1) = (12 -6)/-8`

Where dividing `-8` by `1` results in `-8`

= `-6/8 = -3/4`

Answer 3

`-3/4`

Explanation:

You can do more than one calculation at a time, as long as you keep the individual terms separate.

Although this is all one term, you can simplify one bracket without affecting another. Each part in a different color can be simplified independently from the other parts.

Brackets are done first, so find an answer for each of the three brackets!

`(color(red)(2xx6)-color(blue)((4+2)))/((color(lime)(2-4-6))div(color(magenta)(2-1)))`

`(color(red)(12)-color(blue)((6)))/((color(lime)(-8))div(color(magenta)(1)))`

Now simplify both the numerator and the denominator.

`(12-6)/(-8div1) = 6/-8`

`6/-8 = -3/4`