Question

When evaluating the following expression, which operations must be done first, third, and fifth?: `3-2*(2+4)+5-(3/2)^3`

Answer 1

First: addition inside the bracket.
Third: multiplication
Fifth: addition

Explanation:

We follow the Order of Operations, also known as PEMDAS:

• `color(red)(P)` - Parentheses (also known as Brackets)
• `color(blue)(E)` - Exponents
• `color(green)(M)` - Multiplication
• `color(green)(D)` - Division (this has the same weight as M and so I gave it the same colour)
• `color(brown)(A)` - Addition
• `color(brown)(S)` - Subtraction - (again, same weight as A and so the same colour)

So in the expression

`3-2xx(2+4)+5-(3/2)^3`

we first look for `color(red)(P)`. There are two of them: `2+4` and a fraction `3/2`. We can't really do anything with the fraction for now, so let's do `2+4` first:

`3-2xx(6)+5-(3/2)^3`

Now we look for `color(blue)(E)`, which brings us back to that fraction:

`3-2xx(6)+5-27/8`

Next we look for `color(green)(M)` and `color(green)(D)` - and we have `2xx6`, which we'll be doing third

`3-12+5-27/8`

Now we do our `color(brown)(A)` and `color(brown)(S)`, working from left to right. So the fourth thing we do is `3-12`:

`-9+5-27/8`

and the fifth thing we do is `-9+5`

`-4-27/8`

And to finish this off:

`-32/8-27/8=-59/8`