How do you evaluate `37- ( 6\times 3) + 5\div 2`?

The order of operations dictates the way in which an expression must be solved. It looks like this.

1. P arentheses
2. E xponents
3. M ultiplication
4. D ivision
5. A ddition
6. S ubtraction

You may want to remember it as PEMDAS. It is important to note that for multiplication/division and addition/subtraction, you will complete whichever comes first.

P is first, so we will need to solve what is in the parentheses.

`(6*3)=18`
`37-18+5 -: 2`

E is next, but there are no exponents, so we move on.
MD comes after, but there is no multiplication, so we do the division.

`5-:2=2.5`
`37-18+2.5`

AS is the last step. The subtraction comes before the addition, so we will do that first.

`37-18=19`
`19+2.5`

Then we do the addition, finishing the problem.

`19+2.5=21.5`

We can see that the order of operations helped us get the answer of 21.5.

Identify the individual terms in the expression.

Within each term you do the operations in the order:

• brackets
• powers and roots
• divide and multiply

Once each term has been simplified to a single number, the addition and subtraction is done in the last step.

`" "color(green)(37)color(red)(-6xx3)" "color(blue)(+5div2)" "larr` there are `3` terms

`=color(green)(37)" "color(red)(-18)" "color(blue)(+2 1/2)`

`=" "19" "color(blue)(+" "2 1/2)`

`= 21 1/2`