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

Oct 29, 2017

You need to follow the order of operations.

#### Explanation:

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.

$\left(6 \cdot 3\right) = 18$
$37 - 18 + 5 \div 2$

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.

$5 \div 2 = 2.5$
$37 - 18 + 2.5$

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.

Oct 29, 2017

$21 \frac{1}{2}$

#### Explanation:

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.

$\text{ "color(green)(37)color(red)(-6xx3)" "color(blue)(+5div2)" } \leftarrow$ there are $3$ terms

$= \textcolor{g r e e n}{37} \text{ "color(red)(-18)" } \textcolor{b l u e}{+ 2 \frac{1}{2}}$

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

$= 21 \frac{1}{2}$