# How do you simplify 4 + 2 times 5 - 3 + 1 / 2  using PEMDAS?

Mar 16, 2016

$\frac{23}{2} = 11 \frac{1}{2}$

#### Explanation:

PEMDAS is just a mnemonic device which stands for the order of algebraic operations

1. Parenthesis
2. Exponents
3. Multiplication
4. Division
6. Subtraction

Reading from left to right, there are no parenthesis. So we can ignore P. There are no exponents, so we can ignore E. There is a multiplication, so we execute that operation first:

$4 + 10 - 3 + \frac{1}{2}$

There is technically division in the form of the fraction 1/2, so you could convert that to 0.5. However, adding 1/2 to a number is not problematic, so we can also retain the fraction if we want.

Next there is the addition of 4+10,

$14 - 3 + \frac{1}{2}$

Now, though the acronym PEMDAS implies that you must do all addition before you do subtraction, that is not true. They are interchangeable. You can do subtraction prior to addition without ever screwing up your answer. So do $14 - 3 = 11$, giving

$11 \frac{1}{2} = \frac{23}{2}$