# How do you simplify -5+2(8/13)-6times2 using order of operations?

Jun 2, 2017

$- \frac{205}{13}$ or $- 15 \frac{10}{13}$

#### Explanation:

The order of operations can be remembered by the mnemonic device PEMDAS (often P lease E xcuse M y D ear A unt S ally). This acronym refers to the order of operations, which is:

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

You are given

$- 5 + 2 \left(\frac{8}{13}\right) - 6 \times 2$

Parenthesis
You are given parenthesis, but there are no expressions to simplify. You can leave this as it is.

NOTE: You might be tempted to plug $8 \div 13$ in your calculator. Unfortunately, this gives you a fraction which repeats forever as $0. \overline{615384}$. This will give an answer which is not exact and so should be avoided in this problem.

Exponents
There are no exponents in this problem. Move on to the next letter.

Multiplication
You can now multiply terms
$- 5 + \frac{2 \times 8}{13} - 12 = - 5 + \frac{16}{13} - 12$

Division
If the fraction could be reduced, reducing factions counts as division. However, because the fraction is already in lowest terms, you can move on to the next step.

There are no two numbers you can add. Move on.

Subtraction

$- 5 + \frac{16}{13} - 12 = - \frac{5 \times 13}{13} + \frac{16}{13} - 12 = - \frac{65}{13} + \frac{16}{13} - 12$

$= - \frac{49}{13} - 12 = - \frac{49}{13} - \frac{12 \times 13}{13} = - \frac{49}{13} - \frac{156}{13}$

$= - \frac{205}{13}$

Jun 2, 2017

$= - 15 \frac{10}{13}$

#### Explanation:

Count the number of terms first, before you do any calculations.
Simplify each term to a single answer.

Within each term you do operations in the following order:

• brackets first
• then powers and roots
• multiply and divide

Each term will simplify to one answer - add or subtract at the end.

$\textcolor{red}{- 5} \textcolor{b l u e}{+ 2 \left(\frac{8}{13}\right)} \textcolor{g r e e n}{- 6 \times 2} \text{ } \leftarrow$ there are 3 terms

$= \textcolor{red}{- 5} \textcolor{b l u e}{+ \frac{16}{13}} \textcolor{g r e e n}{- 12} \text{ } \leftarrow$ add 3 terms

$= \textcolor{red}{- 5} \textcolor{b l u e}{+ 1 \frac{3}{13}} \textcolor{g r e e n}{- 12}$

$= 1 \frac{3}{13} - 17$

$= - 15 \frac{10}{13}$