**Standard order of operations**
**1. Parentheses and fraction bars†**Use the standard order of operations shown here to calculate the values of all expressions inside parentheses or brackets *first,* working from the innermost parentheses out. When dealing with a fraction bar, think of the entire numerator and denominator as being enclosed in parentheses, so calculate the numerator and denominator separately.

**2. Exponents**Raise all numbers to the indicated powers.

**3. Multiplication and division**Do all the multiplications and divisions from left to right. *Note on division: *When division of integers leads to a fraction, it is often best to leave the fraction in reduced form rather than approximating by a decimal. (So, sometimes there is no calculation to do, as in $2/3,$ for instance.)

**4. Addition and subtraction **Do the remaining additions and subtractions from left to right.

†
Fraction bars are the horizontal lines separating the numerator and denominator in a fraction, as in $\dfrac{3-4}{6}$. The division signs $\div$ and $/$ *do not count* as fraction bars.
**Remembering the order of operations: PEMDAS**
**P** | | **P**arentheses and fraction bars |

**E** | | **E**xponents |

**MD** | | **M**ultiplication and **D**ivision (from left to right) |

**AS** | | **A**ddition and **S**ubtraction (from left to right) |

**Examples:**
**1. **To calculate $6/3+4-1$:

- Parentheses and fraction bars: There are none in this example.
- Exponents: There are none in this example.
- Multiplication and division: Do the single division $6/3$:
$\color{indianred}{6/3} + 4 - 1 = 2 + 4-1$.

- Addition and subtraction: Do the remaining additions and subtractions from left to right:
$\color{indianred}{2+4} - 1 = 6 - 1 = 5$.

**2. **To calculate $6/(4-6) \times 2 -2^3$:

- Parentheses and fraction bars: First calculate the value of the entire quantity in parentheses (using the the order of operations as necessary).
$\color{indianred}{6/(4-6)} \times 2 -2^3 = 6/(-2) \times 2 -2^3$.

- Exponents: Raise all numbers to the indicated powers.
$6/(-2) \times 2 -\color{indianred}{2^3} = 6/(-2) \times 2 - 8$.

- Multiplication and division: Do all the multiplications and divisions from left to right:
$\color{indianred}{6/(-2)} \times 2 - 8 =\color{indianred}{-3 \times 2} - 8 = -6 - 8$.

- Addition and subtraction: Do the remaining additions and subtractions from left to right:
$\color{indianred}{-6 - 8} = -14$.

**
Some for you **
Apply the standard order of operations to calculate the following. If the answer is a fraction, represent it in lowest terms.