The Calculations' Order (PEMDAS)

PEMDAS is an acronym for the words:

1. Parentheses
2. Exponents

3. Multiplication

   Division

4. Addition

   Subtraction

It refers to the order in which these calculations need to be performed.

Examples 1

1. $4\cdot5+2=?$

   calculations' order:

   • Multiplication before Addition

   $4\cdot5+2$ $=20+2$ $=22$

2. $14-9+6=?$

   calculations' order:

   • Addition and Subtraction in the order they occur

   $14-9+6$ $=5+6$ $=11$

3. $9\div3\cdot2=?$

   calculations' order:

   • Multiplication and Division in the order they occur

   $9\div3\cdot2$ $=3\cdot2$ $=6$

4. $12-8\cdot5\div4+7=?$

   calculations' order:

   • Multiplication and Division before Addition and Subtraction
   • Multiplication and Division in the order they occur
   • Addition and Subtraction in the order they occur

   $12-8\cdot5\div4+7$ $=12-40\div4+7$ $=12-10+7$ $=2+7$ $=9$

Examples 2

5. $(24\div4-8)\cdot7=?$

   calculations' order:

   • Parentheses before Multiplication and Division
   • Multiplication and Division before Subtraction

   $(24\div4-8)\cdot7$ $=(6-8)\cdot7$ $=-2\cdot7$ $=-14$

6. $(5+4)\cdot2^{3}=?$

   calculations' order:

   • Parentheses before Exponents
   • Exponents before Multiplication

   $(5+4)\cdot2^{3}$ $=9\cdot2^{3}$ $=9\cdot8$ $=72$

7. $14-(3+16\div4)\cdot2=?$

   calculations' order:

   • Parentheses before Multiplication and Division
   • Multiplication and Division before Addition and Subtraction

   $14-(3+16\div4)\cdot2$ $=14-(3+4)\cdot2$ $=14-7\cdot2$ $=14-14$ $=0$

8. $6\cdot(20\div2-7)+4^{2}=?$

   calculations' order:

   • Parentheses before Exponents
   • Exponents before Multiplication and Division
   • Multiplication and Division before Addition and Subtraction

   $6\cdot(20\div2-7)+4^{2}$ $=6\cdot(10-7)+4^{2}$ $=6\cdot3+4^{2}$ $=6\cdot3+16$ $=18+16$ $=34$