Order of Operations

Order of Operations

Take notes as you complete this lesson!

Order of Operations

• This is the process used to evaluate expressions.

• evaluate -- to find the answer

• expression -- like a equation, but without an equal sign

• P - parentheses or grouping

• E - exponents

• MD - multiplication/division *whichever comes first left to right

• AS - addition/subtraction *whichever comes first left to right

Multiple Choice

 $63\div3+4\times2$  Evaluate.

• 50

• 29

• 5.72

Explanation

 $63\div3+4\times2$  *divide 63 by 3 to get 21

 $21+4\times2$  *multiply 4 by 2 to get 8

 $21+8$  *add 21 and 8 to get 29

 $29$   *final answer

Multiple Choice

 $6\left(4-1\right)\ +\ 7$  Evaluate. *Note that when a number is directly beside parentheses it means multiply.

• 30

• 25

• 16

Explanation

 $6\left(4-1\right)+7$  *parentheses first
 $6\times3+7$  *multiply next
 $18+7$  *add last
 $25$  

Multiple Choice

 $\frac{1}{2}\left(16+4\right)-2$  Evaluate.

• 8

• 10

• 18.5

Explanation

 $\frac{1}{2}\left(16+4\right)-2$  *parentheses first
 $\frac{1}{2}\times20-2$  *multiply next
 $10-2$  *subtract last
 $8$  

Exponents

An exponent or power tells us how many times to multiply the base number by itself.

Example:  $3^4=3\times3\times3\times3=81$  

Multiple Choice

 $4^2+6\times2^3$  

• 64

• 56

• 52

• 44

Explanation

 $4^2+6\times2^3$  *exponents first
Note that  $4^2\ =\ 4\times4\ =\ 16$  and $2^3\ =\ 2\times2\times2\ =\ 8$  
 $16\ +\ 6\times8$  *multiply next
 $16\ +\ 48$  *add last
 $64$  

Multiple Choice

 $-5+-4\div2+\left(-3\right)^2$  

• -13.5

• 6

• 2

Explanation

 $-5+-4\div2+\left(-3\right)^2$  *exponents first, remember a negative times a negative is a positive
 $-5+-4\div2+9$  *division next; negative divided by positive is negative
 $-5+-2+9$  *add
 $-7+9$  *add
 $2$  

Multiple Choice

 $5-2\left(1+2\times4\right)-6\times-2$  

• -31

• -25

• -7

• -1

Explanation

 $5-2\left(1+2\times4\right)-6\times-2$  *multiply inside parentheses
 $5-2\left(1+8\right)-6\times-2$  *add inside parentheses
 $5-2\times9-6\times-2$  *multiply
 $5-18-6\times-2$  *multiply again
 $5-18--12$  *subtract
 $-13--12$  *subtracting a negative is equivalent to adding a positive
 $-1$  

Multiple Choice

 $\frac{3}{4}+\left(\frac{1}{2}\right)^2-\frac{2}{3}\times4$  

• -1 2/3

• -2 1/6

• 3 2/3

Explanation

 $\frac{3}{4}+\left(\frac{1}{2}\right)^2-\frac{2}{3}\times4$  *exponent
 $\frac{3}{4}+\frac{1}{4}-\frac{2}{3}\times4$  *multiply
 $\frac{3}{4}+\frac{1}{4}-\frac{8}{3}$  *add
 $1\ -\frac{8}{3}$  *find common denominator
 $\frac{3}{3}-\frac{8}{3}$  *subtract
 $-\frac{5}{3}$  *simplify
 $-1\ \frac{2}{3}$  

Demos Calculator

Practice entering these problems into the desmos calculator, which is the calculator you will use during the EOG.

https://www.desmos.com/scientific

Multiple Choice

 $\frac{8}{9}+\left(2+3\div1\right)^2-\frac{1}{3}$  

• 25 5/9

• 10 5/9

• 25 7/6

• 10 7/6

Explanation

 $\frac{8}{9}+\left(2+3\div1\right)^2-\frac{1}{3}$  *divide inside parentheses
 $\frac{8}{9}+\left(2+3\right)^2-\frac{1}{3}$  *add inside parentheses
 $\frac{8}{9}+\left(5\right)^2-\frac{1}{3}$  *exponent
 $\frac{8}{9}+25-\frac{1}{3}$  *add
 $25\ \frac{8}{9}-\frac{1}{3}$  *find common denominator
 $25\ \frac{8}{9}\ -\frac{3}{9}$  *subtract
 $25\ \frac{5}{9}$