Rules for arithmetic and algebra expressions that describe what sequence to follow to evaluate an expression involving more than one operation.

Step 1: First perform operations that are within grouping symbols such as parenthesis (), brackets [], and braces {}, and as indicated by fraction bars.Parenthesis within parenthesis are called nested parenthesis (( )).

Step 2: Evaluate Powers (exponents) or roots.

Step 3: Perform multiplication or division operations in order by reading the problem from left to right.

Step 4: Perform addition or subtraction operations in order by reading the problem from left to right.

53621 53621 53621

5327

5945

53621 5221 5221

102131

5327

Performing operations left to right only

Performing operations using order of operations

The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results. Method 2 is the correct method.

The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results. Method 2 is the correct method.

Can you imagine what it would be like if calculations were performed differently by various financial institutions or what if doctors prescribed different doses of medicine using the same formulas and achieving different results?

Can you imagine what it would be like if calculations were performed differently by various financial institutions or what if doctors prescribed different doses of medicine using the same formulas and achieving different results?

218654 Follow the left to right rule: First solve any multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.

Follow the left to right rule: First solve any multiplication or division parts left to right. Then solve any addition or subtraction parts left to right. 218654

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

2189

369

The order of operations must be followed each time you rewrite the expression.

The order of operations must be followed each time you rewrite the expression. 45

DivideDivide

MultiplyMultiply

AddAdd

652 2

652 2

6252

650

44

Exponents (powers)Exponents (powers)

MultiplyMultiply

SubtractSubtract

Follow the left to right rule: First solve exponent/(powers). Second solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.

Follow the left to right rule: First solve exponent/(powers). Second solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

The order of operations must be followed each time you rewrite the expression.

The order of operations must be followed each time you rewrite the expression.

Exponents (powers)Exponents (powers)

MultiplyMultiply

SubtractSubtract

Follow the left to right rule: First solve parts inside grouping symbols according to the order of operations. Solve any exponent/(Powers). Then solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.

Follow the left to right rule: First solve parts inside grouping symbols according to the order of operations. Solve any exponent/(Powers). Then solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

The order of operations must be followed each time you rewrite the expression.

The order of operations must be followed each time you rewrite the expression.

2843 2

2843 2 Grouping symbols

Grouping symbols

643 2

6163

648

8 DivideDivide

Exponents (powers)Exponents (powers)

MultiplyMultiply

SubtractSubtract

Follow the left to right rule: Follow the order of operations by working to solve the problem above the fraction bar. Then follow the order of operations by working to solve the problem below the fraction bar. Finally, recall that fractions are also division problems – simplify the fraction.

Follow the left to right rule: Follow the order of operations by working to solve the problem above the fraction bar. Then follow the order of operations by working to solve the problem below the fraction bar. Finally, recall that fractions are also division problems – simplify the fraction.

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

The order of operations must be followed each time you rewrite the expression.

The order of operations must be followed each time you rewrite the expression.

)418(2

43 2

)418(2

43 2

Work above the fraction bar

Work above the fraction bar

3

Simplify: Divide

Simplify: Divide

243

163)418(2

48

)418(2

Work below the fraction bar

Work below the fraction bar Grouping symbolsGrouping symbols

)14(2 AddAdd16

48

1648

Exponents (powers) 33 = (3)(3)(3) = 27

Exponents (powers) 33 = (3)(3)(3) = 27

Subtract 29 - 5Subtract 29 - 5

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s).

The order of operations must be followed each time you rewrite the expression.

The order of operations must be followed each time you rewrite the expression.

6)5( 23 nyxGrouping symbolsGrouping symbols

Add: 2 + 27Add: 2 + 27

Evaluate when x=2, y=3, and n=4 6)5( 23 nyxSubstitute in the values for the variables

Substitute in the values for the variables

64)532( 23

64)5272( 2

64)529( 2

6424 2 Exponents (powers) 62 = (6)(6) = 36

Exponents (powers) 62 = (6)(6) = 36

61624 68 14Subtract 24 - 16Subtract 24 - 16

AddAdd

Follow the left to right rule: First solve parts inside grouping symbols according to the order of operations. Solve any exponent/(Powers). Then solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.

Follow the left to right rule: First solve parts inside grouping symbols according to the order of operations. Solve any exponent/(Powers). Then solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right.