ORDER OF OPERATIONSORDER OF OPERATIONS

LESSON 2LESSON 2

Rules for BEDMASRules for BEDMASRule 1:  Rule 1:   Simplify all operations inside Simplify all operations inside

parentheses.parentheses.Rule 2:  Rule 2:   Simplify all exponents, Simplify all exponents,

working from left to rightworking from left to right..Rule 3:  Rule 3:   Perform all multiplications and Perform all multiplications and

divisions, working from left to right.divisions, working from left to right.Rule 4:  Rule 4:   Perform all additions and Perform all additions and

subtractions, working from left to right.subtractions, working from left to right.

BEDMASBEDMASB – BracketsB – BracketsE – ExponentsE – ExponentsD – Division from left to rightD – Division from left to rightM – Multiply from left to rightM – Multiply from left to rightA – Add from left to rightA – Add from left to rightS – Subtract from left to rightS – Subtract from left to right

EXAMPLE 1EXAMPLE 1 Evaluate this arithmetic Evaluate this arithmetic

expression expression 18 + 36 18 + 36 ÷ 3÷ 322

SOLUTION:SOLUTION:

18 + 36 18 + 36 ÷ 3÷ 322 = 18 + 36 = 18 + 36 ÷ ÷ 99 Simplify all Simplify all exponents ( Rule 2)exponents ( Rule 2)

EXAMPLE 1EXAMPLE 1 Evaluate this arithmetic Evaluate this arithmetic

expression expression 18 + 36 18 + 36 ÷ 3÷ 322

SOLUTION:SOLUTION:

18 + 36 18 + 36 ÷ 3÷ 322 = 18 + 36 = 18 + 36 ÷ ÷ 99 Simplify all exponents Simplify all exponents ( Rule 2)( Rule 2)

18 + 18 + 36 36 ÷ 9÷ 9 = 18 + 4= 18 + 4 Division ( Rule 3)Division ( Rule 3)

EXAMPLE 1EXAMPLE 1 Evaluate this arithmetic Evaluate this arithmetic

expression expression 18 + 36 18 + 36 ÷ 3÷ 322

SOLUTION:SOLUTION:

18 + 36 18 + 36 ÷ 3÷ 322 = 18 + 36 = 18 + 36 ÷ ÷ 99 Simplify all exponents Simplify all exponents ( Rule 2)( Rule 2)

18 + 18 + 36 36 ÷ 9÷ 9 = 18 + 4= 18 + 4 Division ( Rule 3)Division ( Rule 3)

18 + 418 + 4 = 22= 22 Addition ( Rule 4)Addition ( Rule 4)

EXAMPLE 2EXAMPLE 2 Evaluate 5Evaluate 522 x 2 x 244

Solution:Solution:5522 x 2 x 244 Copy Question DownCopy Question Down

EXAMPLE 2EXAMPLE 2 Evaluate 5Evaluate 522 x 2 x 244

Solution:Solution:5522 x 2 x 244 Copy Question DownCopy Question Down= 25 x 2= 25 x 244 Simplify Exponent ( Rule Simplify Exponent ( Rule

2 )2 )

EXAMPLE 2EXAMPLE 2 Evaluate 5Evaluate 522 x 2 x 244

Solution:Solution:5522 x 2 x 244 Copy Question DownCopy Question Down= = 2525 x 2 x 244 Simplify Exponent ( Rule Simplify Exponent ( Rule

2 )2 )= 25 x = 25 x 1616

Simplify Exponent ( Rule Simplify Exponent ( Rule 2 )2 )

EXAMPLE 2EXAMPLE 2 Evaluate 5Evaluate 522 x 2 x 244

Solution:Solution:5522 x 2 x 244 Copy Question DownCopy Question Down= = 2525 x 2 x 244 Simplify Exponent ( Rule Simplify Exponent ( Rule

2 )2 )= 25 x = 25 x 1616

Simplify Exponent ( Rule Simplify Exponent ( Rule 2 )2 )

= 400= 400 Multiplication ( Rule 3 )Multiplication ( Rule 3 )

EXAMPLE 3

EVALUATE 289 – (3 X 5)2

EXAMPLE 3

EVALUATE 289 – (3 X 5)2

SOLUTION:

289 – (3 x 5)2 Copy Question Down

EXAMPLE 3

EVALUATE 289 – (3 X 5)2

SOLUTION:

289 – (3 x 5)2 Copy Question Down

= 289 – (15)2 Simplify Parentheses ( Rule 1)

EXAMPLE 3

EVALUATE 289 – (3 X 5)2

SOLUTION:

289 – (3 x 5)2 Copy Question Down

= 289 – (15)2 Simplify Parentheses ( Rule 1)

= 289 - 225 Simplify Exponents ( Rule 2)

EXAMPLE 3

EVALUATE 289 – (3 X 5)2

SOLUTION:

289 – (3 x 5)2 Copy Question Down

= 289 – (15)2 Simplify Parentheses ( Rule 1)

= 289 - 225 Simplify Exponents ( Rule 2)

= 64 Subtraction ( Rule 4)

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9 SOLUTION:

8 + (2 x 5) x 38 + (2 x 5) x 344 ÷ 9÷ 9 Copy Down QuestionCopy Down Question

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9 SOLUTION:

8 + (2 x 5) x 38 + (2 x 5) x 344 ÷ 9÷ 9 Copy Down QuestionCopy Down Question

= 8 + = 8 + (10)(10) x 3 x 34 4 ÷ 9÷ 9 Simplify Parentheses(Rule 1 )Simplify Parentheses(Rule 1 )

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9 SOLUTION:

8 + (2 x 5) x 38 + (2 x 5) x 344 ÷ 9÷ 9 Copy Down QuestionCopy Down Question

= 8 + (10) x 3= 8 + (10) x 34 4 ÷ 9÷ 9 Simplify Parentheses(Rule 1)Simplify Parentheses(Rule 1)

= 8 + (10) x = 8 + (10) x 8181 ÷ 9÷ 9 Simplify Exponents ( Rule 2)Simplify Exponents ( Rule 2)

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9 SOLUTION:

8 + (2 x 5) x 38 + (2 x 5) x 344 ÷ 9÷ 9 Copy Down QuestionCopy Down Question

= 8 + (10) x 3= 8 + (10) x 34 4 ÷ 9÷ 9 Simplify Parentheses(Rule 1)Simplify Parentheses(Rule 1)

= 8 + (10) x 81 = 8 + (10) x 81 ÷ 9÷ 9 Simplify Exponents ( Rule 2)Simplify Exponents ( Rule 2)

= 8 + = 8 + 810810 ÷ 9÷ 9 Perform all Multiplications Perform all Multiplications and Divisions, working from and Divisions, working from left to right ( Rule 3)left to right ( Rule 3)

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9 SOLUTION:

8 + (2 x 5) x 38 + (2 x 5) x 344 ÷ 9÷ 9 Copy Down QuestionCopy Down Question

= 8 + (10) x 3= 8 + (10) x 34 4 ÷ 9÷ 9 Simplify Parentheses(Rule 1)Simplify Parentheses(Rule 1)

= 8 + (10) x 81 = 8 + (10) x 81 ÷ 9÷ 9 Simplify Exponents ( Rule 2)Simplify Exponents ( Rule 2)

= 8 + 810 = 8 + 810 ÷ 9÷ 9 Perform all Multiplications Perform all Multiplications and Divisions, working from and Divisions, working from left to right ( Rule 3)left to right ( Rule 3)= 8 + = 8 + 9090

EXAMPLE 4

EVALUATE 8 + (2 x 5) x 34 ÷ 9 SOLUTION:

8 + (2 x 5) x 38 + (2 x 5) x 344 ÷ 9÷ 9 Copy Down QuestionCopy Down Question

= 8 + (10) x 3= 8 + (10) x 34 4 ÷ 9÷ 9 Simplify Parentheses(Rule 1)Simplify Parentheses(Rule 1)

= 8 + (10) x 81 = 8 + (10) x 81 ÷ 9÷ 9 Simplify Exponents ( Rule 2)Simplify Exponents ( Rule 2)

= 8 + 810 = 8 + 810 ÷ 9÷ 9 Perform all Multiplications Perform all Multiplications and Divisions, working from and Divisions, working from left to right ( Rule 3)left to right ( Rule 3)= 8 + 90= 8 + 90

= = 9898 Addition ( Rule 4 )Addition ( Rule 4 )

YOU TRY THESE• 1) 32 x 43

• 2) 27 – 256 ÷ 43

• 3) 9 x (5 + 3)2 – 144• 4) 7 + 3 x 24 ÷ 6

1) 32 x 43

• Solution:

332 2 x 4x 433 Copy Question DownCopy Question Down= 9 x 64= 9 x 64 Simplify Exponents Simplify Exponents

(Rule 2)(Rule 2)= = 576576 Multiplication ( Rule Multiplication ( Rule

3 )3 )

2) 27 – 256 ÷ 43

• Solution:

27 – 256 ÷ 427 – 256 ÷ 433 Copy Question DownCopy Question Down= 27 – = 27 – 256÷64256÷64

Simplify Exponents (Rule Simplify Exponents (Rule 2)2)

= 27 – 4= 27 – 4 Division ( Rule 3 )Division ( Rule 3 )= 23= 23 Subtraction ( Rule 4 )Subtraction ( Rule 4 )

3) 9 x (5 + 3)2 – 144• Solution:

9 x (5 + 3)2 – 144

Copy Question DownCopy Question Down

= 9 x (8)= 9 x (8)22 - 144 - 144 Simplify Parentheses ( Rule Simplify Parentheses ( Rule 1)1)

= 9 x 64 - 144= 9 x 64 - 144 Simplify Exponents Simplify Exponents ( Rule 2)( Rule 2)

= 576 - 144= 576 - 144 Multiplication ( Rule 3 )Multiplication ( Rule 3 ) = = 432432 Subtraction ( Rule 4 )Subtraction ( Rule 4 )

4) 7 + 3 x 24 ÷ 6• Solution:

7 + 3 x 27 + 3 x 244 ÷ 6 ÷ 6 Copy Question DownCopy Question Down= 7 + 3 x 16 ÷ = 7 + 3 x 16 ÷ 66

Simplify Exponents Simplify Exponents ( Rule 2)( Rule 2)

= 7 + 48 ÷ 6= 7 + 48 ÷ 6 Perform all Multiplications Perform all Multiplications and Divisions, working from and Divisions, working from left to right ( Rule 3)left to right ( Rule 3)= 7 + 8= 7 + 8

= 15= 15 Addition ( Rule 4 )Addition ( Rule 4 )