ORDER OF OPERATIONS

LESSON 2

Something to Think About: Does the order matter?

-5 + 4 =

10 – 3 + 1 =

4 x 6 ÷ 2 =

9 ÷ 3 x 6 =

4 + (-5) =

1 – 3 + 10 =

4 ÷ 2 x 6 =

6 ÷ 3 x 9 =

How about now?

5 x 2 – 4 =

What would happen if we did the subtractions first/

2 – 4 x 5 =

So how do we know what to do first?

RULES TO FOLLOW• Rule 1:

– Simplify all operations inside brackets.• Rule 2:

– Simplify all exponents, working from left to right.

• Rule 3:– Perform all multiplications and divisions,

working from left to right.• Rule 4:

– Perform all additions and subtractions, working from left to right.

BEDMAS

B – BracketsE – ExponentsD – Division from left to rightM – Multiply from left to rightA – Add from left to rightS – Subtract from left to right

EXAMPLE 1

Evaluate this arithmetic expression

18 + 36 ÷ 32

SOLUTION:

18 + 36 ÷ 32 = 18 + 36 ÷ 9 Simplify all exponents ( Rule 2)

EXAMPLE 1

Evaluate this arithmetic expression

18 + 36 ÷ 32

SOLUTION:

18 + 36 ÷ 32 = 18 + 36 ÷ 9 Simplify all exponents ( Rule 2)

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

EXAMPLE 1

Evaluate this arithmetic expression

18 + 36 ÷ 32

SOLUTION:

18 + 36 ÷ 32 = 18 + 36 ÷ 9 Simplify all exponents ( Rule 2)

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

18 + 4 = 22 Addition ( Rule 4)

EXAMPLE 2

Evaluate 52 x 24

Solution:

52 x 24 Copy Question Down

EXAMPLE 2

Evaluate 52 x 24

Solution:

52 x 24 Copy Question Down= 25 x 24 Simplify Exponent ( Rule

2 )

EXAMPLE 2

Evaluate 52 x 24

Solution:

52 x 24 Copy Question Down= 25 x 24 Simplify Exponent ( Rule

2 )= 25 x 16

Simplify Exponent ( Rule 2 )

EXAMPLE 2

Evaluate 52 x 24

Solution:

52 x 24 Copy Question Down= 25 x 24 Simplify Exponent ( Rule

2 )= 25 x 16

Simplify Exponent ( Rule 2 )

= 400 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 34 ÷ 9 Copy Down Question

EXAMPLE 4

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

8 + (2 x 5) x 34 ÷ 9 Copy Down Question

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

EXAMPLE 4

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

8 + (2 x 5) x 34 ÷ 9 Copy Down Question

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

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

EXAMPLE 4

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

8 + (2 x 5) x 34 ÷ 9 Copy Down Question

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

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

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

EXAMPLE 4

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

8 + (2 x 5) x 34 ÷ 9 Copy Down Question

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

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

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

EXAMPLE 4

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

8 + (2 x 5) x 34 ÷ 9 Copy Down Question

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

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

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

= 98 Addition ( Rule 4 )

Example 5

When you have a division questions like this, it is the same as having brackets around everything on the top and bottom.

32254

2

32

2542

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:

32 x 43 Copy Question Down

= 9 x 64 Simplify Exponents (Rule 2)

= 576 Multiplication ( Rule 3 )

2) 27 – 256 ÷ 43

• Solution:

27 – 256 ÷ 43 Copy Question Down

= 27 – 256÷64

Simplify Exponents (Rule 2)

= 27 – 4 Division ( Rule 3 )

= 23 Subtraction ( Rule 4 )

3) 9 x (5 + 3)2 – 144• Solution:

9 x (5 + 3)2 – 144

Copy Question Down

= 9 x (8)2 - 144 Simplify Parentheses ( Rule 1)

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

= 576 - 144 Multiplication ( Rule 3 )

= 432 Subtraction ( Rule 4 )

4) 7 + 3 x 24 ÷ 6• Solution:

7 + 3 x 24 ÷ 6 Copy Question Down

= 7 + 3 x 16 ÷ 6

Simplify Exponents ( Rule 2)

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

= 15 Addition ( Rule 4 )