Arithmetic – Order of Operations

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Operator

• A mathematical task that needs to perform between two integers or

two expressions.

• Operations & Operators

• To multiple two numbers: * [ 2*3 ]

• To add two numbers: + [2+3]

• To subtract a number from other number: - [2-3]

• To divide a number with other number: / [2/3]

• To find the power of a number: ^ [2^3]

• To find the root of a number: √ [ √2 ]

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Order of Operations

• Exponents, Roots > Multiplication, Division > Addition, Subtraction

1. Firstly, look for the exponents or roots and solve it.

2. Secondly, perform the multiplication or Division operations on the result of

Step 1.

3. Thirdly, perform the addition or subtraction on the result of Step 2.

• What if you want to perform Addition operation before the

Multiplication ?

• Use Parentheses. ()

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PEMDAS

• PEMDAS is an easy way to remember the operator precedence.

• Parentheses

• Exponents/Roots

• Multiplication

• Division

• Addition

• Subtraction

• Please Excuse My Dear Aunt Sally. Easy to remember?

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PEMDAS

Examples

• Find the value of 6 + 4^2?

• Sol: 6 + 4^2

6 + 16 E

22 A

Ans : 22

• Find the value of 6 + 3 + 2^2 ?

• Sol: 6 + 3 + 2^2

6 + 3 + 4 E

Ans: 13 A

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Examples

• What if want to add 3 and 2 in the expression [ 6 + 3 + 2^2 ] first

before apply the square?

• Add the parentheses for what ever operation you to have a precedence for.

• So 6 + 3 + 2^2 becomes 6 + (3 + 2)^2

• Solve 6 + (3+2)^2

• 6 + 5^2 P

• 6 + 25 E

• 31 A

• Answer is 31.

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Examples

• Solve 7( -10/3 + 5/6 * 7)

• Sol: 7(-10/2 + 5/4 * 8) [Solve parentheses. Apply PEMDAS for

the Expression in Parentheses]

( -10/2 + 40/8 ) M

( -5 + 5 ) D

(0) A

--------------------------------------------------------------------------------------------------

7 * 0 M

0 Final Result

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Examples

• Solve 3 * 4-(6^(2-10/5)/(√25-9)* √(25-9))

Sol:

3 * 4 – (6 ^ (2-2)/(5-9)*4)

12 – (6^0/4*4)

12 – (1/4*4)

12 – 1

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Examples

• Solve 15x + 5(4x+6/2 + 3x-2)

Sol:

15x + 5 ( 4x + 3 + 3x-2)

15x + 5 (7x + 1)

15x + 35x + 5

50x + 5

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Examples

• Solve

Sol:

6 + 12/6 – 2

6+2-2

6

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