Use the following acronym to help you remember the order of operations…
BEDMAS or PEMDAS (Please Excuse My Dear Aunt Sally)
Brackets Exponents Division Multiplication Addition Subtraction
Parentheses Exponents Multiplication Division Addition Subtraction
ORDER OF OPERATIONS
Some equations can have many different answers if the operations (e.g. adding, subtracting, multiplying, dividing, etc.) are calculated in different orders. For example, to answer an equation like:
3×4+8÷2
You might multiply, add then divide:
Step 1) 3 × 4 = 12
Step 2) 12 + 8 = 20
Step 3) 20 ÷ 2 = 10
OR…… You might add, multiply then divide:
Step 1) 4 + 8=12
Step 2) 3 × 12 = 36
Step 3) 36 ÷ 2 = 18
OR ……… You could divide, add then multiply:
Step 1) 8 ÷ 2 = 4
Step 2) 4 + 4 = 8
Step 3) 3 × 8 = 24
As you can see, without a rule to dictate the order of operations, it would be possible to get many different answers from one equation. The term Order of Operations therefore refers to a specific order that you should always use when calculating the operations in any mathematical equation so that you always get the same answer.
The Rule for Order of Operations
Step 1: Brackets.
Calculate the operations that have been grouped by brackets.
Step 2: Exponents.
Calculate all the exponents.
Step 3: Multiply and Divide.
Calculate both multiplication and division from left to right.
Step 4: Add and Subtract.
Calculate addition and subtraction from left to right.
A useful acronym, or memory aid, that will help you to remember this order is BEDMAS:
Brackets Exponents Division Multiplication Addition Subtraction
Now let’s try it! Before we had the equation3×4+8÷2. Following BEDMAS, we know that division and multiplication come before addition. If we do the division and multiplication from left to right, we arrive at the following order of operations:
Step 1) We multiply: 3 × 4 = 12, making the original equation 12 + 8 ÷ 2
Step 2) Then we divide: 8 ÷ 2 = 4, making the original equation 12 + 4
Step 3) Lastly, we add: 12 + 4 = 16