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Order of Operations
What is the answer to this statement?
2 + 3 x 5
The same statement can give two different answers, mathematicians agreed that everyone would use the same order when solving problems.
When solving a problem, you must always follow this order:
- Do anything inside parenthesis
- Solve any exponents.
- Multiply and divide from left to right.
- Add and subtract from left to right.
We can use the phrase to help you remember this:
Please Excuse My Dear Aunt Sally
Use of Parenthesis :
- They act like a grouping symbol, not when they are representing multiplication.
- When a parenthesis is written right next to a number or variable with nothing in between, this means multiplication should be done in step 3.
- If there is any symbol in between, it is a grouping symbol and must be done first.
For example, 8(4) means to multiply 8 and 4 since there is nothing between 8 and the parenthesis.
But there is no multiplication in 6 + (4 - 1). Since there is a '+' sign in between 6 and the parenthesis, the parenthesis are a grouping symbol, so subtract '4 - 1' first.
Let's illustrate through an example used above.
2 + 3 x 5
Which answer is right?
17 , because, according to order of operations, we must multiply 3 x 5 before we add 2.
If someone wants to add 2 + 3 first, how would they do that?
Well, they'd have to add parenthesis and it would look like this:
Then, the answer would be 25.
- 18 - 2 x 3
Using the order of operations, solve the expression.
12
So, 18 - 2 x 3 = 12.
- 29 - (2 + 6)
Using the order of operations, solve the expression.
21
So, 29 - (2 + 6) = 21.
- 7 - 18 ÷ 9 + 1
Using the order of operations, solve the expression.
6
So, 7 - 18 ÷ 9 + 1 = 6.
- 16 ÷ 8 x 3 - 1
Using the order of operations, solve the expression.
So, 16 ÷ 8 x 3 - 1 = 5.
Order of Operations
- We use PEMDAS to solve order of operations.
- P : stands for parenthesis
- E : stands for exponents
- M : stands for multiplication
- D : stands for division
- A : stands for addition
- S : stands for subtraction
- Use "Please Excuse My Dear Aunt Sally" to remember the order PEMDAS.
- Multiplication and division rank equally (got left to right). And same goes for addition and subtraction.
