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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**

**Remember: Multiplication and division rank equally (go left to right). And same goes for addition and subtraction.**

**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**

**25**

**17**

**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.

**[First, multiply 2 and 3]**

**[Now subtract 6 from 18]**

12

**So, 18 - 2 x 3 = 12.**

**29 - (2 + 6)**

Using the order of operations, solve the expression.

**[First, solve the operation in parenthesis]**

**[Now subtract 8 from 29]**

21

**So, 29 - (2 + 6) = 21.**

**7 - 18 ÷ 9 + 1**

Using the order of operations, solve the expression.

**[First, divide 18 by 9]**

**[Now subtract 2 from 7]**

**[Now add 5 and 1]**

6

**So, 7 - 18 ÷ 9 + 1 = 6.**

**16 ÷ 8 x 3 - 1**

Using the order of operations, solve the expression.

**[First, divide 16 by 8]**

**[Now multiply 2 and 3]**

**[Now subtract 1 from 6]**

**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.