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Order of Operations

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What is the answer to this statement?

2 + 3 x 5

2 + 3 x 5
2 + 3 x 5
5 x 5
2 + 15
25
17

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.

Order1

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

   2 + 3 x 5
   2 + 3 x 5
= 5 x 5
= 2 + 15
= 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:

(2 + 3) x 5
= 5 x 5
= 25

Then, the answer would be 25.

Find the answer using order of operations.
  • 18 - 2 x 3

Using the order of operations, solve the expression.

 
18 - 2 x 3
[First, multiply 2 and 3]
 
18 - 6
[Now subtract 6 from 18]

12

So, 18 - 2 x 3 = 12.

  • 29 - (2 + 6)

Using the order of operations, solve the expression.

 
29 - (2 + 6)
[First, solve the operation in parenthesis]
 
29 - 8
[Now subtract 8 from 29]

21

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

  • 7 - 18 ÷ 9 + 1

Using the order of operations, solve the expression.

 
7 - 18 ÷ 9 + 1
[First, divide 18 by 9]
 
7 - 2 + 1
[Now subtract 2 from 7]
 
5 + 1
[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.

 
16 ÷ 8 x 3 - 1
[First, divide 16 by 8]
 
2 x 3 - 1
[Now multiply 2 and 3]
 
6 - 1
[Now subtract 1 from 6]

So, 16 ÷ 8 x 3 - 1 = 5.

Summary
  • 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.

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