Order of operations
The order of operations is a very important skill to have. You use it every day even if you are not aware of this.
Say for instance,you go to the supermarket. Suppose peanuts cost $3.00 per pound and a bottle of water is 1 dollar. You get yourself 2 pounds of peanuts and 1 bottle of water.
How much money do you pay?
Since 1 pound of peanuts is 3 dollars and you bought 2 pounds, peanuts cost 6 dollars. Add that to the amount you pay for the water(1 dollar), you paid a total of 7 dollars.
You may have figured this out without any major problems. However, if I present you with the following equation,which model the problem above, you might have a tendency to add 3 to 1 and multiply the result by 2.
2 × 3 + 1
Doing this will give 8 and it is not equal to 7.
To get the right answer, you must do multiplication first.
When doing computations,always follow the order of operations and always perform the operations according to the following
rules.
Rule #1:
1. If grouping symbols are used such as parentheses, perform the operations inside the grouping symbols first.
2. Evaluate any expressions with exponent
3. Multiply and Divide from left to right
4. Add and Subtract from left to right
Rule #1 can be used when you see multiplication, division, or both successively such as in the following problem:
4
^{2} - 6 × 2 ÷ 4 × 3 + 5
Do exponent:
16 - 6 × 2 ÷ 4 × 3 + 5
Multiply and Divide from left to right
16 - 12 ÷ 4 × 3 + 5
16 - 3 × 3 + 5
16 - 9 + 5
Add and Subtract from left to right
16 - 9 + 5
7 + 5
12
Rule #2:
Rule #2 is called
PEMDAS
The following mnemonic may help you remember the rule:
PEMDAS ( Please Excuse My Dear Aunt Sally )
The P stands for Parentheses
The E stands for Exponents
The M stands for Multiply
The D stands for Division
The A stands for Add
The S stands for Subtraction
You can use PEMDAS when you don't see multiplication, division, or both successively such as in the following problem
(2 + 5
^{2} ) + 4 × 3 - 10
Do parenthesis:
(2 + 25 ) + 4 × 3 - 10
27 + 4 × 3 - 10
Do multiplication
27 + 12 - 10
Add
39 - 10
Subtract
29
More examples
10 - 14 ÷ 2 = 10 - 7 = 3 (Division comes before subtraction)
Remember that if you see multiplication and division at the same time, perform the operation from left to right.
4 + 5 ÷ 5 × 6 = 4 + 1 × 6 = 4 + 6 =10
Order of operations quiz. See how you understand this lesson.
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