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.

A real-life example of PEMDAS

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 is a model of 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 rule.

Rule:

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.

The rule can be used when you see multiplication, division, or both successively such as in the following problem:

Order of operations problems

First, study the example in the figure carefully!

PEMDAS
Example #1:

42 - 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

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

Even though M comes before D in PEMDAS, the two operations have the same power. By the same token, even though A comes before S, the two operations have the same power.

More examples of the order of operations


Example #2:

(2 + 52 ) + 4 × 3 - 10

Do parenthesis:

(2 + 25 ) + 4 × 3 - 10

27 + 4 × 3 - 10

Do multiplication

27 + 12 - 10

Add

39 - 10

Subtract

29

Example #3:

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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