# Order of Operations With Signed Numbers

Instructor: Tammy Galloway

Tammy teaches business courses at the post-secondary and secondary level and has a master's of business administration in finance.

In this lesson you'll learn how to calculate mathematical problems when the problem includes addition, subtraction, multiplication, division, parentheses, and exponents. We'll also explain how to calculate these type of problems using negative numbers.

## Order of Operations

Jennifer is enrolled in her first math college class. She's apprehensive about this class since she did not do well in high school math.

The professor starts his lecture by saying, 'Please Excuse My Dear Aunt Sally!' Jennifer looks around the classroom to see if anyone else comprehends what he is saying, but there are only blank stares on the students' faces.

Please Excuse My Dear Aunt Sally (PEMDAS) has nothing to do with my aunt; it's a phrase to help us remember how to calculate a mathematical problem when there is more than one operation. Operations include addition, subtraction, multiplication, and division. These math problems can also include parentheses, exponents, and signed numbers. Signed numbers is a fancy way of describing positive and negative numbers, while exponents tell us how many times to multiply the number by itself.

## PEMDAS

The phrase represented by PEMDAS is an acronym standing for 'P' - parentheses, 'E' - exponents, 'M' - multiplication, 'D' - division, 'A' - addition, 'S' - subtraction. This tells you the order in which to complete the operations. Let's say we have the following problem:

The final answer is 78. Remember, it's important to follow PEMDAS to accurately calculate the answer. One caveat that is important to mention is if a problem has both multiplication and division, you go in order from left to right, completing both operations at the same time. The same is true with addition and subtraction.

The above table helps you understand what to do when you have negative numbers in addition problems. Let's start at the beginning of the table with the easiest, most familiar problem. The first mathematical problem is adding two positive numbers together. The 'what to do' column shows we add them together and the sign is positive.

The next mathematical problem shows adding two negative numbers. For example, for -3 + -5, we add the numbers together and know our answer is negative, thus -8. Lastly, for a positive number plus a negative number, like 10 + -12, we subtract and take the sign of the largest number. Since the largest number in this problem is 12, our answer is -2.

What if the problem was 10 + -8? We again would subtract and the sign of the largest number is positive. Therefore, our answer is 2.

## Signed Numbers with Subtraction

Signed number with subtraction is pretty easy if you know the rules for addition. If you look at the 'what to do' column, you'll see it says to add the opposite for all of the subtraction mathematical problems. Let's look at an example, -3 - -5. If we add the opposite, we would turn subtraction into addition and change the -5 to its opposite, which would be positive 5. Now we can rewrite the problem as -3 + 5.

Find the signed number with addition table and the rule for adding a positive and negative number, and you'll find the answer is 2.

Let's look at subtracting a positive number and negative number, 8 - -3. If we add the opposite, we turn the subtraction problem into an addition problem and the -3 to its opposite, which is positive 3. Now we can rewrite the problem as 8 + 3 = 11.

The last signed number with subtraction example is subtracting a positive and positive number, such as 8 - 10. Adding the opposite, the subtraction sign is changed to an addition sign, positive ten is -10, and the problem would be rewritten as 8 + -10. Following the signed number with addition rules, the answer would be -2.

## Signed Numbers with Multiplication and Division

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