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Adding & Subtracting Negative Decimals

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  • 0:00 Decimals Are All Around Us
  • 1:18 Do I Add or Subtract?
  • 2:50 What Sign Do I Use?
  • 4:00 A Special Case
  • 4:41 Lesson Summary
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Lesson Transcript
Instructor: Kimberly Osborn
The rules associated with adding and subtracting negative decimals can seem confusing. Don't fret! This lesson will teach you an easy trick that you can use to become a master at working with these pesky numbers.

Decimals Are All Around Us

One of the most common uses of decimals in every day life is money. Every person in the world needs to have a basic understanding of money to survive, plain and simple. When you go shopping, and the cashier hands you back change, you are working with decimals. When you take out a car loan with an interest rate, you are working with decimals. Even buying a soda from the vending machine requires the use of decimals. They are all around us and, unfortunately, there is no hiding from them. Though you may not come across them as often, it is important to know how to add and subtract negative decimals, or decimals less than zero. They might seem a little scary at first, but what if I told you that there is a very simple trick that you can use to remember exactly what to do when adding or subtracting negative and positive decimals?

Now, you might be a little doubtful that there is some magical device out there that will erase the anxiety you feel when tasked with adding and subtracting decimals. But, all you need to know are the magic words SADS and SOB. To help you out, I have even put them in a sentence for you (mind you, I had to take a little creative license here):

When you SADS, you SOB.

In other words, when you are sad, you sob, or cry. The next few sections will explain exactly how this simple sentence will make adding and subtracting negative decimals a piece of cake!

Do I Add or Subtract?

The first step when adding and subtracting negative decimals is to decide whether to add or subtract. Now, it might seem self-explanatory just by looking at the signs. We have always been taught that when you see a plus sign (+), you add, and when you see a minus sign (-), you subtract. However, when you are working with negative numbers, the rules are a little bit different. This is where SADS comes into play. SADS stands for 'Same-Add, Different-Subtract.' This means that when the signs are the same, you should use addition, and when the signs are different, you should use subtraction. Let's look at some examples to see exactly what I mean by this.

-2.3 - 5.4

In Example 1, we are subtracting 5.4 from -2.3. Our first step would be to circle the signs in front of each number. This shows us that both signs are negative (don't forget, subtraction signs are seen as negative and addition signs are positive). Now, using our rules of SADS, we know that when the signs are the same, we use addition. So we will be adding 5.4 and 2.3 together to get an answer of 7.7. Stay tuned for the next section to help us determine what sign goes in front of our solution.

-2.3 + 5.4

In Example 2, we are adding 5.4 to -2.3. Again, our first step would be to circle the signs in front of each number. This shows us that we have a positive and a negative. SADS tells us that when the signs are different, we should subtract. We always subtract from the larger number so, we will be subtracting 2.3 from 5.4 for a solution of 3.1.

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