# Adding and Subtracting Decimals

## Adding and Subtracting Decimals

Although it may be easier to deal only with whole numbers, such as 2, 45, or 120, if you look carefully, decimals appear frequently throughout our daily lives.

For example, an item at a store could cost $2.75, or your favorite basketball player may average 19.7 points per game. You could take out a loan with a 4.45% interest rate, or the winner of the 100-meter relay may have completed the race in 12.67 seconds.

In order to use decimals effectively, it is important to be able to utilize and manipulate decimals in mathematical expressions.

Today, we’re going to cover the basics – addition and subtraction.

We’ll start with a simple example of adding decimals, so let’s try it: 32.61 + 11.54

The first step, like you can see, is to line up the two decimals like so:

32.61

+ 11.54

———————-

Note that because of the commutative property of addition, it does not matter which decimal is placed first (however it will make a difference when we do subtraction).

Make sure that the decimal points in each number are lined up exactly. If your decimals are not lined up correctly, you will end up with the wrong answer.

Once you have your two decimals lined up, you begin to solve the problem as you would with any addition problem.

First, we add the two numbers in the hundredths place, 1 and 4, which gives us 5 in the hundredths place. 1 + 5 = 4. We then add 6 and 5 which are in the tenths place, and that gives us 11 – so we carry the 1 over here. Bring down our decimal, and now we have 2 + 1 + this other 1, so it’s 3, 4. And now we add 3 and 1 and we get 4. So our final answer is 44.15.

Let’s move over to subtraction. We’ll start with a simple problem: 7.5 – 2.8

Just as with addition, the first step is to line up the numbers with the decimal point in the same place. Your expression should look like this:

7.5

– 2.8

——————-

Begin to subtract as you would any subtraction problem. Starting in the tenths column, you will need first to borrow from our ones column because 5 – 8 doesn’t work out. So, take 1, make this 6, and then carry it over. So now we have 8 being subtracted from 15, which gives us 7. Bring down our decimal, and now we have 2 being subtracted from 6, which gives us 4. So our final answer is 4.7.

Finally, let’s do one more subtraction problem: 10.53 – 4.274

Once again, we line up our two numbers, making certain that our decimal points are in the same position. Your expression should look like this:

10.53

– 4.274

————————–

You may want to add zeros to balance out, so it looks, just feels like it’s full there, which is fine. You can not add them, and that’s fine too.

10.530

– 04.274

—————————

Once again, in this problem we need to begin by borrowing from our hundredths place. So we make this a 2 and bring our 1 over so now we have 4 being subtracted from 10 which gives us 6. Then we have 7 being subtracted from 2 which doesn’t work, so we need to borrow again. This becomes 4, carry over a 1 to have 12 so 7 being subtracted from 12, that gives us 5. No we have 2 being subtracted from 4 which gives us 2. Bring down our decimal point, we have 4 being subtracted from 0, which we know does not work, so this becomes 0. Carry our 1 and we have 10 – 4 which gives us 6. So our final answer is 6.256.

You should now have a strong understanding as how to add and subtract decimals. Remember to always line up your numbers and make sure the decimals of each number are in the same place! Thanks for watching, and see you guys next time!