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# Decimals: Adding and Subtracting

### Decimals: Adding and Subtracting

There are certain ways to add and subtract decimal numbers that makes it a little easier.

The decimal number $3.75$ is the same as $3 + ...$

$4.5 + 4.2$ is the same as $8 + ...$

When you add decimal numbers together, you first add the ones together

Here that is $4 + 4 = 8$

Then you add the decimals together

Here that is $0.5 + 0.2=0.7$

Then you add the sum of the ones and the sum of the decimals together

Here that is $8 + 0.7 =8.7$

So!

$4.5 + 4.2 = 8.7$

Now, what is the sum of the ones here?

What is the sum of the decimals?

What is $11 + 1.3$?

So when you add the decimals and the result is more than $1$

you add the extra $1$ to the ones you already have before you add the decimals.

What is the sum of the ones here?

What is the sum of the decimals here?

Finally, what is $8.205+6.917$ then?

To recap!

First you added the **ones** together $8+6=14$
The you added the **decimals** together $0.205+0.917=1.122$
Then you added the **two** **sums** together $14 + 1.122=15.122$

What is $5.352 + 3.824$?

Now! What is $4.25+2.7$?

To recap! You can follow a few steps to make adding decimals a little easier

First you find the sum of the **ones**.
Then you find the sum of the **decimals**.
Finally you add the **two** **sums** together.

Be careful when the sum of the decimals comes to more than $1$

Then you have to remember to add the extra $1$ to the ones.

Don't be confused if the number of decimals is not the same

For example $1.6$ is the same as $1.60$ or $1.600$, so you can add as many zeros as you want if that makes it easier for you.

When you subtract decimal numbers, you also start with the ones. What do you get when you have subtracted the ones from each other here?

What do you get when you subtract the decimals from each other here?

What do you do now?

A) Add the two differences together. B) Subtract the two differences from each other.

So finally, what is $5.7-2.1$?

To recap!

First you **subtracted** the ones from each other $5-2=3$
The you **subtracted** the decimals from each other $0.7-0.1=0.6$
Then you **added** the two differences together $3+0.6=3.6$

What is $6.97-4.17$?

What do you get when you subtract the ones from each other here?

What do you get when you subtract the decimals from each other here?

Now, what is $7+(-0.3)$?

So! When you subtract, you might come to a negative

Remember that adding a negative, like $-0.3$, would be the same as **subtracting** $0.3$

What is $6.25-3.4$?

Summary! You can add decimal numbers by following a few steps

First you find the sum of the **ones**.
Then you find the sum of the **decimals**.
Finally you add the **two** **sums** together.

You can subtract decimal numbers by following similar steps

First you **subtract** the ones from each other.
Then you **subtract** the decimals from each other.
Finally you **add** the two differences together.

Be careful if the decimals give you a negative difference!

For example, $7+(-0.3)$ is the same as $7-0.3$