Adding and Subtracting Decimal Numbers

 Key vocabulary

 Place holder: A zero that holds an empty gap in a place value column without changing the original number

Adding and subtracting decimal numbers is just like adding and subtracting regular numbers, but with a little twist!

First, let's talk about adding decimal numbers.

Example 1

When adding decimals it is very important that we focus on putting the numbers into the correct columns in our column addition.

Let’s help ourselves by putting the labels on top of our numbers

By putting the numbers we can now clearly see which numbers go in which column.

Let’s start by putting our Tth (tenths) in their columns. We have a 7 and a 5

We can see that the 7 and the 5 are in the same column. Good start

Now let’s put the decimal point in place:

SECRET TIP.. if your decimal points are on top of each other.. then you KNOW that the rest of your numbers will be in the correct place. So it is VERY important that your decimal points are in line.

Now let’s put our O (ones) in place, we have a 5 and a 4

Finally we can put the T (tens) in the correct place

Notice that our decimal points are all in a perfect line! This is a very good sign and means we have, most likely, put the rest of our numbers in the correct place

Now we can begin to answer this question

We must always start from the smallest value, in this example our smallest value is the Tth (tenths) column

Therefore we can add .7 + .5 which = 1.2

1.2 is a 2 digit number and cannot fit in the Tth (tenths) column so we have to carry across to the 0 (Ones) column

1.2 = 1 one and 2 tenths

Let's move the 1 into the 0 (Ones) column, waiting to be added to the other Ones, and put the 2 tenths into the Tth (tenths) column:

Great.. let’s put our decimal point into the answer now too so that we don’t forget it at the end!

Awesome, now we can add our O (Ones) column

In our O (Ones) column we have a 5, 4 and now the 1 that we created from the previous part

5 + 4 + 1 = 10

10 is another 2 digit number

10 = 1 ten & 0 ones

Let’s move the 1 ten into the Tens column waiting to be added to the other Tens and put the 0 in the ones column:

Finally, we can finish by adding up our T (tens) column

In our T (tens) column we have a 4, 3 and 1

4 + 3 + 1 = 8

Therefore 45.7 + 34.5 = 80.2

Now, let's talk about subtracting decimal numbers.

When subtracting decimal numbers, again, we want to line up the decimal points so they're on top of each other. Then, you can subtract the numbers just like you normally would.

Let’s have a look at this example:

Let’s start by lining up our numbers:

Hmm, this doesn’t look right does it..

But all the numbers are lined up! It must be right!?

Ahh! We can see here a very common mistake. It is very easy to forget to make sure that the decimals are in line and simply just put the numbers in so that they look neat.

Let’s try again – this time we will start by putting our decimals in line first

Now that are decimals in place we can arrange the other numbers easily

However, this example is a bit tricker because we have different amounts of digits before and after the decimal point

By having different amounts of digits it makes it harder to ensure we put the numbers in the correct column.

Let's start by putting our smallest values first.

We can see that the first number has a tenth but the second number has a hundredths.

This means that our smallest value is ‘hundredths’

IMPORTANT: It is very important that we put the numbers on to the place value columns, IN THE ORDER that the question is written.

 This means that 35.7 MUST be on the top of our column subtraction and 3.52 MUST go on the bottom. This is because we are taking 3.52 AWAY from 35.7

So, let’s begin..

We only have a hundredth in the second number, so we will put this number 2 in the hundredths column on the bottom row:

Both numbers have digits in the ‘tenths’ column, so we can put those in now:

Next we can put in our ‘ones’ in the correct column:

Finally we can put our ‘tens’ in place. The first number 35.7 is the only number with a digit in the tens place.

So, let’s put it in the right place:

Great! We are almost ready to begin!

BUT! We have some gaps in our columns!

We cannot just leave these gaps. If we leave them then we might make mistakes.

For example:

When we look at the ‘hundredths’ column we can see only a 2.

This might mean that we put the answer as a 2. But this would be wrong.

This is because the real question is 0-2 which we can’t do, we would have to borrow from next door!

Let’s see how that works…

Our first job is to fill these gaps. We will put a ‘0’ that we call a ‘placeholder’

We call it a placeholder because it is holding the place of a digit, without changing the value of the number at all.

35.70 is the same as 35.7

And…

03.52 is the same as 3.52

But now we are finally ready to begin our question

We always start at our smallest value, which in this example is the ‘hundredths’

0 – 2 = we cannot do this without going into negative numbers

So we can borrow from next door:

We have ‘looked next door’ and borrowed 1 tenth from that column.

Now we can do:

10 – 2 = 8

Next we can calculate the tenths column

6 – 5 = 1

Let’s put our decimal point in place…

Next, we will calculate the ‘ones’

5 – 3 = 2

Finally, we calculate the ‘tens’

3 – 0 = 3

Excellent!

So…

35.7 – 3.52 = 32.18