- Category: Arithmetic
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So far we have been subtracting normal numbers, also known as “whole numbers.” In this lesson we will learn how to subtract decimal numbers. Don’t worry- it’s quite easy, and you already know how to add decimal numbers.
Let’s start with our first example.
0.7 - 0.3 = ?
When we needed to add two decimal numbers together we used the columnar addition method. Since it helped us so much before, we’ll use it again here.
Let’s write this subtraction problem in columnar subtraction method.
First we will draw the vertical dotted line to assist us. This is just for practice- once you’ve got a hang of decimal subtraction you won’t need the line, but for now, let’s keep it.
Next we will write the first number, which is 0.7, on the dotted line so that it’s decimal point is on the dotted line. This is what it should look like:
Next we will write the other number, which is 0.3, below 0.7 the same way we wrote 0.7. We will make sure that the decimal place of 0.3 is on the dotted line like this,
Next, we will draw a horizontal line after the bottom number like this.
Now that we have written both of the numbers we need to show that we are subtracting these two numbers and we also we need make space for the answer. We will do that by writing the minus sign to the left of the bottom number and writing the = sign below it to make room for the answer.
We are now ready to subtract.
We started with the right most column when we subtracted two digit numbers in earlier lessons, and we follow the same rule here: always start from the right most column.
We have 7 on top and 3 on bottom. Remember the "top minus bottom" rule? When subtracting a column of numbers we will take away the bottom number from the top one. So we have
7 - 3 = 4. Let's write 4 below this column, in the answer space.
We have subtracted one column. We will now move to the next column. But the next column is the column of decimal points. We will not do any subtractions in this column, we simply write a decimal point below the column in the answer space.
Now we will start to subtract the next column. We have,
0 - 0 = 0. We will write this below the column.
....And our first decimal subtraction is complete. Nice work!
Now we can now say that
0.7 - 0.3 = 0.4
Let's do another example. This time we will make it a little bit challenging. .
1.3 - 0.9 = ??
First we will write this in columnar subtraction method.
To do that we will start with the vertical dotted line.
We will then write the first number, 1.3, on the line so that its decimal point is on the line.
Next we will write the other number on the line just like we wrote 1.3
Finally, we will draw the horizontal line and then we will write the minus sign and the equal sign in the usual places like this,
Now that the set up is over we will get into the actual math.
Let's start subtracting from the right most column.
When we try to subtract using the top minus bottom method we will have to take away 9 from 3, which we cannot do. You can’t kick 9 soccer balls if you only have 3 in front of you.
When something like this happened we used to burrow one from the next column and add it as a ten to our top number. We will do the same in this case too. We will skip the decimal point column and check the next column. We have 1 on the top. We can borrow 1 from it and add it as a ten to 3.
Now we will write the new numbers on top and erase the old numbers.
Now we can start subtracting the right most column. We have,
13 - 9 as 4 Let’s write it at the bottom of the column,
The next column is the decimal points column. We will write a decimal point at the end of the column like this.
After that we subtract the next column,
Remember to use “top minus bottom” method,
0 - 0 = 0. We can write this below the column and complete the answer.
OK! Great job. Now that we have the answer we can say that,
1.3 - 0.9 = 0.4
Let’s do one more subtraction problem.
89.34 - 23.44 = ??
First we will start with the dotted line.
Then we will write the first number - which is the number on the left side of the minus sign. We will write this number on the dotted line so that the decimal place is on the dotted line.
In the same way below this number we will write the next number. Make sure that the decimal place is on the dotted line.
Now we can add the final touches. We need to add a minus sign, a horizontal line to separate the answer, and an equals sign at the bottom. Once this is all done, we can start subtracting.
We will start from the right most columns. So subtracting the right most column using “top minus bottom” method, we have
4 - 4 = 0. We will write the 0 at the bottom of our column.
We will subtract the next column now. Looks like we will have to borrow 1 from the next column, because we can’t take away 4 from 3.
Let’s borrow one from the next number column and add it as a ten to our top number. Don’t forget to erase your old numbers that you’ve borrowed from.
Now we can subtract,
13 - 4 = 9. Let’s write 9 below this column.
The next column is the decimal point column, so all we have to do is write the decimal point below.
Now we will subtract the next column,
“top minus bottom” gives us, 8 - 3 = 5. Let’s write it over there.
Almost done! Taking away the bottom number from the top number in our final column we get the answer as 6. Because,
8 - 2 = 6. Let’s write it there.
We’re finally done! You can now say that
89.34 - 23.44 = 65.90
In this lesson we explored how to subtract decimal numbers. The important things to remember are to write your numbers so that their decimal digits are on the dotted line, and remembering to borrow whenever we need to.
See you in the next lesson!